Experimental investigation on electrodes of HID lamps at low and high operation frequencies. Dissertation

Transcription

1 Experimental investigation on electrodes of HID lamps at low and high operation frequencies Dissertation zur Erlangung des Grades eines Doktor-Ingenieurs der Fakultät für Elektrotechnik und Informationstechnik an der Ruhr-Universität Bochum Jens Reinelt Bochum 2009 LEHRSTUHL FÜR ALLGEMEINE ELEKTROTECHNIK UND PLASMATECHNIK

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5 Dissertation eingereicht am: Tag der mündlichen Prüfung: Berichter: Prof. Dr.-Ing. Peter Awakowicz Prof. Dr. em. Jürgen Mentel

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7 Contents i Contents Important symbols and abbreviations List of figures Abstract iii ix xvii 1 Introduction History of HID lighting High pressure discharge lamps Thesis layout Fundamentals Basics of arc discharges Basic plasma processes Basic plasma properties Thermal equilibrium Radiation processes inside a plasma Radiation transport Electrodes of arc discharges Surface effects on electrodes Heat conduction of electrodes Heat balance of a periodically charged electrode Acoustic resonances Skin effect Experimental setup Lamps under investigation The Bochum model lamp Ceramic Metal Halide Lamps The function of metal halides and rare earths Electrical lamp supply Lf setup Rf setup Diagnostics Photography Spectroscopy Triggering and phase resolved measurements Electrode temperature measurements and power calculation Plasma spectroscopy

8 ii Contents Spectroscopic measurements inside the model lamp Spectroscopic investigations at the YAG lamps Electrical measurements Error estimations Measurements and results Fundamental research at the Bochum model lamp Optical investigations of the arc attachment Electrode temperature measurements Electrical measurements Spectroscopic measurements Determination of cathode and anode fall voltage YAG lamp results Pure Hg YAG lamps YAG lamps with MH fillings Gas phase emitter effect Emitter effect for complex lamp fillings Conclusions and outlook Results at the model lamp Results at the YAG lamps Outlook Bibliography 123 A Appendix A - 1

9 Symbols and Abbreviations iii Important symbols and abbreviations Symbols A A + A A i A nm c 0 c p C Cts δ D d E ε 0 ε r ε λ ε λ,nm ε λ,cont ε nm ε(λ, T ) ɛ tot e e fast E kin E r E i E F E E ex E arc Atom Ionized atom Excited atom Atom in excited state i Transition probability from a state n to a state m Speed of light Heat capacity Effective velocity of sound Counts on CCD camera Skin depth Damping constant Electrode diameter Vacuum permittivity Relative permittivity Spectral emission coefficient Spectral line emission coefficient Spectral continuum emission coefficient Total line emission coefficient Emissivity Total surface emissivity Electron charge Accelerated electron Kinetic energy Energy of species in a state r Ionization energy r Fermi energy Vacuum energy level Excitation energy Axial electric field of the arc

10 iv Symbols and Abbreviations Φ f f com Work function Frequency Commutation frequency γ specific heat ratio cp c ν g r Statistical weight of a state r g 0 Statistical weight of the ground state h PLANK constant I λ Spectral radiance I BB Spectral radiance of a black body i arc Arc current j tot Total current density j e Electron current density j i Ion current density j em Current density caused by thermionic emission j ep Current density caused by back-diffusion of electrons κ Heat condictivity k B Boltzmann constant k Absorption coefficient λ d Debye-Hückel length λ pen Penetration depth λ nm Wavelength in the region nm λ Hg,1 Mercury line at nm λ Hg,2 Mercury line at nm λ DyI Dysprosium line at nm λ DyII Dysprosium ion line at nm L λ Surface radiance l arc Arc length l E Electrode length µ 0 Vacuum permeability m Mass M Magnification M tot Total magnification m e Electron mass m Ar Atomic mass of Argon ν Frequency ν nm Discrete photon energy n Density of states n e Electron density n i Ion density n r Density of excited atoms in state r Ground state density n 0

11 Symbols and Abbreviations v ω p P nm P in q p q rad q cond q rec q kin q neutral q em q ep q tc ρ m ρ q r E σ SB σ(t ) τ 0 T e T j T h T amb T sim T bot T tip t exp t delay U u arc u a,el u c φ v V sup ξ fb, ξ ff Z 0 Z e Z i Angular frequency Pressure Line profile Lamp input power Power flux density Radiated power Conducted power Power flux by recombination Power flux by kinetic energy of ions Power flux from back diffusion of neutrals Power flux by emitted electrons Power flux from back diffusion of electrons Power flux caused by the heavy particles to the electrode Mass density Mass density of quartz Electrode radius Stefan-Boltzmann constant Electrical conductivity Optical thickness Electron temperature Temperature of species j Temperature of heavy particles j Ambient temperature Simulated temperature Electrode bottom temperature Electrode tip temperature Exposure time Delay time Inner energy Arc voltage Electrical anode sheath voltage Cathodic sheath voltage Phase angle Particle velocity Supply voltage Biberman factors Atom partition function Electron partition function Ion partition function

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13 Symbols and Abbreviations vii Abbreviations ASDF CCD CP CZC DyI 3 DT ESV FTIR HF Hg HID ICCD IED IDF LED LTE plte MF NTD NT OES RF SNR TD VHF VI VZC Atomic State Distribution Function Charge Coupled Device Commutation Peak Current Zero Crossing Dysprosium Iodide Dysprosium / Thallium Electrode Sheath Voltage Fourier-Transform Infrared Spectrometry High Frequency band (3 30 MHz) Mercury High Intensity Discharge Intensified Charge Coupled Device Ion Energy Distribution Ion Distribution Function Light Emitting Diode Local Thermal Equilibriuum Partial Local Thermal Equilibriuum Medium Frequency band (0.3 3 MHz) Sodium / Thallium / Dysprosium Sodium / Thallium Optical Emission Spectroscopy Radio Frequency Signal to Noise Ratio Thallium / Dysprosium Very High Frequency band ( MHz) Voltage-Current (trace/characteristic/probe) Voltage Zero Crossing

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15 List of Figures ix List of Figures 1.1 Example of a HID lamp: Xenon-/D- lamp The dependence of potential upon current for various kinds of discharges. The numerical values apply approximately to discharges in neon at p = 1Torr in a tube 50cm long, with flat-copper electrodes of area 10cm 2. In some gases the curve shows a slight maximum in the region BCD. ([1]) Schematic drawing of a typical potential curve along the axis of an arc discharge Definition for the normal vectors on the surface of a disc cut out of the electrode Calculated skin depth for tungsten versus temperature for different frequencies Schematic drawing of the Bochum model lamp Schematic drawing of an electrode holder Schematic drawing of a YAG lamp Spectrum of a D2 automotive lamp with the sensitivity curve of the human eye Switched-DC current signal from the low frequency power supply with and without commutator for the operation of YAG lamps Low frequency power supply with and without commutator for a improved switched DC current signal Block diagram of the rf operation setup Schematic drawing of the imaging camera system with zoom lens and shutter Schematic drawing of the spectroscopy system Block diagram of the trigger setup Timing diagram for the trigger delay Image of the electrode parallel to the entrance slit of the spectrograph Spectrum recorded at the model lamp for the electrode temperature determination Values for the emissivity of tungsten from DeVos Emissivity of tungsten depending on temperature at the measuring wavelength of 718 nm Temperature curve with artificially increased temperature at the electrode tip Example for a simulation of the electrode temperature of the whole electrode length Definition of the coordinate system for the time dependent power loss calculation Example for the simulation result of the electrode temperature curve. Parameter: Model lamp, d E = 1mm, l E = 20mm, p = 0.26MPa, i = 3A switched-dc Image of the electrode and plasma perpendicular to the entrance slit of the spectrograph

16 x List of Figures 3.21 Spectrum and evaluated spectral radiance for an argon spectrum at λ = 750nm. a) Full 2D spectrum recorded with the CCD camera. b) Cut through the spectrum at r= Inverse Abel transformation. The distribution of the rotational symmetric value f(r) should be reconstructed out of the measured parallel projection h(y) Example for a Boltzmann plot Spectrum of the argon continuum at a center wavelength of 455nm inside the model lamp. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i RMS = 3A, Gas argon, pressure p = 0.26 MPa Example for an electron density profile Example for the spectrum of the two mercury lines being used to evaluate the plasma temperature. b) Spatially resolved line radiation density I L (λ) after the integration over the two mercury lines at λ 1 = nm and λ 2 = nm Spectrum showing the two dy lines for the dy density calculations. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm Image of the Dy line with integration boundaries and indication of the underground continuum. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm Image of the Dy ion line with integration limits and identification of the underground continuum. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm Example for the measurement and the subsequent extrapolation of the ESV Two different kinds of arc attachment at electrodes. Parameter: electrode diameter d E = 1.5 mm, electrode length l E = 20 mm, i = 4A DC, gas argon, pressure p = 0.26 MPa Arc attachment on the upper electrode over one period for LF and RF operation, the first five pictures are in the anodic phase the last five pictures in the cathodic phase, Parameter: f = 50 Hz / 50 khz. Gas: argon, pressure p = 0.26 MPa, exposure times for 50 Hz / 50 khz : 100 µs / 2 µs a) electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with î = 1 A, b) electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with î = 2 A Arc attachment on HID electrodes during RF operation for the upper and lower electrode, Parameter: f = 15 khz / 1 MHz, Gas: argon, pressure p = 0.26 MPa, electrode diameter d E = 1 mm, electrode length l E = 20 mm Images of arc attachment depending on frequency and current for the lower electrode, Parameter: f = 50 khz / 75 khz / 250 khz, Gas: argon, pressure p = 0.26 MPa, electrode diameter d E = 1 mm, electrode length l E = 20 mm Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1, 2 and 3A, Gas argon, pressure p = 0.26 MPa

17 List of Figures xi 4.6 Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 and 5A, Gas argon, pressure p = 0.26 MPa Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3, 4 and 6A, Gas argon, pressure p = 0.26 MPa Mean electrode tip temperatures for the anodic and cathodic phase and over one full rf period. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1, 2 and 3A, Gas argon, pressure p = 0.26 MPa Spectroscopically measured temperature between the electrode tip up to 3.5mm behind for 25 Hz and 2 khz. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1 A, Gas: argon, pressure p = 0.26 MPa Spectroscopically measured temperature between the electrode tip and a distance 0.5 mm apart from the tip for 25 Hz and 2 khz. The numbers on the right side of graphic a) indicate the position within the RF period starting with 1 at the beginning of the anodic phase at ϕ = 0 and proceeding with n = Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1 A, gas argon, pressure p = 0.26 MPa Input power into the electrode over one period for various frequencies. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i=1,2 and 3 A, Gas argon, pressure p = 0.26 MPa Input power into the electrode over one period for various frequencies. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc and sin-wave with i RMS = 3 A, Gas argon, pressure p = 0.26 MPa Arc voltage U arc over one period for various frequencies, Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 1, 2 and 3 A, Gas: argon, pressure p = 0.26 MPa Mean power input P input into the discharge over one period for various frequencies and current. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = A, Gas: argon, pressure p = 0.26 MPa Arc voltage U arc over one period for various frequencies, Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave and switched-dc with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa Mean power input P input into the discharge over one period for various frequencies. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave and switched-dc with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa Current signal over one ac period for various frequencies. Parameter: f = 10 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa

18 xii List of Figures 4.18 Mean power input P input and tip temperature T tip into the discharge over one period for various frequencies. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa ESV(t) over one ac period for various frequencies, Parameter: f = 10 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, switched-dc with i RMS = 2 A, Gas: argon, pressure p = 0.26 MPa ESV at the position ϕ = 1 π plotted over frequency, Parameter: f = 10 Hz khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, switched-dc with i RMS = 2 A, Gas: argon, pressure p = 0.26 MPa ESV(t) over one period for various frequencies, Parameter: f = 50 Hz khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 1, 2 and 3 A, Gas: argon, pressure p = 0.26 MPa Arc attachment at an anode under ac operation. Parameter: f = 50 Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa Phase average of the electron temperature and density along the middle axis of the arc measured at several positions. Parameter: f = 50 Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 4 A, Gas: argon, pressure p = 0.26 MPa Anodic and cathodic electron temperature and density at a position 62.5µm in front of the electrode tip for various frequencies. For the frequency of 5 and 10 khz no phase resolution is possible. The inscribed values are average values over several ac periods. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 4 A, Gas: argon, pressure p = 0.26 MPa Phase averaged electron density over distance in front of an ac operated electrode at a frequency of 50Hz and 5kHz. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i = 3 A, Gas: argon, pressure p = 0.26 MPa Phase resolved electron temperature over one period for various frequencies in a distance of 62.5 µm in front of the electrode. Parameter: f = 10 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa Phase resolved electron temperature over one period for various frequencies in a distance of 62.5 µm in front of the electrode. Parameter: f = 50 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i = 3 A, Gas: argon, pressure p = 0.26 MPa Time dependent Black-Box model of the cathodic boundary layer Input power into the electrode at exposed positions within the cathodic phase, Parameter: f = 10 Hz - 10 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin and square wave with i RMS = 3A, Gas: argon, pressure p = 0.26 MPa Calculated cathode and anode fall voltage over frequency, Parameter: f = 10 Hz - 10 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin and square wave with i RMS = 3A, Gas: argon, pressure p = 0.26 MPa.. 87

19 List of Figures xiii 4.31 Input power into the electrode over one period for different frequencies. Parameter: f = 25 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1A, Gas: argon, pressure p = 0.26 MPa Images of arc attachment at a pure Hg YAG lamp. a) Phase resolved images over one period at a low and a high frequency. b) Image of the anodic and cathodic arc attachment for various frequencies. Parameter: Hg, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Electrode tip temperature and input power over one period for various frequencies. Parameter: Hg, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Electrode tip temperature of a Hg YAG lamp over one period for various frequencies. Parameters: Hg, current i = 0.8A sin wave, electrode diameter d E = 0.45mm Mercury temperature of a Hg YAG lamp over one period for various frequencies measured in a distance of 122µm in front of the electrode surface. Parameters: Hg, frequency f = 125 Hz - 2 khz, current i = 0.8A sin wave, electrode diameter d E = 0.45mm, electrode length l E = 5 mm Mercury temperature of a Hg YAG lamp over one period for various distances z and two operating frequencies. Parameter: Hg, frequency f = 50 Hz / 2 khz, electrode diameter d E = 0.45 mm, electrode length l E = 5 mm, i = 0.8A sin wave Arc attachment over one rf period for a YAG lamp. First five images are taken in the anodic phase, images 6-10 in the cathodic phase. Parameters: NTD1, frequency f = 23kHz, current i = 0.6A, electrode diameter d E = 0.36mm, exposure time t exp = 4µs Arc attachment for a YAG lamp in a frequency range from kHz. Parameters: NTD2, current i = 0.6A, electrode diameter d E = 0.36mm, exposure time t exp = 10µs Arc attachment for a YAG lamp in a frequency range from Hz. Image 1 5 represent the anodic phase, image 6 10 the cathodic phase. All images are scaled to one global minimum/maximum value. Parameters: NTD1, current i = 0.6A switched-dc, electrode diameter d E = 0.36mm Arc voltage over one period for various currents. Parameter: NTD1, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, sin wave Arc voltage over one period for various frequencies. Parameter: NTD1, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, sin wave Input power into a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm Electrode tip temperature of a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm Electrode input power of a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm

20 xiv List of Figures 4.45 Images of cathodic arc attachment for different YAG lamp types. The left column shows images with an alternating look-up table and the right column image which are scaled to one global minimum/maximum value. Parameters: NT, NTD1, DyI, frequency f = 50Hz, current i = 0.6A switched-dc, electrode diameter d E = 0.36mm Dysprosium atom and ion density over one phase for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: DyI, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Maximum values of the Dy atom and Dy ion density depending on frequency in a distance of 125µ m in front of the electrode. Parameter: DyI, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Dysprosium atom and ion density within one period for various frequencies. Parameter: DyI, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A sin wave Dy atom density along the arc z axis in the anodic and cathodic phase for different frequencies. Parameters: DyI, current i = 0.8A switched-dc, electrode diameter d E = 0.45mm Electrode tip temperature and input power over one period for various frequencies. Parameter: DyI, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, î = 0.8A Dy atom and ion density for frequencies of 50Hz and 2kHz for electrode diameters of d E = 360, 450 and 500µm over one rf period. Parameter: DyI, electrode length l E = 5 mm, i = 0.8A switched-dc Electrode tip temperature and input power for frequencies of 50Hz and 2kHz for electrode diameters of d E = 360, 450 and 500µm over one rf period. Parameter: DyI, electrode length l E = 5 mm, i = 0.8A switched-dc Dy atom density and electrode power loss over electrode surface. The values are average values over the anodic respectively cathodic phase. Parameter: DyI, electrode diameter d E = 0.36, 0.45 and 0.5mm, electrode length l E = 5mm, i = 0.8A switched-dc Dy atom density and electrode tip temperature for various cold spot temperatures for two frequencies. At position 1 the strongest cooling is applied and at position 8 the strongest heating. Parameters: DyI, current i = 0.8A switched-dc, electrode diameter d E = 0.45mm Delta lambda and absolute line intensity (summed over 25nm) of the 589nm Na line 125µm in front of the upper electrode for a NTD1 lamp over one period. Parameter: NTD1, electrode diameter d E = 0.45mm, electrode length l E = 5mm, sin wave with i = 0.8A Phase resolved Dy atom and ion density, tip temperature and input power for a NTD1 YAG lamp for various frequencies. First half period is the anodic, second half period the cathodic phase. Parameter: NTD1, electrode diameter d E = 0.45mm, electrode length l E = 5mm, i = 0.8A switched-dc Electrode tip temperature in dependence on the Dy atom density in front of a cathode for different YAG lamps. Parameter: electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, frequency f = 50Hz - 1kHz, i = 0.8A switched-dc

21 List of Figures xv 4.58 Phase resolved Dy atom and ion density for a low and a high frequency for different lamp fillings. For the high frequency the values are average values over the anodic respectively cathodic phase. Parameter: DyI, TD, electrode diameter d E = 0.45mm, electrode length l E = 5mm, i = 0.8A switched-dc Mercury temperature over one period for different YAG lamps at a low (50Hz) and a high (2kHz) frequency. Parameter: electrode diameter d E = 0.45 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Phase resolved electrode tip temperature for a low and a high frequency for different lamp fillings. For the high frequency the values are average values over the anodic respectively cathodic phase. Parameter: DyI, TD, electrode diameter d E = 0.45mm, electrode length l E = 5mm, i = 0.8A switched-dc. 119

22 xvi List of Figures

23 Abstract xvii Abstract Nowadays high intensity discharge lamps (short HID lamps) are used in many fields for lighting purposes. The most familiar types of HID lamps are the so-called Xenon lamp as a cars head light, the UHP (Ultra High Pressure) lamp in video projectors or for lighting of public and industrial facilities. The success of HID lamps can be attributed to their high efficiency and long lifetime. A further improvement of these qualities is necessary to keep in business against new technologies coming to the market as for instance the LED technology. One possibility is the high frequency operation of HID lamps for the realization of compact, efficient and cost-effective HID lamp drivers and lighting systems. This mode can lead to an often undesired effects in the lamp bulb and at the electrodes. To adjust the lamp design to the operating frequency a detailed investigation of the effects on the electrodes depending on frequency is necessary. Within the scope of this thesis experimental investigations supported by simulations on HID lamps are performed. The lamps are operated at frequencies between 1 Hz and 2 MHz. In the first part of this work the results of electric, pyrometric and spectroscopic measurements at the Bochum model lamp are presented. The investigations show a change in the kind of arc attachment with increasing frequency. Phase resolved measurements of the electrode temperature reveal that with increasing frequency the temperature difference between anode and cathode vanishes and that the temperature converges to a constant value. For the calculation of the electrode power balance a time dependent model is developed. Together with measured data this model gives information about the input power into the electrode and the interaction between plasma and electrode. It can be shown that with increasing frequency the anode sheath voltage increases and even exceeds the cathodic sheath voltage. Also it is for the first time shown that the heating of the electrodes by the plasma becomes partly independent of the current under ac operation. In the second part of this work ceramic metal halide lamps (YAG lamps) with a special design for research purposes are investigated. For the arc attachment and the electrode temperature simultaneous observations are made as for the model lamp. Furthermore measurements imply that the so called gas-phase emitter effect, which is caused by the ingredient dysprosium, is no longer only occurring within the cathodic phase. With increasing frequency this effect becomes also active within the anodic phase. With increasing frequency this leads to a decreasing electrode temperature. Generally it can be shown that the influence of the electrodes on the discharge decreases with increasing frequency and the plasma properties become more dominant.

24 1 1. Introduction 1.1 History of HID lighting Artificial lighting is very important for the daily life all over the world. It allows to extend activities as working, travel or entertainment to times beyond the daylight hours. Globalization would be impossible if half of the earth would always be in darkness. But the illumination has its price. Artificial lighting needs a lot of electrical power. Nearly 20% of the world wide produced electricity is used for lighting purposes. Especially in times of high energy prices and a growing ecological awareness due to the climatic changes the task is to build energy saving light sources. In some countries, e.g. Australia, incandescent lamps are a phased-out model due to their low power efficiency of 5 8%. This means that only a marginal part of the input power is transferred into visible light. Thus the main criteria for designing new lamps is a high power efficiency. Furthermore the lamps should be very stable over their lifetime. This lifetime should also exceed the lifetime of incandescent lamps by a factor of 5. Another important criteria for a new lamp design is the color rendering of the lamp. It describes the possibility of the lamp to illuminate objects as natural (by daylight) as possible. Lamps which fulfill these criteria are the so called discharge lamps. The principle of a gas discharge lamp is to convert electric power into radiation by means of an electrical discharge in the gas medium of the lamp. The discharge inside the lamp is called a weakly or moderate ionized plasma. This plasma normally is generated inside a discharge tube between two lamp electrodes. A plasma is an ionized gas consisting of neutrals, ions, electrons, excited particles and photons. The procedure by which radiation is generated inside the plasma can simplified be described as follows: Due to an external electrical field the free, light electrons are accelerated inside the plasma. By collisions with heavy particles they transfer energy to these particles. The collisions can be elastic or inelastic. By inelastic collisions part of the energy of the electrons is transferred to the atoms. This effect leads to several processes as excitation, ionization and dissociation which are responsible for the production of radiation. The radiation is produced if the atoms are deexcited to their lower energy states. In general this process of energy transfer to the gas is called ohmic heating. The class of discharge lamps can be divided into two parts. The low pressure discharge lamps and the high pressure discharge lamps. Low pressure discharge lamps are characterized by a pressure below 10 3 bar and a large discharge volume. They have a low luminance and power density and the plasma is far away from equilibrium. This means that the electrons have a high temperature compared to the cool heavy particles. A typical low pressure discharge lamp is the fluorescent lamp. It is typically filled with noble gases working as a buffer and

25 2 1. Introduction an additional gas by which photons are generated. Mercury is the first choice of a photon generating gas since it has a high vapor pressure and can easily be excited. The main radiation by mercury is produced in the UV region below a wavelength of 300nm. This radiation is converted into visible light by a phosphor layer at the inner wall of the discharge tube. There are several other types of low pressure discharge lamps but since the main focus of this work is put on high pressure discharge lamps they are not further discussed. 1.2 High pressure discharge lamps The high pressure discharge lamps, also called High Intensity Discharge (HID-) lamps, are normally operated at a pressure above one MPa up to a few MPa. One of the most popular HID-lamps is the so called xenon-lamp used as a car headlight. The success of this lamp can be attributed to the high light output and the good contrast level what improves the security. Also the long lifetime of approximately 8000 hours (compared to 2000 hours of a conventional halogen lamp) is a further reason for using this lamp. HID- Figure 1.1: Example of a HID lamp: Xenon-/D- lamp lamps are applied in other fields of lighting, too. They are installed in horticulture, lighting of places and stadiums, for projection systems (e.g. beamers), shop lighting,.... Due to the high pressure the mean free path of the electrons is much shorter than in low pressure lamps. This implies a higher collision rate of the electrons with the heavy particles. This results in a considerable energy transfer from the electrons to the heavy particles. Thus inside the arc column an equilibrium of the electron and heavy particle temperature can be assumed. Depending on the operation parameters of a lamp the temperature is typically between 1400K and 8000K. At these high temperatures the excitation of atoms is very high. The resulting population densities of the excited states can be described by a Boltzmann distribution. Thus radiation is generated by transitions from excited to less excited states as well as from excited to the ground state. This implies an emitted spectrum of the lamp consisting of a much higher number of lines than the spectrum of a low pressure lamp which mainly consists of resonance lines. The higher number of spectral lines improves the color index of the lamp and by adding more appropriate ingredients this spectrum can be adjusted to a specific color. The possibility to vary the spectra of the HID lamps by changing the lamp filling opens up

26 1.3. Thesis layout 3 even more new fields of application. In spite of these unique features there is still a lot of research performed on HID lamps. Due to new technologies, as the LED lighting, a steady improvement of the lamp performance and efficacy is necessary to keep the position in the market. One new way within this development is the use of new operating methods. The operation of HID lamps with higher frequencies is a very promising attempt. The possibility of HF operation would allow the realization of compact, efficient and cost-effective HID lamp drivers and lighting systems. In the past one major problem inhibited the use of higher operation frequencies, the occurrence of acoustic resonances inside the lamp bulb. The acoustic resonances are standing pressure waves which are excited in HID lamps. They are determined by the lamp pressure and the volume of the discharge vessel. The problematic region in which the acoustic resonances occur is between 5kHz and 300kHz. They lead to an unstable lamp operation and in certain case to the destruction of the lamp. With new technologies it is possible to build lamp driver systems which allow to operate the HID lamps above the critical frequency range in which the acoustic resonances occur. But there are various observations that the lamp behavior changes under operation with these high frequencies. One major field of study is put on the electrodes and the transition region from plasma to electrode, the plasma boundary layers. The electrodes are a key parameter of the whole lamp system. The electrode temperature determines how much material is removed from the electrode by evaporation. In addition material can be removed from the electrodes by sputtering and other processes. This material condenses at the coldest part of the lamp which is the lamp bulb. The deposition of the material on the bulb results in a blackening over lifetime. If the bulb blackens, more and more light is kept inside the lamp leading to a lower light output and a higher lamp temperature. If the temperature increases to much the lamp can be destroyed. Thus the electrode temperature is a main factor limiting the lamp lifetime. There a several approaches to lower the electrode temperature. The electrode geometry is the easiest way to influence the temperature. Another way is doping the electrode with thorium. It lowers the work function of the electrode resulting in lower electrode temperatures. A quite new way of influencing the temperature is the so called gas phase emitter effect. Therefore materials as dysprosium are put into the lamp as iodides. During operation the dysprosium iodide evaporates and dissociates. At the electrode tip a thin layer of dysprosium arises possessing the thickness of a monolayer. This also leads to a reduction of the work function and thus of the electrode temperature. 1.3 Thesis layout Chapter 2 deals with the basics of electrical discharges. The main focus is put on the processes between electrode and plasma which take place at the electrode surfaces or in the vicinity of the electrodes. Also radiation processes are discussed. Furthermore the heat balance of the electrodes is considered. Chapter 3 shows the experimental setup used for the various diagnostics which are applied to the lamps. The lamps used for these investigations, the Bochum model lamp and ceramic metal halide lamps, are explained. In chapter 4 the measurements and the results are presented. The chapter is divided into two parts. The first deals with the fundamental research at the Bochum model lamp. In the

27 4 1. Introduction second part the results from the measurements at the YAG lamps are presented. Chapter 5 gives a summary of this work and an outlook for future measurements and investigations.

28 5 2. Fundamentals This chapter briefly describes some fundamentals of plasma physics. The main focus is put on the properties of arc discharges and the relevant processes occurring in them. In the second part of this chapter the main processes concerning the electrodes of arc discharges are discussed. 2.1 Basics of arc discharges In its initial state gas is non conductive and the atoms are not excited. An application of voltage produces an electric field which accelerates the charge carriers. Thus an electrical current is generated and an electrical discharge is formed. If free charge carriers are generated in a gas volume by ionization, the mixture of atoms, ions and electrons is called plasma. Now the gas becomes conductive. Electrical discharges can be separated into different classes depending on the strength of current. Figure 2.1 gives a rough overview of the different classes of electrical discharges. If for the given geometry in figure 2.1 the current exceeds 0.5A the electrical discharge is called arc discharge. The current is not limited and can easily reach values of a few ka. The region of glow and arc discharges are the important parameter ranges for discharge lamps. The second important parameter is the gas pressure which is in the range of a few Pa to approx. 10kPa for glow discharges. For arc discharges the pressure is typically in the atmospheric pressure range > 50kP a and is not limited. The visible appearance of an arc discharge by light radiation is called electrical arc. An important parameter of an arc discharge is the slope of the potential between the electrodes. The typical potential distribution within an arc discharge is shown in figure 2.2. Very important are the different scales on the z axis. On a global view the dimension of the anode and cathode fall regions is much smaller than the arc length. Only in these small regions the potential curve is influenced by space charges. As the axial electric field E column inside the cylindric arc column is nearly constant the course of the potential is linear. The voltage of the arc column can be describes as U column = l column E column. (2.1) l column is the length of the arc column. Because of the small dimensions of the space charge sheath, the length of the arc column can be estimated being equal to the length of the electric arc l arc. For a vertically operated arc this length is equal to the distance between the electrodes. In the vicinity of the electrodes the course of the potential becomes highly non linear. These regions are called cathode and anode fall region. The anode fall region has got a dimension of about 1mm. The curve of the potential in front of

29 6 2. Fundamentals R V supply i V V B random bursts A Townsend and Dark, self sustained discharge B - photo electric currents V C increasing illumination corona D + subnormal glow discharge normal glow discharge E abnormal glow discharge transition region arc Amp F G Figure 2.1: The dependence of potential upon current for various kinds of discharges. The numerical values apply approximately to discharges in neon at p = 1Torr in a tube 50cm long, with flat-copper electrodes of area 10cm 2. In some gases the curve shows a slight maximum in the region BCD. ([1]) Áz ( ) U a;el U column U c ~¹m Cathode fall region ~cm Arc column ~mm Anode fall region z Figure 2.2: Schematic drawing of a typical potential curve along the axis of an arc discharge.

30 2.1. Basics of arc discharges 7 the anode is based on spectroscopic [2] and theoretical [3] investigations. The integral anode fall U a,el shows only the deviation of the anode potential from the extrapolated column potential [4]. In contrast to the anode fall region, the region of the cathode fall has only a dimension of a few ten µm. Within this region the local thermodynamic equilibrium is highly disturbed. Strong gradients of temperature, charge carrier densities and the potential occur. The voltage drop in this region is called cathode fall U c. The region was very extensively investigated in the PhD theses of Nandelstaedt, Luhmann, Lichtenberg, Dabringhausen, Redwitz and Langenscheidt [5, 6, 7, 8, 2, 9] Basic plasma processes In order to sustain the electrical arc after ignition new charge carriers have to be generated. This is done inside the plasma volume by several processes. The main process is the ionization by collision. In this case a fast electron performs an inelastic collision with an atom. If enough energy is transferred from the electron to the atom an additional electron is released from the atom. A + e fast A + + e + e (2.2) the process may happen in both directions. If the process is read from right to the left side it is called three body recombination. In this case an electron and ion recombine to an atom by energy transfer to an additional electron which is necessary to fulfill the energy and momentum conservation law. A second process is the excitation of an atom by a collision with a fast electron. A + e fast A + e (2.3) The light emission of an arc discharge is produced by several processes. The emission of line radiation may be caused by an excited atom which passes over from a higher state n with the energy E n to a lower state m with the energy E m by emission of a photon with the energy hν nm. A n A m + hν nm (2.4) hν nm = E n E m is the discrete energy of the photon. h stands for the PLANCK constant (h = Js) and ν is the frequency. A further process is the emission of a recombination continuum or free bound continuum. In this case a photon with the energy hν is produced by a recombination of an ion and an electron. A + + e A + hν (2.5) The energy of the photon is composed of the ionisation energy of the atom and the kinetic energy E k = 1 2 m ev 2 e of the free electron hν = E i m ev 2 e, (2.6) E k varies according to the energy distribution of the electrons. The reverse process is called photo ionisation. A third important process is the emission of a free-free continuum produced by the deceleration of electrons in the field of ions which is called Bremsstrahlung.

31 8 2. Fundamentals Basic plasma properties As stated above a plasma is an ionized gas with free charge carriers. In general the plasma volume is quasi-neutral. This implies that there are as many positive (ions) as negative (electrons) charge carriers. In case of a single ionized plasma this means n e = n i (2.7) n e is the density of electrons and n i the density of ions. The quasi neutrality is no longer valid if the plasma is observed on a very small scale. The typical size which defines this region is the DEBYE length. ɛ0 k B T e λ d = (2.8) e 2 n e k B is the BOLTZMANN constant, e the elementary charge, ɛ 0 the vacuum permittivity and T e the electron temperature. A more general expression for a single component plasma is n e = N k n i,k (2.9) k=1 with n i,k the density of the k charged ions and N the highest ionisation stage. For a multi component plasma composed of a gas mixture the right hand side of equation 2.9 has to be summed up over all components. The pressure in a plasma is described by DALTONs law. It is also valid for a multi component plasma and expresses the total pressure p as a sum of the partial pressures p j of the different species j. m m p = p j = n j k B T j (2.10) j=1 k B is the BOLTZMANN constant and T j the temperature of the species j and m the number of species. T j may be different for different species, e.g. for the electrons and heavy particles. In arc discharges the collision rate of the gas particles is very high. This implies velocity distributions for the particles which assign temperatures to the different species. Because of the high collision rate MAXWELL distributions arise. The MAXWELL distribution defines the temperature T j of a species j as j=1 T j = m j v 2 j 3k B. (2.11) m j is the mass of one particle and v 2 j the mean square of the particle velocity. Inserting the mean kinetic energy E kin = m j 2 v2 j in 2.11 E kin = 3 2 k BT j (2.12) indicates that the temperature of a particle represents also the mean kinetic energy of a particle. In high pressure plasmas with high electron densities the electrons can be described by the MAXWELL distribution due to the strong electron-electron interaction [10]. The distance,

32 2.1. Basics of arc discharges 9 which an electron can pass between two collisions, the mean free path, is much smaller than the dimension of the plasma volume. The macroscopic field has only a small influence on the instantaneous movement of the electrons and can be described as a superimposed drift motion. The electrons mainly perform an undirected thermal motion caused by the high collision rate. Thus a defined temperature T e can be given for the electrons. Of course a temperature can also be given for the ions and atoms. By reason of the nearly identical masses of the ions and atoms in arc discharges one temperature T h can be used for both species. This is the temperature for the so called heavy particles. Because of the much higher mass of the ions and atoms compared to the lighter electrons the temperature of the heavy particles within a gas discharge is lower than the temperature of the electrons Thermal equilibrium The thermal equilibrium is a very important reference state to characterize high pressure plasmas. Depending on the plasma parameters it has to be distinguished between partial deviations from thermal equilibrium. A detailed discussion of them can be found in [2] and [11] Complete thermal equilibrium To realize a complete thermal equilibrium the following conditions have to be fulfilled: 1. Every process takes places as often as the inverse process (detailed equilibrium). 2. The velocity distributions of all particles within the plasma respond to a Maxwell distribution. 3. The temperature for all particles is equal. 4. The temperature and pressure must be independent of species and time. 5. The population of energy-levels is given by a BOLTZMANN distribution. The BOLTZMANN distribution is defined as n r = g ( r exp E ) r, (2.13) n 0 g 0 k B T with n r the density of excited atoms with the energy E r, n 0 the density of atoms in the ground state, g r the statistical weight of a state r with the energy E r, g 0 the statistical weight of the ground state and T the absolute temperature (in K). The BOLTZMANN distribution can be extended by the consideration of ionized atoms. This expansion leads to the SAHA-EGGERT equation n e n i n 0 = 2Z i (2πm e k B T e ) Z 0 h ( exp E ) i, (2.14) k B T

33 10 2. Fundamentals with n e, n i, n 0 the electron-, ion- and atom densities, Z i, Z 0 the ion- and atom partition function and E i the ionization energy of the neutral gas. The partition function is the product of the BOLTZMANN factor and the statistical weight Z 0,i = j ( g j exp E ) j. (2.15) k B T This partition function describes the sum of all possible energy states and probabilities of their population in dependence on the plasma temperature T. Thus Z i /Z 0 represents the ratio of the partition functions of the ions and atoms [12]. The complete thermal equilibrium is an ideal conception for a plasma which does not exist for technical plasmas. Local thermal equilibrium A more realistic description of technical plasmas is given by the local thermal equilibrium (LTE). In comparison to the complete thermal equilibrium the values for pressure and temperature are now position dependent. All other conditions of the complete thermal equilibrium remain unchanged. The Boltzmann distribution and the SAHA equation are treated as a sufficient accurate approximation. Partial local thermal equilibrium For real plasmas the assumption of a partial local thermal equilibrium (plte) is often useful. It is characterized by defined deviations from LTE. Very often the assumption is made that the temperature of the electrons T e is different from the temperature of the heavy particles T h, T e T h. A stronger deviation from LTE is present if only the population of higher energy levels in the vicinity of the ionisation limit can be given by a Boltzmann distribution. If the deviations from a complete thermal equilibrium are to massive the plasma has to be described by a collision-radiative model. In arc discharges the boundary layers, especially the cathodic boundary layer, show strong deviations from thermal equilibrium. The main deviations are T e T h, lower charged particle densities compared to Saha equation and a violation of the quasi neutrality. For these conditions a modified SAHA equation can be derived [13] Radiation processes inside a plasma Inside a plasma radiation is caused by several processes. Additionally these processes cause different types of radiation which will be discussed next.

34 2.1. Basics of arc discharges 11 Continuum radiation Continuum radiation is mainly caused by two mechanisms inside the plasma. The first mechanism is the recombination which is described in 2.5. A free electron recombines with an ion and emits a photon with the energy E = hν. Caused by the energy distribution of free electrons, the energy extends over a broad energy band and thus over a broad wavelength range. The lower limit of the energy band is determined by the ionisation energy which is released by recombination. The recombination may take place into the ground state or an excited state of the atom. The second process which leads to continuum radiation is the free-free transition of an electron caused by the acceleration and deceleration due to the field of an ion. This radiation is named Bremsstrahlung. Line radiation Line radiation occurs if an atom is de-excited by the transition of an electron from an upper state n n to a lower state n m. Because of the discrete energy levels, only photons are emitted with a discrete frequencies ν nm. Thus the wavelength λ nm exhibits a discrete value given by with c 0 the speed of light. c 0 = λ nm ν nm, (2.16) A combination of both types of radiation has to be considered if the plasma radiation is analyzed. The total radiation is combined to a spectral emission coefficient ε λ (λ) ε λ (λ) = ε λ,nm (λ) + ε λ,cont (λ). (2.17) The spectral emission coefficient ε λ,nm (λ) of an emission line is defined as ε λ,nm (λ) = 1 4π A nmh c 0 λ nm n n P nm (λ) (2.18) with n n the population density of the upper state, A nm the transition probability and P nm (λ) the line profile. The latter describes the broadening of the spectral line in dependence on wavelength. P nm (λ) is normalized as follows: Broadening of line profiles can be caused by several effects: 0 P nm (λ)dλ = 1. (2.19) 1. DOPPLER effect: Line broadening caused by the thermal movement of the emitting particle 2. Pressure broadening: Collisions of the excited particles with neutrals lead to a line broadening 3. STARK-broadening: Collisions with charged particles [14]

35 12 2. Fundamentals The STARK-broadening is the dominant broadening mechanism in plasmas with a high density of charged particles. The total line emission coefficient for a specified line can be written as ε nm = 1 4π A nmh c 0 λ nm n n. (2.20) It is an integral of the spectral emission coefficient over the wavelength Radiation transport The radiation generated within the plasma volume has to pass a certain distance before it reaches the boundaries of the discharge. Along this way parts of the radiation can be absorbed and new radiation of the same wavelength can be generated. Thus the radiation which is visible from outside is an integration of several emission and absorption processes along a line-of-sight. The change of the spectral radiance I λ along an infinitesimal step of line-of-sight is described by the radiation transport equation [15] di λ (λ, x) dx = ε λ (λ, x) k λ (λ, x)i λ (λ, x). (2.21) ε λ represents the emitted radiation and k λ describes the absorption processes. An integration of 2.21 with the boundary condition I λ (x = 0) = 0 yields +R ( R ) I λ (λ) = ε λ (λ, x) exp k λ (λ, ξ)dξ dx. (2.22) x The absorption coefficient k(λ, ξ) can be expresses as R k(λ, ξ) = e2 4ε 0 mc 0 n a (x) λ2 0 c 0 P (λ) (2.23) with n a (x) the local density of the absorbing atoms a, f the oscillator strength and P (λ) the normalized profile function, which describes the line broadening. The dimensionless integral τ 0 (λ) τ 0 (λ) = +R R k(λ, ξ)dξ, (2.24) gives information about the absorption strength of a plasma and is named the optical thickness [16]. If τ 0 1 absorption processes can be neglected, k(λ, r) 0. In this case the observed line is named optically thin. 2.2 Electrodes of arc discharges The electrodes of HID lamps are under intense stress during operation. They are operated near to their load limit due to the enormous temperatures the electrodes have to handle. The

36 2.2. Electrodes of arc discharges 13 cathodes of HID lamps emit electrons thermionically which mainly sustain the arc current. The energy which is needed for the thermionic emission of electrons is supplied by power from the arc plasma. The anodes are heated by the electrons delivered by the work function which is released within the electrode when the free electrons enter the solid electrode. In both cases the electrodes are heated up to temperatures which are mostly above 3000K. Due to this very high temperatures tungsten is the only material which can comply the requirements. Tungsten has a melting temperature of 3695K, the highest of all metals Surface effects on electrodes The processes on the electrode surface are very important for the whole discharge. At the surface the interaction between the plasma and the solid state electrode takes place. Some of these processes are the same for anode and cathode but there are also processes which have to be described separately. For both electrode types the cooling due to the emission of electromagnetic radiation has to be considered. Above all an electrical current and a heating power coming from the plasma has to be coupled into the electrodes. A very important parameter for the discharge is the thermionic electron emission of the cathode because these electrons mainly sustain the arc current. Power flux density and current density The heating of the electrode surface is mainly caused by the power flux density q p from the plasma. This value cannot be measured directly. The same problem occurs for the total current density j tot. Both values have to be derived from measurements and simulations of the total power which is coupled into the electrodes. For the cathode a detailed description of this processes can be found in the work of Dabringhausen [8]. The results of these processes are the so called transfer-functions q c,p = q c,p (T, U c ) j g,c = j g,c (T, U c ). (2.25) Until now for the anode no equivalent model could be developed. A detailed description of the anode boundary layer can be found in the work of Redwitz [2, 17, 4]. Electrode radiation Every solid body with a temperature T > 0 emits thermal temperature radiation. The emitted radiation is nearly always a continuum radiation caused by lattice vibrations due to thermal excitation. The excitation energy is emitted as electro-magnetic radiation of different wavelength. The surface radiance L λ,b of an ideal black body is given by PLANCKs law. It depends on the temperature of the black body and on wavelength. L λ,b (λ, T ) = c 1 πλ 5 1 exp c 2 λt 1 (2.26)

37 14 2. Fundamentals c 1 and c 2 are the PLANCK constants and defined as c 1 = 2πhc 2 0 = W m 2 (2.27) c 2 = hc 0 k B = mk. (2.28) For real radiators PLANCKs law has to be expanded. The so called emissivity ε(λ, T ) depending on temperature and wavelength has to be taken into account. For an ideal black body the emissivity is ε(λ, T ) = 1. For real radiators the emissivity is reduced ε(λ, T ) < 1 due to the surface constitution for instance the surface roughness. This is also the case for tungsten and the surface radiance is now given by L(λ, T ) = L λ,b (λ, T ) ε(λ, T ). (2.29) For electrodes of HID lamps the radiation acts as a cooling effect. The radiation emitted by the surface dissipates power from the electrode. The local power flux density q rad can be described by the STEFAN-BOLTZMANN law q rad = σ SB ɛ tot (T ) ( T 4 T 4 amb). (2.30) In this equation T is the local surface temperature, σ SB is the Stefan-Boltzmann constant, ɛ tot the total emissivity of the surface and T amb the ambient temperature in the vicinity of the surface. The total emissivity ɛ tot is gained by an integration over the wavelength from λ = 0 to λ = : ɛ tot = ε(λ) dl(λ,t ) 0 dλ dl λ,b (λ,t ) 0 dλ dλ dλ. (2.31) Thermionic electron emission As a basis for the description of emission mechanisms of electrons by solid bodies the model of free electrons is used. Within the model of free electrons the electrons inside the conductance band of metals are treated as quasi free moving and this movement is only determined by kinetic energy. They have no potential energy depending on their position. For this model the density of states N depending on the energy E for a three dimensional case is N(E) = 1 2π 2 ( 2me h 2 ) 3 2 E 1 2. (2.32) In the case of T = 0K the FERMI energy E F separates the occupied and the unoccupied states. It depends on the density of the free electrons n inside the metal according to E F = h2 2m e ( 3π 2 n ) 3 2. (2.33) If now T > 0K energetically higher states are populated by a fraction of electrons. Their distribution is given by the FERMI distribution function f ( ( ) 1 E EF f(e) = exp + 1) (2.34) k B T

38 2.2. Electrodes of arc discharges 15 with the temperature T of the solid body. Thus n(e) = f(e)n(e) = 1 2π 2 ( 2me h 2 ) 3 2 E 1 2 exp ( E E F k B T ) + 1 (2.35) is the population density of the energy states. An electron can be emitted by the metal if its kinetic energy is higher than the work function φ of the metal. The work function φ is defined as eφ = E E F (2.36) and depends on the material. E is the energy of the vacuum level. The work function is a very important parameter of the electrodes. For pure tungsten its average value is given by φ = 4.55eV, but only if the surface of the electrode is nearly flat and there are no defects in the lattice structure. In the following table the major reasons for variation of the work function are summarized. Crystal orientation If different faces of a crystal lattice are considered, the work function may vary for different orientations. Thus it is necessary to use an averaged value for the work function. Schottky effect The work function is reduced by applying an external electrical field onto the surface. This effect is called Schottky effect. The potential which an electron has to overcome to be emitted by the material is reduced by the field. This effect takes place at a field strength above 10 7 V. The conditions in which such a high field strength m would occur may be reached within the cathodic boundary layer. Anomalous Schottky effect For the anomalous Schottky effect it is necessary to consider the dependence of the work function on the crystal orientation. For different orientations the work function has different values. By strong electrical fields the effective work function is lowered. Now crystal orientations with a high work function are no longer active. It implies a decreasing emitting surface. Emitter effect A further effect which is influencing the work function of the electrodes is the so called emitter effect. It is produced by a dipole layer on the electrode surface by which the effective work function is reduced. The diploe layer can be formed by a monolayer of electropositive atoms. This effect is described in detail in chapter If now the temperature is higher than zero T > 0K electrons are excited and can populate states with an energy E above E F which means also with an energy above E (see equation 2.34). The higher the temperature of the metal the higher is the number of electrons with a kinetic energy E > E. Electrons will leave the solid body if the velocity component v perpendicular to the surface meet the condition 1 2 m ev 2 E F + eφ. (2.37) The emitted electrons form a current density j e from the electrode which can be written as j e = 4πm ( ee (k h 3 B T ) 2 exp eφ ). (2.38) k B T

39 16 2. Fundamentals This formula is named RICHARDSON-DUSHMANN equation. A more detailed description of this effect can be found in [18]. It shows that the electron current density is only dependent on the temperature and the work function of the metal. Furthermore A R = 4πm eek 2 B h 3 (2.39) should be a constant but in reality this term often depends on the material. For the cathode the thermionic electron emission is the most important process because the cathode delivers the electrons which sustain the arc current. Within the treatment of arc discharges there are further mechanism which may lead to an electron emission. One effect is the field emission. In this case a field strength of 10 9 V has to occur which m pulls electrons out of the electrode via the quantum mechanic tunnel-effect. This high field strength does normally not occur at electrodes in arc discharges. The second effect is the so called secondary electron emission. This effect takes place if ions are accelerated by the electric field and hit the cathode surface. At first an electron is emitted which recombines with an ion to an excited atom. The excitation energy E ex is equal the ionisation energy E i reduced by the work function eφ. Electrons can escape if the sum of the kinetic energy of the excited atom and the excitation energy is higher than the work function at the moment when the particle hits the surface: 1 2 m hv 2 h + E ex = 1 2 m hv 2 h + E i eφ eφ, (2.40) m h and v h are the mass and velocity of the excited atoms. The secondary electron emission can be neglected in the parameter range treated in this work Heat conduction of electrodes For a quantitative description of the electrodes some assumptions have to be made. The volume V of the electrodes as well as the mass density ρ m does not change with temperature T and pressure p. This implies that all processes are isochore and isobaric. For a general treatment only a small piece of the electrode with the volume V has to be considered. According to the first thermodynamical theorem the time dependent change of the inner energy U of this volume in dependence on time can be written as du dt = ρ m c p (T ) T dv. (2.41) V t c p (T ) is the heat capacity of the material. Furthermore the power balance of the volume can be written as ρ m c p (T ) T V t dv = SdV q cond nda. (2.42) V A The first term on the right hand side is a source term, the second term is written as a loss term. q cond is the heat flux density through the surface A of the volume V. n is the normal vector which is directed perpendicular to the surface out of the volume. If the heat flows into the material q cond n < 0. Thus the second term on the right side of equation 2.42 becomes

40 2.2. Electrodes of arc discharges 17 positive. By using the integral theorem of GAUSS it can be written q cond nda = q cond dv. (2.43) Furthermore the FOURIER law for heat conduction A V q cond = κ(t ) T (2.44) can be used which always describes the heat flux in the direction of decreasing temperature. κ(t ) is the heat conductivity of the material depending on the material temperature. Inserting equation 2.43 and 2.44 into equation 2.42 leads to ( ρ m c p (T ) T ) (κ(t ) T ) dv = SdV. (2.45) t V This expression is valid for all volume elements. Hence equation 2.45 can be written as ρ m c p (T ) T t V (κ(t ) T ) = S. (2.46) The source term S e.g. describing the JOULE heating inside the solid object caused by the electric current can be neglected (S = 0) for the operation parameters used in this work. A more detailed description of this term can be found in the work of Dabringhausen [8]. The equation describing the heat conduction within the electrode is now a nonlinear partial differential equation of second order depending on the temperature T = T ( r, t) inside the electrode solid body Heat balance of a periodically charged electrode In case of a periodically charged electrode the time dependent heat equation can be modified. With a constant time τ for one period and an angular frequency ω = 2π the phase angle can τ be defined as ϕ = ωt = 2πt.With τ equation 2.46 becomes T t = ω T (ωt) = ω T ϕ (2.47) ρ m c p (T )ω T (κ(t ) T ) = 0. (2.48) ϕ This equation can now be reduced onto the special case of a cylindric electrode. A small disc is cut out of an electrode with the radius r E and the thickness dz. In figure 2.3 this disk is indicated with the orientation of the normal vectors on its surfaces. With this definitions eq becomes (κ(t ) T )dv = κ(t ) T da = ρ m c p (T )ω T dv. (2.49) ϕ A The integral over the surface can now be divided into three parts according to κ(t ) T da = A κ(t ) T da + A 1 κ(t ) T da + A 2 κ(t ) T da. A 3 (2.50)

41 18 2. Fundamentals r E A 1 dz A 3 A 2 Figure 2.3: Definition for the normal vectors on the surface of a disc cut out of the electrode With the assumption of a rotational symmetry for a cylindrical electrode T can be reduced to T = T r e r + T z e z. (2.51) Solving the integrals for the different surfaces and using the STEFAN-BOLTZMANN law as a boundary condition for the cylinder barrel, eq becomes A [ ( T ) κ(t ) T da = reπκ(t 2 ) z A 1 ( ) ] T z A 2 2πr E ɛ tot σ SB T 4 dz. (2.52) Furthermore the time, respectively phase dependent term can be written as ρ M c p (T )ω T ϕ dv ρ Mc p (T )ω T ϕ r2 Eπdz. (2.53) As a result of these assumptions and transformations the heat balance of a periodically charged electrode becomes reπ 2 ( κ(t ) T ) = 2πr E ɛ tot σ SB T 4 + r 2 z z Eπρ M c p (T )ω T ϕ. (2.54) 2.3 Acoustic resonances As mentioned in chapter 1 the occurrence of standing pressure waves (acoustic resonances) limits the frequency range for high frequency (HF) operation of HID lamps. The occurrence of acoustic resonances was first reported by Campbell [19]. The effect of the acoustic resonances can be described by 2 p t 2 + D p t C2 2 p = (γ 1) N t. (2.55)

42 2.4. Skin effect 19 In this equation p is the local pressure, D the damping constant, C the effective velocity of sound, γ the specific heat ration cp c ν and N the local acoustic power. A rough estimation for N is N = P P rad P cond (2.56) with P the HF electric power, P rad the radiative loss and P cond the conductive loss. For equation 2.55 a solution for amplitude and phase of the pressure wave in the vicinity of an acoustic resonance is jω(γ 1)N(ω) p(ω) = (2.57) ω 2 ω0 2 + jωd with ω the power frequency and ω 0 the resonance frequency. The resonance frequencies can be calculated for a cylindrical discharge vessel by ( n ) 2 ( αlm ) 2. ω lmn = πc + (2.58) L R L is the tube length and R the tube radius. α lm is the m th zero of the first derivative of the Bessel function J l of order l and n = 0, 1, 2,... the longitudinal wave number. The value for the effective sound velocity C has to be determined empirically for every lamp type. It has to include the temperature profile of the discharge. Additionally for longitudinal and radial / azimuthal resonances different values for C have to be used. Keijser [20] has shown, that acoustic resonances in the low frequency region can be determined quite easily but for large numbers of l, m and n the calculation is nearly impossible. He has shown by simulations that gaps in the frequency spectrum between 10 and 150kHz occur which allow an operation of HID lamps without acoustic oscillations. But these gaps are very small and the position of these gaps is different for every lamp type and the orientation of the lamp during operation (horizontal or vertical). It was also found that a stable operation of HID lamps above a certain frequency of several 100kHz is possible. 2.4 Skin effect In materials, to which a current with a higher frequency is applied, the so called Skin-effect occurs. The skin effect is the tendency of the HF current to distribute itself within the conductor, in this case the electrodes, so that the current density near the surface of the electrodes is larger than that at its core. Thus the skin effect causes the effective resistance of the electrodes to increase with the frequency of the current. The skin effect is described by the skin depth. It is a measure of the distance over which the current falls to 1/e of its original value. The skin depth varies with the properties of the material and is defined by δ = 1 π f µ 0 µ r σ (2.59) with µ r the permeability of the material, f the frequency of the applied current and σ the electrical conductivity of the material. The electrical conductivity is depending on temperature. σ(t ) of tungsten can be determined from 1 σ(t ) = (2.60) ρ 0 (1 + α 0 T )

43 20 2. Fundamentals with ρ 0 = 0.055Ω mm2 m α 0 = K (2.61) (2.62) for pure tungsten. The permeability of tungsten can only be estimated since no reference data is available. In the classification scheme it is attributed to the group of the paramagnetic elements [21]. Hence the value of the permeability can be set to µ r = 1 taking into account very high temperatures of the electrodes during operation. With these data the skin depth for tungsten can be calculated. Figure 2.4 shows the calculated skin depth in dependence on temperature for different frequencies. As the skin depth decreases with increasing frequency the values for the frequency of 2 MHz show that the skin effect has no influence on the experiments for lower frequencies. For a frequency of 2 MHz and a temperature of 3000 K the skin depth is 0.29 mm which has to be compared to the radius of the electrodes. Thus the thicker YAG lamp electrodes have a radius of mm which is less than the skin depth. 2 MHz is a very high frequency for lamp operation which is normally not used. The maximum frequency in the experiments is 1 MHz. This means that a skin effect can be neglected within the electrodes. 3 Skin depth = mm mm 23 khz 300 kkz 2 MHz 0.75mm 0.29mm Temperature = K Figure 2.4: Calculated skin depth for tungsten versus temperature for different frequencies

44 21 3. Experimental setup In this chapter the experimental setup is described. The setup will be divided into three parts. The first part describes the lamps used in this work. On one hand there is the Bochum model lamp with its periphery and at second the research lamps which are similar to commercial HID lamps. The second part deals with the peripheral setup. This contains the different electrical supplies for the low frequency operation and the rf operation. The third and last part contains the measuring setup with the different diagnostic tools. 3.1 Lamps under investigation The lamps for this project are chosen under several points of view. The Bochum model lamp is a very simple type of an HID lamp. It is used for fundamental investigations and for the development of measuring techniques which can later be transferred to real lamps. The test lamps have also a special design for investigation purposes. The lamp bulb is produces of a transparent ceramic material and the geometry has been upscaled. But in general the lamps are similar to commercial HID lamps. They belong to a subspecies of the HID lamps, the ceramic metal halide lamps The Bochum model lamp Within this work a fundamental investigation of HID lamp electrodes should be performed. For this purpose a good accessibility of the electrodes and the near electrode region for optic measurements is absolutely essential. Commercial lamps mostly do not fulfill these criteria. They often have translucent vessels making spectroscopic measurements or photographic observations impossible. Additionally the geometries of these lamps are very complex and the dimensions are small. Because of the commercial use the lamps are designed to produce a high light output. Thus the high plasma radiation complicates measurements at the electrodes drastically. Also the complex gas mixtures and salt fillings of these lamps make the measurements very difficult. Many effects take place at the same time and overlap each other. Hence a clear verification of a certain effect is often impossible. At last it is not possible to change the lamp parameters like electrode diameter, electrode length, arc length, pressure, etc..

45 22 3. Experimental setup To avoid most of these problems the so called Bochum model lamp was invented. The main stepping motor spindel electrode holder electrode discharge vessel electrode slide free of play linear bearing Figure 3.1: Schematic drawing of the Bochum model lamp

46 3.1. Lamps under investigation 23 development of the model lamp was performed by Luhmann and a detailed description of the experimental lamp setup can be found in his work [6]. Within the last years some adoptions of the model lamp have been made by Dabringhausen, Redwitz and Lichtenberg. These changes are described in [8, 2, 7]. The Bochum model lamp is shown in figure 3.1 as a schematic drawing. The discharge tube which is made of fused silica is mounted in metallic sockets. The metallic sockets have several purposes. They manage the gas supply and serve as a feed-through for the electrode holders. Additionally they seal the discharge vessel and the electrode holders. The system is evacuated by a vacuum pumping station which consists of a membrane roots pump (BALZERS MD-4T) and a turbo molecular pump (BALZERS TMU 260). The electrode holders are isolated from the whole system because they are used for the electrical connection. Furthermore the holders can be moved very precisely by stepping motors inside the tube. This gives the possibility to vary the electrode position and thus the arc length even during operation of the lamp. The electrodes are cooled by silicon oil which is flowing around the part of the electrode which electrode outer tube entrainment thread soldering electric connector inner tube main block inlet outlet of the coolingfluid Figure 3.2: Schematic drawing of an electrode holder remains inside the electrode holders as it is illustrated in figure 3.2. A Refrigerated/Heating Circulator (JULABO FP45-MS) pumps the silicon oil which is kept on a constant temperature of 293K through the electrode holders. The oil is led through an inner tube to the tip of the electrode holder, flows around the electrode and afterwards back through the outer tube. By this process the electrode is cooled and the electrode temperature at the soldering point is fixed to a constant value Ceramic Metal Halide Lamps At the beginning of this section the disadvantages of commercial ceramic metal halide lamps for measurements have been listed. Nevertheless it is indispensable to perform measurements at these kind of lamps because the model lamp can only be operated with noble gases. To reduce the perturbing effects special lamps for investigations have been designed by the Philips Company Advanced Development Lighting (ADL), Eindhoven. These test lamps exhibit some special features. The general design is shown in figure 3.3. One special feature is the lamp bulb which is made of Yttrium-Aluminum-Garnet (Y 3 Al 5 O 12 ). Henceforth these lamps are called YAG lamps.

47 24 3. Experimental setup The YAG material is transparent so that the lamp electrodes become accessible for optical measurements in contrast to a commercial lamp bulb which normally is translucent. The YAG material is very expensive and lifetime is limited to approximately 60 hours. These properties make the material commercially inappropriate. The electrodes of these lamps are made of pure tungsten without any doping by thorium sealing 5 mm electrode 7 mm plasma salt pool mm Figure 3.3: Schematic drawing of a YAG lamp oxide or other substances. They are implemented as straight rods without a coil at the electrode tip. The electrode length from the point where they are bruised gas-tight into the bulb to the tip is approximately 5mm. The gap between the electrodes is approximately 7mm. These values may vary in the range of a few percent because all of these YAG lamps are hand crafted and unique. The inner volume of the discharge vessel is about 0.314cm 3. The filling of the YAG lamp consists of a mixture of the two noble gases argon (Ar) / krypton (Kr) with a pressure of 300mbar in the cold state. The gas filling is necessary for the ignition of the lamp. Furthermore the lamps contain a dose of about 6mg of mercury (Hg). These fillings are the same for all YAG lamps. Additionally the lamps are filled with metal halides which are responsible for the light color and the performance of the lamp. The lamps investigated in this work are filled with sodium iodide (N ai), thallium iodide (T li), dysprosium iodide (DyI 3 ), holmium iodide (HoI) and thulium iodide (T mi). An overview over the several salt compositions used here is given in table 3.1. In the off-state the mercury is present in the liquid state and the metal halides are solid as salts. After ignition the lamp heats up causing first an evaporation of the mercury followed by the salts. Due to this evaporation the pressure inside the lamp bulb is increased. The mercury mainly determines the pressure during operation in the steady state. In table 3.1 the operation pressure is given for the used amount of mercury. The pressure of 19.8bar is adjusted if a lamp power of P input = 75W is applied. At this input power all mercury is evaporated so that a constant partial pressure of mercury is guaranteed. This kind of operation state is called unsaturated operation. Due to the vertical lamp operation the liquid salts accumulate at the bottom of

48 3.1. Lamps under investigation 25 Lamp type Ar/Kr pressure Hg dose NTD1 300mbar 6mg 19.8bar NTD2 300mbar 6mg 19.8bar NT 300mbar 6mg 19.8bar Dy 300mbar 6mg 19.8bar TD 300mbar 6mg 19.8bar Hg 300mbar 6mg 19.8bar Metal halides Na Tl Dy/Ho/Tm 8mg (4mg) 83.7% 7.2% 9.8% 8mg (4mg) 86% 9% 5% 8mg (4mg) 94% 6% 1mg mg 100% - 50% 50% Table 3.1: Table of the used YAG lamp types and their filling components the lower electrode where it comes in contact with the lamp bulb. This coldest area is called cold spot. The cold spot temperature is depending on the power which is coupled into the lamp. Furthermore the temperature of the cold spot determines the partial pressure of the different additives. The metal halides do not evaporate completely in the case of standard operation at P input = 75W. It implies a saturated operation. A variation of the cold spot temperature for example caused by a higher or lower input power results in changes of the amount of evaporated salts. Thus it is possible to change the partial pressures of the metal halides inside the lamp by varying the cold spot temperature. The YAG lamps are mounted inside an outer bulb by a wire frame. The outer bulb has several functions. On one hand it has a protection function in case of destruction of the lamp vessel. On the other hand it shields the harmful UV light which is emitted by the lamp. The outer vessel is evacuated and sealed. Thus it shields the inner bulb thermally from the surrounding and allows a well defined heat distribution of the inner lamp, in order to ensure a constant cold spot temperature and a stable lamp operation. The outer lamp bulb is equipped with a E27 thread for standard lamp sockets The function of metal halides and rare earths In chapter 1 the function principle of an HID lamp is briefly described. Chapter gives a more detailed description of the radiation processes inside a HID lamp. In this section the purpose of the metal halides and rare earths is shown and the used materials in the investigated lamps are described. Lamps should have a good color rendering index (CRI) so that illuminated objects look quite natural. For this purpose radiation should be emitted uniformly distributed over the wavelength within the sensitivity range of the human eye. Figure 3.4 shows the emitted spectrum of a metal halide lamp and the sensitivity curve of the human eye. To produce uniformly distributed radiation over the visible wavelength range many lines are necessary. These lines are produced by the metal halides which are added to the lamp filling next to mercury and the noble gases. The metal halides exhibit a lot of different excitation states and thus many spectral lines at different wavelength positions complete the spectrum. For the

49 26 3. Experimental setup design of a lamp metal halides are chosen which have lines at wavelength positions which are in best accordance with the application of the lamps. If the lamp is used for general lighting Figure 3.4: Spectrum of a D2 automotive lamp with the sensitivity curve of the human eye it is required that not to many lines are excited outside the visible wavelength range. The energy consumed by the emission of these lines would be a loss power. Regarding these requirements, the rare earths have several advantages. On the one side they possess many excitation states and optical transitions in the visible spectral range but the intensity of the lines is very small. Thus for the design of the lamp spectrum they are interesting as they produce a more continuous spectrum. Another interesting purpose of the rare earth is their influence on the electrodes. During operation of the lamp the rare earths are evaporated and are transported to the electrodes. Thus it is possible that a thin film of electro-positive rare earth atoms in the order of a monolayer is generated on the electrode surface. This monolayer will reduce the work function φ of the electrode resulting in an increased electron emission and a decreased electrode temperature. Additionally the heating of the electrode during the anodic phase may be reduced. This in turn has a positive effect on the lamp lifetime. The whole effect is called gas-phase emitter effect as it is described by Langenscheidt and Westermeier [9, 22]. Table 3.2 list all of the used ingredients of the lamps used in this work. 3.2 Electrical lamp supply As described in chapter 2.3 acoustic resonances occur within the YAG lamps so that an operation in some parts of the frequency spectrum is not possible. Further on, it is impossible

50 3.2. Electrical lamp supply 27 Element Nr. Atom mass Melting Boiling Density 1. Ionization [g/mol] point[k] point [K] [g/cm 3 ] energy [ev ] Sodium Na Argon Ar Krypton Kr Iod I Dysprosium Dy Holmium Ho Thullium Tm Tungsten W Mercury Hg Thallium Tl Table 3.2: Table of the used YAG lamp types and their filling components to find a suitable power source which allows an operation from very low frequencies (1 Hz) or even DC operation to high frequencies of 2 MHz. Therefore two separate power supplies are used. One for DC or low frequency AC operation and a second setup for high frequency AC operation Lf setup For low frequency operation a voltage-controlled current source is used, namely a DCU/I amplifier from FEUCHT ELEKTRONIK. It provides a current up to 28 A and a voltage of max. 400 V. The maximum steady state power is limited to 2250 VA. The amplifier may be used in dc operation with both polarities or in ac operation up to 30 khz. The amplifier amplifies any voltage signal connected to its BNC input by a factor of 10. For controlling the output signal, the amplifier exhibits two monitoring outputs. One serves for the current and the other one for the voltage signal. The rise time of the output signal is short enough to operate an arc discharge, in spite of its negative differential resistance, without any pre resistance in series with the discharge. In case of ac operation two different kinds of waveforms are used. Most HID lamps are operated with sinusoidal or switched dc currents. The lamp is operated with currents from î = 1...6A. In contrast to this high currents the YAG lamps are operated with currents in the range from î = A. At these low currents the amplifier does not provide a straight switched dc signal for frequencies f > 500Hz. Figure 3.5 a) shows the current signals for various frequencies. For low frequencies the switched dc signal shows a fast rise to the maximum amplitude immediately after current zero crossing. For frequencies above 500Hz the current amplitude reaches its maximum after a fourth of

51 28 3. Experimental setup Current = A Hz 500 Hz 1000 Hz 2000 Hz Current = A Hz 2000 Hz /2¼ ¼ 3/2¼ 2¼ Phase (a) LF setup /2¼ ¼ 3/2¼ 2¼ Phase (b) LF setup with commutator Figure 3.5: Switched-DC current signal from the low frequency power supply with and without commutator for the operation of YAG lamps one rf period. Concerning the power balance of the discharge this result implies a reduction of the input power. Therefore an additional commutator is used for the operation of the YAG lamps. This device has been built by the company PHILIPS. The corresponding setup scheme is shown in figure 3.6. Signal Generator Amplifier Igniter Lamp (a) Low frequency power supply for the model lamp Signal Generator Signal Generator U = 2.8 V Amplifier U = 280 V Commutator f = 0.1 Hz - 2 MHz R V Igniter Lamp i max (b) Low frequency power supply for the YAG lamps = 2 A Figure 3.6: Low frequency power supply with and without commutator for a improved switched DC current signal The commutator is powered by the amplifier (Feucht Elektronik) with a constant dc voltage

52 3.2. Electrical lamp supply 29 of V sup = 280V. A signal generator specifies the commutation frequency f com of the device. Since the commutator only detects the rising edge of the input signal the applied signal must be adjusted to twice the frequency of the desired output signal. The desired lamp current has to be adjusted by the resistant which is installed in the lamp circuit. The maximum amplitude of the output current is î max = 2A. The current signal is shown in figure 3.5 b). The model lamp can be ignited in two different ways. The easiest and mainly used method is to adjust the electrodes at their final operating positions with their desired gap. After the positioning the amplifier is switched on. The maximum voltage of the amplifier is not high enough to ignite the lamp on its own. Thus a Tesla gun (from LEYBOLD-HEREAUS) is used to produce free charge carriers inside the lamp bulb which together with the applied voltage result in a breakthrough and afterwards in the ignition of the discharge. The second possibility to ignite the lamp is to bring both electrodes into contact with each other. After switching on the amplifier the electrodes are slowly displaced until they have reached their final position. For the short distance after ignition the voltage of the amplifier is sufficient to feed the discharge. In contrast to the model lamp the YAG lamps are ignited with an additional igniter as shown in figure 3.6. The igniter delivers short voltage pulses of approximately 2.5kV which are high enough for a breakthrough and thus the ignition of the lamp. After the lamp has reached a stationary operation the igniter is short-circuited so that V/I probes can be attached without damage Rf setup For an operation with frequencies higher than 20kHz a second electrical setup is applied which is shown in figure 3.7. The basis of this setup consists of a broadband amplifier from the type AR 500A100A from AMPLIFIER RESEARCH. The maximum power the amplifier can provide is 500W CW instantaneously within a frequency range from 10kHz to 100MHz. The frequency is controlled by a HP33120A signal generator. To operate the lamp properly it is necessary to use a matching circuit between lamp and amplifier. In comparison to active matchboxes as they are commonly used for low pressure plasma chambers the matchbox applied in this setup is a passive one. It can be adjusted to several impedance values from 25Ω to 250Ω. The chosen value should be equal to the resistance of the lamp. Because of the fixed values at the matchbox this state rarely occurs. Thus the power reflected towards the amplifier never becomes zero. Further on an adaption of the matchbox during operation is not possible. This implies as long as the frequency is varied during operation the reflected power increases because the resistance of the lamp changes. Often the reflected power is much higher than the forwarded power. This is tolerated as long as the sum of forwarded power ( 75W) and reflected power is below the max power of the amplifier. This low-cost solution is of course not technically perfect but sufficient for this application. A power meter of the type PZ4000 from YOKOGAWA, which continuously measures current and voltage, controls the input power of the lamp and keeps it constant over time. For ignition a second power circuit is realized. It consists of an igniter and a standard ballast. The ballast is an inductor which limits the current of the lamp. The igniter is short circuited after ignition and the ballast operates the lamp at a power of 70W and 50Hz. After the lamp is in steady state operation the vacuum relays are used to switch over to the amplifier. During the switch over phase the lamp shortly is operated with both sources at the same time. Thus it is necessary

53 30 3. Experimental setup amplifier AR 500A100A signal generator 110V, 70W, 10kHz-1MHz YAG/ model lamp supply voltage lamp voltage ingnition circuit operation circuit match box power analyzer Yokogawa PZ4000 motorrelais relais 15kV switch relais 15kV C B switch relais 15kV relais 15kV igniter max. 5kV ballast D button HF-shielded area 24V DC A switch switch E motorrelais switch box isolationtransformer 230 V 1-3 A 50Hz Figure 3.7: Block diagram of the rf operation setup to keep this time as short as possible to avoid an overload of the lamp. The separate ignition circuit is necessary since the amplifier cannot handle the high voltage pulses of the igniter during ignition. The vacuum relays are equipped with a disruptive discharge protection of 20kV. As long as the model lamp is operated with the high frequency setup the ignition circuit is blocked. The lamp electrodes have to be short circuited and the amplifier has to be used directly. The igniter is undersized for an ignition of the model lamp and the ballast cannot provide a sufficient current. The ignition procedure is described in Diagnostics This chapter describes the diagnostic methods which are used in this work. It also includes the interpretation methods of the gained data Photography A very important diagnostic method is the optical observation of the electrode and the near electrode region. The taken images provide a lot of information about the arc attachment on the electrode. For this purpose a camera SENSICAM FASTSHUTTER of the PCO company

54 3.3. Diagnostics 31 is used. A schematic drawing of the camera setup is shown in figure 3.8. The camera has a 3 filter shutter zoom-objectiv digital camera Figure 3.8: Schematic drawing of the imaging camera system with zoom lens and shutter resolution of 1280x1040 pixel. The pixel size of 6.7µm 6.7µm implies a chip size of 2/3. To gain a higher signal level the camera can be operated by using the so called binning. For the binning operation 2, 4, 8 or 16 pixel are summed up in one or both directions to a larger pixel. The binning operation only affects the image resolution not the image size. It is also possible to define a region of interest on the CCD sensor by the camera software. During the readout process this defined region is considered for a faster readout. The exposure time of the camera T exp can be adjusted between 100ns and 100ms in steps of 1ns. For a reduction of the noise level of the CCD the chip is actively cooled by a Peltier element down to a temperature of 13 C. A zoom lens NAVITAR ZOOM 6000 images the electrode on the CCD chip. The zoom lens consists of the 6.5x vario-zoom lens NAVITAR coupled with a 2x adapter tube NAV- ITAR and a C-mount adapter NAVITAR The lens system supplies a variable magnification M from M = 1.4x to M = 9x. The focus length is nearly constant 92mm and the depth of focus varies between 1.8mm and 0.2mm depending on the magnification. The quantum yield of the CCD sensor is given in appendix A. In case of short exposure times the images are often affected by the so called smear effect [23]. The smear effect occurs if the imaged object emits light after the end of the exposure time. During the read out process of the camera an additional exposure of the CCD takes place. Charge carriers are accumulated on the CCD which often results in smeared images. This effect is reduces by a electro mechanical shutter which is mounted in front of the zoom lens. The shutter (here UNIBLITZ VS14) closes at least 3ms after the exposure time of the camera has ended. Thus a further exposure of the chip is cut off. Because of the very high light intensities of the investigated lamps it is often necessary to use filters in front of the camera. These filters are mainly neutral density filters from NEW- PORT to block light uniformly over the whole wavelength range. In some cases narrow-band interference filters are used to gain 2D information on the line emission of certain species. This information can be correlated with spectroscopic measurements Spectroscopy The spectroscopy is a very powerful investigation method within this work. The spectroscopic setup is shown in figure 3.9. The system can be segmented into three parts, the optical imaging system, the camera and the spectrograph.

55 32 3. Experimental setup r CCD-Camera CCD-Camera 2. Spectrograph Entrance-Slit Dove-Prism Grating Filter Mirror tower with beam splitter Model lamp YAG lamp Zoom Objective Shutter Filter 3 Spectrograph Figure 3.9: Schematic drawing of the spectroscopy system Optical imaging system The optical system images the relevant area being investigated onto the entrance slit of the spectrograph. A first achromatic lens is positioned in a distance of the focus length in front of the object. The lens transforms the punctual emission of the object into parallel light. It is first led through a DOVE prism with the dimension of 30 30mm. The DOVE prism gives the opportunity to rotate the image around its middle axis without optical disturbances. The lamps are operated vertically and the entrance slit of the spectrograph is orientated in the same direction. If spectra with a radial resolution have to be recorded the image has to be rotated by 90. Also deviations from a vertical orientation of the electrodes can be corrected if spectra along the electrodes are recorded. Behind the DOVE prism a beam splitter splits the light into two identical parts. Fifty percent of the light transmits the beam splitter onto a second achromatic lens. This lens focusses the image onto the entrance slit of the spectrograph. The other part of the light is transferred to a mirror which is adjusted above the beam splitter. This part of the light can be analyzed by a second spectrograph. The advantage of achromatic lenses is their correction of the chromatic abberation. This wavelength depending error makes the usage of normal spherical lenses impossible. Both used achromatic lenses have the same focussing length f = 310mm. It implies a magnification M of the image onto the entrance slit with M = 1. The diameter of the achromatic lenses is 80mm. Within a wavelength region from 400nm 800nm their transmission factor is 97%. Beyond this range the transmission strongly decreases. Two apertures are inserted into the optical path. One is mounted directly in front of the first achromatic lens. Its main task is to limit the aperture angle. For a small aperture angle less light is transmitted onto the entrance slit. It may lead to a worse signal to noise ratio of the camera. On the other hand if the aperture angle is to wide, the effect of vignetting may occur. A detailed description of this effect can be found in [2].

56 3.3. Diagnostics 33 The spectrograph The spectrograph used in this work is an imaging spectrograph from CHROMEX of type 250is. Its optics is given by a CZERNY-TURNER configuration. The used mirrors are specially shaped toroidal mirrors which focus and collimate the incident light. Their special form helps to minimize optical errors. Thus the spectrograph gains a spatial high resolution along the entrance slit. The aperture ratio of the spectrograph is set to f/4.0. Furthermore the spectrograph is equipped with three different gratings. The gratings exhibit line densities of 150, 600 and 1200 lines per millimeter. They are mounted on a turnable rack which can be adjusted by stepping motors. The entrance slit of the spectrograph is also motorized and can be set to opening width between 10µm and 2mm. Due to the arrangement of the mirrors and the grating, the spectrographs magnification from the focus plane on the entrance slit to the focal plane on the CCD chip is M = Combined with the magnification of the optical path the total magnification M tot of the optical setup is M tot = The focal length of the spectrograph is 250mm. The spectral resolution is at least 0.15nm (FHWM) for the grating with the highest line density. The CCD camera For the detection of the output signal of the spectrograph a CCD camera SENSICAM QE from PCO is used. It is mounted with a adapter 90 rotated at the spectrograph. Thus the resolution of the camera along the entrance slit is 1376 pixel and along the wavelength axis it is 1280 pixel. The pixel have a dimension of 6.45µm 6.45µm. Taking the total magnification of the setup into account the maximum length which can be detected along the entrance slit is 6.78mm. The camera possesses the possibility of using an internal binning as it is described in The CCD chip is actively cooled by a Peltier element to -14C to reduce the noise level. The dynamic range of the camera is 14 bit. This implies a maximum count rate of 4096 counts per pixel. The linearity of the ratio between incident light and output signal of the camera is very high. The exposure time of the camera t exp can be varied between 500ns and 3600s. Its very good triggering features due to its very fast internal operation makes the camera a first choice for high speed photography. The CCD chip of the camera is sensitive in a wavelength region from 280nm to 1100nm. In appendix A the spectral quantum efficiency over wavelength of the camera is shown. It describes the amount of generated electrons per 100 incident photons in dependence on wavelength. Both spectrograph and camera are mounted on a motorized cross-table. This allows an easy positioning of the entrance slit. Calibration The whole setup described above has to be calibrated in absolute values of radiance to obtain absolute population densities from spectroscopic measurements. For calibration a tungsten ribbon lamp (Wi17g3 from OSRAM) is used as a standard. The tungsten ribbon lamp is

57 34 3. Experimental setup positioned at the same place as the lamp under investigation. Thus the identical optical setup can be used for the calibration. For a fixed current of I T RL = A the spectral surface radiation densities of the tungsten ribbon lamp L T RL are known for all wavelengths. The tungsten ribbon lamp has to be imaged at several positions along the entrance slit since only an area of 1mm of the tungsten ribbon is usable for the calibration. Therefore approximately five images are necessary for a complete calibration spectrum Cts T RL for the special choice of a middle wavelength. The calibration spectra Cts T RL are used to convert intensities which are recorded in counts Cts meas into W m 2 sr 1 according to L meas = Cts meas Cts T RL L T RL. (3.1) Triggering and phase resolved measurements The operation of HID lamps with ac operation currents requires a common well defined starting time for all measurements which is kept constant. This is important since some measuring methods integrate a signal over a certain time and afterwards transmit it to a computer or other storage. One example for such an integrating method is picture recording. The camera records a pictures with a certain exposure time. Afterwards the picture is stored which takes the readout time. Under ac operation the frequency determines the time which is available for time resolved imaging. For time resolved photos at least 10 pictures per period are necessary. For example at a frequency of 50 Hz only 2ms per picture are available. By adding the read out time, which is in the same order of magnitude, 50 Hz is not ideally recorded time resolved. The best possibility to solve this problem is the phase resolved picture recording. For phase resolved recording the starting point of the exposure is shifted stepwise over the period. After one exposure the image is transferred to the computer. Now the next image is taken with a new starting point shifted within the period compared to the starting point before. Thus between two images several ac periods will elapse. The images are recorded phase resolved and not time resolved. The requirements for this procedure arise from this example. It is necessary to have a fixed reference signal, reoccurring periodically. A good choice in our case is the zero crossing of a voltage or current signal in ac operation. The second need is the time delay after this starting point which has to be adjusted accurately and other trigger impulses should not occur between two measurements. Trigger generation In this work the triggering method developed by Langenscheidt [24] is used. The reference time is generated on the output side of the amplifier. Normally it is easier to use the sync signal of the frequency generator on the primary side. But in this case the delay time caused by the amplifier is too long. Moreover it varies in dependence of the operation parameters. An extra circuit for a compensation of this time would be needed. Thus the trigger signal is deduced from the voltage zero crossing (VZC) of the lamp. This is mandatory since the current does not rise fast enough after zero crossing to generate an exact trigger impulse. The uncertainty of this trigger impulse can be denoted with a maximum of 2µs. In this work only the rising edge of the voltage signal is used for the generation of a trigger pulse.

58 3.3. Diagnostics 35 Trigger delay In order to shift the trigger signal starting from zero crossing a delay generator is used (STANFORD RESEARCH SYSTEMS DG 535). It owns the feature to delay a signal between 5ps and a few minutes with an absolute accuracy of 1.5ns. The block diagram 3.10 shows the timing sequence for the triggering of a camera. The voltagemonitor ( u b ) comparatorcircuit poweramplifier delayed trigger (DTR2) shutter zero crossing (ZR) & Trigger ( TR) delaygenerator delayed trigger (DTR1) digitalcamera camera ready? ( BUSY) t delay PC t exp image Figure 3.10: Block diagram of the trigger setup corresponding timing diagram is shown in figure The comparator circuit generates for every rising edge of the voltage signal a short pulse (NDG) which is only forwarded to the delay generator (TR) if the camera is ready for taking an image (BUSY ). If the delay generator is ready (DB) he accepts the trigger. In that case the delay generator produces a signal VTR1 for the camera control which is delayed by t delay. The camera starts the exposure according to the falling edge of this signal. Additionally the delay generator controls the electro mechanical shutter with the signal VTR2. The shutter control is started 6ms before the exposure starts. The shutter needs 3ms until it is open 80% and it is closed as fast as possible after the exposure is finished. This procedure is installed for the minimization of the SMEAR effect [23]. The delay time t delay consists of n complete phases τ and the time-shift within the phase t ppos. n is chosen to ensure the system to be causal if t ppos = 0 according to t delay = n τ > 6ms n N. (3.2) The time t cam, the camera is busy, consists of the exposure time of the camera t exp, which is typically between 10µs and 10ms and the transfer time t trans needed for the picture to be transferred from the camera to the computer. For a picture with full resolution this time is approximately 130ms. The trigger signal VTR1 for the camera is elongated by the regeneration time t regen of the electromechanical shutter. The maximum frequency the shutter can handel is 40 Hz. But at this frequency the lifetime of the shutter is significantly reduced. Thus the repetition rate is set to 0.5 Hz. The delay generator enables its input for a new trigger only if T regen = 2s is considered. The delay times are programmed by a GPIB bus which connects the delay generator with a PC. The PC also controls the exposure time of the camera.

59 36 3. Experimental setup u arc i arc a.u. t ppos phase position under investigation CZC BUSY t cam TR DB t delay t regen VTR1 exposure 6ms VTR2 ready for trigger 3ms shutter open ready for next trigger t Figure 3.11: Timing diagram for the trigger delay Electrode temperature measurements and power calculation The electrode temperature is a very important parameter of an HID lamp. It mainly determines the lifetime of a lamp and influences the efficiency of the lamp system. The electrodes strongly interact with the plasma. One process is the thermionic electron emission to sustain the arc current and a second process is that particles diffuse towards the electrodes and may form thin sheaths on the electrode surface. All these processes are depending on the electrode temperature. This makes their surface temperature distribution very important. Furthermore the power loss of the electrodes can be determined by an analysis of their temperature distribution. In former works of Redwitz [2] and Dabringhausen [8] the method of pyrometry is used for the measurement of the electrode temperature. The pyrometry is a contactless optical method allowing the measurement of high temperatures. They are equipped with a sensor adjusted to a certain wavelength interval, mainly in the near infrared region within a few hundred nanometer. With a special optics a small measuring spot is imaged onto the sensor of the pyrometer. The detected radiance is converted into real temperatures by PLANCK s law. The pyrometer being used is designed to measure temperatures from 1073K to 3773K.

60 3.3. Diagnostics 37 The measuring spot diameter is 300µm and the sensor is sensitive within the wavelength region from 700nm to 1100nm. The time needed by the pyrometer for one measurement is at least 1ms. These features show the disadvantages of the pyrometer used here. The spot size of the pyrometer is very large compared to the diameter of the electrodes. Especially the electrodes of the YAG lamps with a diameter of d E = 0.36mm - 0.5mm are nearly in the same dimension as the measuring spot. This may result in uncertainties if the arc attachment does not attach uniformly at the electrode tip. In case of an asymmetric temperature distribution the pyrometer measures integral values over the spot size. In general an exact determination of the electrode tip temperature by pyrometry is very doubtful. Because of the circular shape of the spot, the last trustable temperature value can only be obtained half of the measuring spot diameter (150µm) behind the real electrode tip. For measurements along the electrode z-axis, the electrodes of the model lamp are moved in steps along the pyrometer. At each position one measurement is performed. A complete determination of a temperature curve requires at least 20s. In the case of ac operation this time is too long for phase resolved measurements. The electrode temperature varies strongly over one ac period depending on frequency. First measurements have shown that these variations only occur within a small region at the electrode tip. To detect these variations precisely a high spatial resolution is necessary. The spatial resolution of the pyrometer is determined by the size of the measuring spot to 300µm. This accuracy is too low for phase and spatially resolved temperature measurements in the case of ac operation. A last drawback is the sensitivity of the pyrometer sensor within an extended wavelength interval. Especially the YAG lamps emit intense plasma radiation within the visible and infrared spectral region. Thus the pyrometer may not only detect the radiation of the electrode. Especially in the very significant region of the electrode tip the temperature measurements may be distorted. Spectroscopic electrode temperature measurements In order to avoid some of these problems with standard pyrometers a spectroscopic system can be used for electrode temperature measurements. A spectroscopic method has been developed by REINELT [25]. For this temperature measurement the spectroscopic setup described in chapter is used. Figure 3.12 illustrates the image of an electrode on the entrance slit of the spectrograph. The electrode is oriented parallel to the slit to detect a radiation profile along the electrode z-axis. It is favorable to measure the radiance at a wavelength in the infrared spectral region for temperature measurements at a solid surface. Thus a segment of the spectrum emitted by the electrode is used which is as far as possible in the infrared region, but still within the sensitivity range of the CCD camera. A second condition is that line radiation of the plasma is absent within the recorded spectral interval which may influence the measurement. A suitable wavelength for these measurements is found at λ = 718nm. The spectrum of the model lamp as well as the spectra of the YAG lamps show only very weak plasma radiation within this wavelength region. For the measurements the grating with 1200lines/mm of the spectrograph is chosen and the entrance slit width is set to 100µm. For measurements at higher frequencies with short exposure times a grating can be used with only 600lines/mm. To ensure that radiation

61 38 3. Experimental setup spatial axis projection of electrode and plasma entrance slit Spektrograph Figure 3.12: Image of the electrode parallel to the entrance slit of the spectrograph which is caused by the 2. order of lines excited at low wavelength does not influence the measurement, an edge filter at λ edge = 600nm is used. This filter suppresses all radiation at wavelengths below 600nm. Figure 3.13 shows a complete 2D spectrum at the chosen center wavelength of 718nm. The wavelength is presented by the horizontal axis and the spatial resolution by the vertical axis. The part of the spectrum above the electrode tip indicated in the figure represents the continuum radiation of the electrode and the lower part the continuum and line radiation of the plasma. A course of the radiance along the electrode z-axis is cut out at the center wavelength (718nm). This course of the spectral radiance I λ,718 shows the typical exponential behaviour of the heat radiation of the electrode solid surface. The maximum value of the radiance marks the position of the electrode tip. The further course shows the radiance of the plasma. This method allows to measure the temperature along the electrode by one measurement. The spatial resolution is determined by the pixel size of the CCD camera and the binning being used. With a typically binning of 2 the spatial resolution is 12.9µm. This is sufficient for the requirements of this work. The method does not require a displacement of the electrodes any more. The new method is also usable for ac measurements due to the accurate triggering of the CCD camera. A spatial profile of the spectral radiance of the electrode is recorded by a single measurement. The data have to be transferred into absolute temperature values. To calculate absolute temperature values PLANCK s radiation law is applied. The spectral radiance I BB of an ideal black body radiator can be written as I BB (λ, T ) = 2hc2 0 λ 5 ( ( ) 1 hc0 exp 1). (3.3) λk B T I BB is depending on the temperature T of the emitting surface and the wavelength λ. c 0 is the speed of light. An ideal black body radiator does not occur in reality. Real radiators always have a reduced spectral emissivity ε. For an ideal black body radiator ε = 1. In case of ε < 1 the radiator is called grey body radiator. Tungsten is a grey body radiator with an emissivity which is

62 3.3. Diagnostics 39 center wavelength z axis [z] calibration electrode electrode tip -2-1 wavelength [nm] intensity [Wm sr ] Figure 3.13: Spectrum recorded at the model lamp for the electrode temperature determination depending on temperature and wavelength ε = ε(λ, T ). Thus the surface radiance is I(λ, T ) = ε(λ, T )I BB (λ, T ) with 0 ε(λ, T ) < 1. (3.4) Rearranging equation 3.4 for the calculation of T results in T = c ( ( ) ) 2 c1 ε(λ, T ) ln + 1. (3.5) λ I(λ, T )λ 5 π c 1 and c 2 are the PLANCK constants. If now the values for the emissivity ε(λ, T ) are known the temperature can be calculated. For tungsten, values of the emissivity are published in literature. Comprehensive investigations in the work of Nandelstädt [5] and Dabringhausen [8] showed that the values from DEVOS [26] are the most trustable ones. There are also values from LATYEV [27] but these values for the emissivity are not accurate for temperatures above 3000K. Figure 3.14 shows the emissivity ε of tungsten depending on wavelength and temperature. Since the temperature measurements are performed at one fixed wavelength of 718nm the dependency of the emissivity on wavelength has not to be considered. The resulting data for the emissivity ε(t ) is shown in figure For the temperature calculation the values for the emissivity are determined iteratively. At first values for the emissivity are estimated by fictive temperatures. Within further steps the emissivity is calculated exactly. Two or three iterative steps are necessary for an accurate calculation. At the end of this calculation a course of the temperature along the electrode is obtained which is corrected by the emissivity of tungsten. The resulting temperature curves often show some typical characteristics. At the electrode tip a steep increase of the temperature occurs. Figure 3.16 shows such an increase. The scaling indicates that the affected area is very small. A reason for this increase may be a change of the emissivity of tungsten. The surface structure of the electrode, precisely the roughness may have changed due to an attachment of the arc plasma around the electrode tip. Also the plasma itself may influence the measurement by its continuum radiation. In the work of

63 40 3. Experimental setup by de Vos ² T T = 3695K 3600K 3400K 3200K 3000K 2800K 2600K 2400K 2200K 2000K 1800K 1600K 1400K 1200K 1000K 800K 600K / ¹ m Figure 3.14: Values for the emissivity of tungsten from DeVos nm Emissivity = ² Temperature =K Figure 3.15: Emissivity of tungsten depending on temperature at the measuring wavelength of 718 nm Nandelstädt and Dabringhausen this part of the temperature curve was considered as non trustable. They calculated the tip temperature by a simulation. This is subject of the next chapter.

64 3.3. Diagnostics Temperature / K superelevated electrode temperature z - axis / mm Figure 3.16: Temperature curve with artificially increased temperature at the electrode tip Electrode power loss calculation In the work of Nandelstädt and Dabringhausen [5, 8] a method was developed to simulate the temperature curve along the whole electrode. This is necessary since the temperature values at the electrode tip are not trustable as described above. Additionally the used pyrometer can only measure temperatures down to 1073K. But the electrodes in the model lamp gain temperatures at the soldering point lower than 1073K caused by the cooling inside the electrode holders. Thus only a part of the electrode temperature curve could be measured. To solve this problem the authors used a stationary heat equation because the measurements were mainly performed under dc operation. Additionally they assumed a rotational symmetry of the electrode temperature and neglected the r dependence of T along the electrode rod. Thus the heat balance of a cylindrical electrode becomes ( πre 2 d κ(t sim ) dt ) sim = 2πr E q rad (T sim ) (3.6) dz dz with q rad (T ) = σ SB ɛ tot (T ) ( T 4 T 4 amb). (3.7) This is a nonlinear partial differential equation of 2. order. It can be solved numerically by using two boundary conditions. The boundary conditions are the temperature values at the electrode tip T tip and bottom T bot. This simulated temperature curve is now fitted to the measured temperature curve by a least square algorithm according to N V S T = (T mess,i T sim (z i )) 2 min. (3.8) i=1

65 42 3. Experimental setup By the fitting procedure the constants of integration T tip and T bot are determined. An example for the result of such a simulation is shown in figure Values for the radiated power P rad and the conducted power to the electrode holder P cond 2600 T-Simulation T-Measured T [K] Position z [mm] Figure 3.17: Example for a simulation of the electrode temperature of the whole electrode length can be calculated using the simulated temperature values according to and P rad = A q rad n d A = πr 2 Eσ SB ɛ tot (T tip ) ( T 4 tip T 4 amb) + (3.9) le 2πr E σ SB ɛ tot (T ) ( T 4 Tamb) 4 dz P cond = πr 2 Eκ(T bot ) dt dz 0. (3.10) z=0 For the calculation of the radiated power a constant temperature is assumed for the end face of the electrode. The sum of these both terms is the total power loss of an electrode under dc operation P loss = P rad + P cond. (3.11) Compared to dc operation, the electrode temperature varies continuously over one period under ac operation. In this case the assumption of a stationary heat equation is no longer valid. Now the heat capacity of the electrodes must be taken into account. Thus the heat balance which is used for a cylindrically electrode is r 2 Eπ z ( κ(t ) T z ) = 2πr E ɛ tot σ SB T 4 + r 2 Eπρ M c p (T )ω T ϕ. (3.12) as it is derived in chapter Solving this equation for T numerically by a MATLAB solver is rather expensive. A much simpler way to solve this equation is described now.

66 3.3. Diagnostics 43 Time dependent power loss calculation For the time dependent power loss calculation a thin disk of the electrode of the thickness dz is considered at a certain phase angle ϕ. Figure 3.18 shows the coordinate system for the electrode geometry. According to the assumptions for the stationary case a rotational symmetry is assumed for the electrode. At the position z = 0 the temperature is T = T tip. dz z = 0 T Tip z T(z) electrode Figure 3.18: Definition of the coordinate system for the time dependent power loss calculation Since ϕ is fixed during the measurement = d is valid. Thus equation 3.12 becomes z dz reπ 2 d ( κ(t ) dt ) = 2πr E ɛ tot σ SB T 4 + r 2 dz dz Eπρ M c p (T )ω T ϕ. (3.13) Multiplying eq first with dz and afterwards with κ dt dz 1 2 r2 Eπd ( κ(t ) dt dz results in ) 2 = 2πr E ɛ totσ SBT 4 κ(t )dt + reπωρ 2 M c p (T )κ(t ) T dt. (3.14) ϕ Now this equation can be integrated from T to T tip according to 1 Ttip ( 2 r2 Eπ d κ(t ) dt ) 2 Ttip = 2πr E ɛ tot σ SB T 4 κ(t )dt + (3.15) dz T T r 2 Eπω T Ttip T ρ M c p (T )κ(t ) T ϕ dt. The integration of the left hand term can be accomplished and results in 1 Ttip ( 2 r2 Eπ d κ(t ) dt ) [ 2 ( = 1 dz 2 r2 Eπ κ(t ) dt ) 2 ( κ(t ) dt dz dz T tip ) 2 T ]. (3.16) Now equation 3.15 can be rearranged for dz. It must be considered that according to figure 3.18 dt < 0. The decreasing electrode temperature with simultaneously increasing values for dz z results in the minus sign of the right hand term. κ(t )dt dz = [ (κ(t ) ) dt 2 4 Ttip dz T tip r E ɛ T tot σ SB T 4 κ(t )dt 2ω ] 1 T tip ρ T M c p (T )κ(t ) T dt 2 ϕ (3.17)

67 44 3. Experimental setup The first term on the right hand side under the fraction bar describes the absolute power which is coupled into the electrode by the surface of the electrode tip. This power is named P e,in. It is defined as ( P e,in = reπ 2 κ(t ) dt ). (3.18) dz T tip Now equation 3.17 can be integrated to gain a result for z sim. z sim = Ttip T (z) κ(t )dt [ (κ(t ) ) dt 2 4 Ttip dz T tip r E ɛ T tot σ SB T 4 κ(t )dt 2ω ] 1 T tip ρ T M c p (T )κ(t ) T dt 2 ϕ (3.19) The integral becomes positive by transposing the integration limits. The result is a position z sim according to a temperature value T (z meas ) and a value for the tip temperature T tip. To solve equation 3.19, measured electrode temperature values are necessary. They are obtained by the method described in chapter Since these measurements are performed phase resolved, a value for T can be deduced. Thus the values ϕ for σ SB, ɛ tot, κ, ρ M and c p can be calculated. The unknown parameters in equation 3.19 are P e,in and T tip. To solve the equation a value for P e,in is assumed in a first step and for T tip the measured tip temperature is chosen. The equation is solved and the resulting values for z sim are compared with the measured values for z meas. By a variation of P e,in and T tip and a least square fit this calculation is repeated iteratively until the deviation between the course of z sim and z meas is minimized. The outcome of this computation is a temperature curve z sim (T ) which is fitted to the measured temperature curve as it is shown in figure From this curve the value for the tip temperature T tip can be gained. A second result is a value for P e,in Temperature = K T meas T sim x 10-3 Position on electrode z = m Figure 3.19: Example for the simulation result of the electrode temperature curve. Parameter: Model lamp, d E = 1mm, l E = 20mm, p = 0.26MPa, i = 3A switched-dc

68 3.3. Diagnostics Plasma spectroscopy In this work spectroscopy is not only used for electrode temperature measurements. It is also applied for the determination of the electron density and temperature in the model lamp and for the determination of particle densities in the YAG lamps. Most of the methods are based on absolute measurements of the spectral emission coefficient (see equation 2.17). Data processing For most of the recorded spectra the electrode is orientated perpendicular to the entrance slit of the spectrograph as it is illustrated in figure A Dove prism is inserted into the setup spatial axis projection of electrode and plasma entrance slit Spektrograph Figure 3.20: Image of the electrode and plasma perpendicular to the entrance slit of the spectrograph which is shown in figure 3.9 to rotate the image. Now it is possible to record radially resolved spectra of the plasma. The position of the entrance slit of the spectrograph can be changed along the z-axis of the plasma column by using a motorized cross table. A typically spectrum being measured is shown in figure 3.21 a). This is an example of an argon spectrum measured at the model lamp. The horizontal axis displays the wavelength axis and the vertical axis the spatial resolution in the radial direction. Figure 3.21 b) represents a horizontal cut through the spectrum which visualizes the emission lines of argon and the continuous background. The intensities recorded by the CCD are the result of a so called side-on measurement. By the integration of the emission along the line of sight information about the radial resolution gets lost. This is a general disadvantage of the passive emission spectroscopy. As long as the plasma can be treated as optically thin (see chapter 2.1.4) the spectral intensity I λ (λ, x i ) represented by the signal of one pixel is correlated to the local emission coefficient ε λ I λ (λ, y i ) = xi,2 x i,1 ε λ (λ, y i )dx, [I λ ] = W m 2 sr nm, [ε λ] = W m 3 sr nm (3.20)

69 46 3. Experimental setup Radial position = mm middle axis at r= Wavelength = nm (a) Full spectrum at λ = 750nm Spectral radiance = a:u: Wavelength = nm (b) Spectral radiance at λ = 750nm Figure 3.21: Spectrum and evaluated spectral radiance for an argon spectrum at λ = 750nm. a) Full 2D spectrum recorded with the CCD camera. b) Cut through the spectrum at r=0. The emission coefficient is integrated along the line of sight s(x i,1, x i,2 ) for every position y i according to figure The emission coefficient includes continuum radiation as well as line radiation. The line radiation can be separated from the continuum radiation by a substraction of the background continuum. In case of a cylindrical symmetry of the plasma the radial distribution of the emission coefficient can be gained by an inverse Abel transformation. Inverse Abel transformation The general problem of an Abel inversion is shown in figure The distribution of the rotational symmetric term f(r) is in demand. In many cases this term cannot directly be deduced from a measurement. But integrals along certain pathes of the term f(r) being searched can be measured. If these pathes run linearly and parallel through an object a parallel projection is obtained. This projection is called h(y) in figure Within certain circumstances the term f can be reconstructed from this parallel projection being obtained by measurements. If the distribution of the term f(r) is limited to an area with the radius R and f(r) = 0 for r > R, the parallel projection h(y) of the rotational symmetric distribution is given by line integrals along straight lines parallel to the x-axes in different distances y from the center. h(y) = + R 2 y 2 f R 2 y 2 ( x2 + y 2 ) dx y : 0 y R. (3.21) With the help of an appropriate substitution the Abel transformation can be written as R h(y) = 2 y r f(r) dr. (3.22) r2 y2

70 3.3. Diagnostics 47 y y R fx ( ) x hy ( ) s Figure 3.22: Inverse Abel transformation. The distribution of the rotational symmetric value f(r) should be reconstructed out of the measured parallel projection h(y). This integral equation has the unique inverse f(r) = 1 π R r dh(y) dy 1 dy. (3.23) y2 r2 The integrand shows a singularity at y = r. Furthermore the measured projection h is superimposed by noise at a certain amount of nodes. This noise can cause significant errors within the numerical differentiation of equation For this reason several methods are developed to solve this problem. In the work of PRETZLER [28] these methods are described and weighed up against each other. The Abel inversion is executed by the Fourier method within this work with regard to accurate results for further steps. For the Fourier method a series expansion for the unknown distribution f(r) is performed N g f(r) = a n f n (r), (3.24) n=1 with the expansion functions ( f n (r) = 1 ( 1) n cos nπ r ). (3.25) R This series is similar to a Fourier series. This series expansion inserted in equation 3.22 results in N g R r H(y) = 2 a n f n (r) dr. (3.26) y r2 y2 The integrals n=1 R h n (y) = 2 r r f n (r) dr (3.27) r2 y2 can not be determined analytically and have to be calculated numerically in advance. The coefficients a n are fitted by a least-square-estimator to the data h meas (y k ) measured at N

71 48 3. Experimental setup positions. N (H(y k ) h meas (y k )) 2 min (3.28) k=1 The partial derivative of this condition for the searched coefficient a n delivers a system of equations whereby its m.th row (1 m N g ) is given by N g a n n=1 N k=1 h m (y k )h n (y k ) = N h m (y k )h meas (y k ). (3.29) h i (y k ) with i {m, n} are the previously computed integrals and h meas (y k ) represent the measured data. The solution of this system of equations results in the coefficients a n which determine the searched rotational symmetric distribution f(r) combined with the expansion functions according to equation 3.25 and The Fourier method exhibits the advantage that the measured data are implicitly low pass filtered. They are used for the reconstruction of the radial symmetry. Thus this method is suitable for measured data with a high noise level. A very important assumption for a good reconstruction of the radial distribution is a symmetry of the spatial distribution measured with the spectrograph and an exact determination of the symmetry axis. Symmetry is often a critical parameter in the measurements if they are performed very close to the electrode tip or if a strongly constricted arc attachment is present. This is especially the case for measurements at YAG lamps. Under the given conditions, the maximum of the line profile is not necessarily the symmetry axis of the line. Thus an appropriate determination of the symmetry axis is very important. By equation 3.30, which is taken from [28], a weighting of the curve of measured values h(y) for the determination of the symmetry axis is performed. y (y h(y)) y sym = y h(y) (3.30) k= Spectroscopic measurements inside the model lamp In order to determine the electron temperature T e, spectroscopy based on the Boltzmann plot is applied. For the calculation of the electron density n e, continuum radiation is used. Electron temperature determination The population density of an upper state n n is calculated from the measured emission coefficient of an optical transition between a state n (upper state) and m (lower state). Equation 2.17 yields n n = 4πλ nm ε nm A 1 hc nm. (3.31) If additionally the density for another excited state n is determined the Boltzmann relation reflects for a LTE plasma the density ratio between these two states according to n n = g ( n exp E ) n E n (3.32) n n g n k B T e

72 3.3. Diagnostics 49 In a BOLTZMANN plot reduced population densities are plotted logarithmically versus the energy of the corresponding upper state. The reduced population density is the quotient of population density and statistical weight. An example for a BOLTZMANN plot is shown in figure The reduced population densities are called η n. In literature the distribution function of population densities η n = f(e n ) is often called ASDF (atomic state distribution function). The logarithm of equation 3.32 yields ln n ~1/(kBT e) E = ev n Figure 3.23: Example for a Boltzmann plot ln η n = ln ( nn g n ) = const. E n k B T e. (3.33) Additionally the BOLTZMANN plot provides information whether the excited states of an atom are populated according to the BOLTZMANN relation or not. If the distribution of reduced densities can be connected by a straight line the densities follow the BOLTZMANN relation. In that case the slope of the straight line 1/(k B T e ) gives the population temperature of the states which then matches with the electron temperature T e. If the density values are not located on a straight line this indicates that an uniform population of the states does not exist. In this case the plasma is not in a local thermal equilibrium (LTE). The BOLTZMANN plot being presented is based on the measurement of absolute line intensities and the (reduced) population densities of excited states respectively. To get absolute values of the population densities a calibration is necessary (see chapter 3.3.2). Furthermore the atomic data of the spectral lines need to be known. Especially the transition probabilities A nm and the statistical weights g n are very important. For many nobel gases these data are published. A very comprehensive source is the database of the NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY [29] or the KURUCZ database [30]. Especially for the nobel gas argon many atomic data are published, for instance collision cross sections, ionization cross sections and transition probabilities. Thus argon became a standard gas for scientific investigations. In table 3.3 the data for the argon lines are summarized which are recorded for the electron temperature measurements.

73 50 3. Experimental setup λ nm [nm] E n [ev] g n A nm [10 8 s 1 ] Table 3.3: Argon lines and its data used for diagnostics Electron density determination The electron density n e can be calculated from the continuum radiation of the plasma. As mentioned in chapter the continuum radiation consists of several parts which are represented by their emission coefficients. For argon the spectral emission coefficient is measured at λ = 455nm. Figure 3.24 shows the spectrum recorded at a center wavelength of 455nm. The distribution of the spectral radiance of the argon continuum I λ (455nm) is measured at the marked position for the further calculations. The measurement is performed in a distance of 62.5µm in front of the cathode tip. The emission coefficient is obtained from the measured spectrum of the spectral radiance. The continuum radiation is dominated in the range of the chosen wavelength by the freebound transitions. WILBERS et al. have shown that in argon at a pressure of 0.4MP a and an electron temperature of 13500K [31] the fb-continuum (recombination of an electron with a single charged argon ion) have a rate of 95% in the total continuum. The contribution of the free-free continuum from the interaction of a free electron with single charged ions is about 4%. Since the maximum applied pressure in this work is only 0.26MP a, the part of the fb-continuum is even higher. All other mechanisms make only a contribution of less than 1% to the total continuum radiation at the chosen wavelength and will therefore be neglected. Thus the spectral emission coefficient of the continuum results in ε λ,cont (λ, T e, n e ) = ε λ,fb (λ, T e, n e ) + ε single λ,ff (λ, T e, n e ), (3.34) with ( ( )) n ε λ,fb (λ, T e, n e ) = C 2 e 1 λ 2 g i0 T e Z i ξ fb (λ, T e ) 1 exp hc λk B T e (3.35) ( ) ε single λ,ff (λ, T n e, n e ) = C en i 1 λ 2 T e ξ ff (λ, T e ) exp hc λk B T e. (3.36)

74 3.3. Diagnostics 51 Radial position = mm =445nm Wavelength = nm Figure 3.24: Spectrum of the argon continuum at a center wavelength of 455nm inside the model lamp. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i RMS = 3A, Gas argon, pressure p = 0.26 MPa The constant C 1 is W m 4 Ksr 1. Furthermore ξ fb and ξ ff are the so called BIBERMAN factors. They can be summed up to a single ξ factor according to ( ( ξ(λ, T e ) = ξ fb (λ, T e ) 1 exp hc )) λk B T e ( + ξ ff (λ, T e ) exp hc λk B T e ). (3.37) Taking the abbreviation into account the spectral emission coefficient of the continuum is ε λ,cont (λ, T e, n e ) = ( ) 8n2 e e 2 3 2π ξ(λ, T 3c 2 λ 2 4πε 0 3m 3 e ). (3.38) ek B T e If the emission coefficient is measured in absolute units and if the electron temperature is known, the electron density can be calculated according to n 2 e = λ 2 T e ξ(λ, T e ) 1 ε λ,cont W 1 m 4 K 1/2 sr. (3.39) This method is very advantageously since the influence of the electron temperature (T 1/4 e ) on the electron density is weak. Thus errors due to an uncertain electron temperature are minimized. Of course the BIBERMAN factor is depending on the electron temperature. For argon several scientists calculated [32] or measured [33] the ξ factor. All authors showed that at the chosen wavelength the influence of the electron temperature is low. Thus it is estimated to be independent of the electron temperature. The value for the BIBERMAN factor was calculated for argon at λ = 455nm to: ξ ar = Figure 3.25 shows a density distribution which is calculated from the emission coefficient obtained from the spectrum shown in figure 3.24 and the corresponding electron temperature determined by a BOLTZMANN plot.

75 52 3. Experimental setup 2.5 x n = m e Radial position = mm Figure 3.25: Example for an electron density profile Spectroscopic investigations at the YAG lamps For YAG lamps spectroscopy is applied to observe and characterize the different additives and their influence on the discharge and the electrodes. For these investigations the emission spectroscopy is preferred. To determine absolute particle density of a filling component by emission spectroscopy it is necessary to know the mean kinetic energy of each species. This mean kinetic energy is equivalent to the temperature of the species. As the pressure inside the YAG lamps is very high the assumption of a local thermal equilibrium (LTE) is mostly justified. The collision rate inside the plasma is high enough to adjust a uniform gas temperature for all species and an electron temperature which does not deviate substantially from the gas temperature. E.g. the dysprosium density is determined by several steps. At first an excitation temperature of Hg is determined by a spectroscopic measurement at a mercury emission line. In a second step this excitation temperature is set equal to a global gas temperature for all species. In a last step the dysprosium density is calculated from a measured Dy emission line. Determination of the plasma temperature A method developed by SCHOEPP [34] is applied to the determination of the mercury temperature. The emission of the mercury lines at λ Hg,1 = nm and λ Hg,2 = nm are used. The mercury lines are optically thin under the applied operating conditions. Figure 3.26 a) shows a spectrum of both mercury lines. The lines are strongly broadened and their wings superimpose each other. They are analyzed together since a separate treatment of each line is impossible due to their overlap.

76 3.3. Diagnostics 53 In a first step the continuum radiation is determined and subtracted from the spectrum. Additionally the integration limit are set for the two spectral lines. If the spectrum is disturbed by line radiation from other species this radiation is subtracted from the mercury line radiation. The procedure is repeated for each line on the spatial axis. The output of the integration over the spectral radiance I λ of both lines is the surface radiation density I L (λ) shown in figure 3.26 b). Now a radial distribution of the emission coefficient ε(r) for both lines can be determined Radiance I = Wm nm sr 7 x Integration limits Continuum underground Wavelength = nm (a) Mercury spectrum -2-1 Line radiation density = Wm sr Spatial resolution = mm (b) Line radiation density Figure 3.26: Example for the spectrum of the two mercury lines being used to evaluate the plasma temperature. b) Spatially resolved line radiation density I L (λ) after the integration over the two mercury lines at λ 1 = nm and λ 2 = nm from the lateral distribution of the radiance I L (λ) by Abel inversion. With the use of equation 2.10 and 2.20 as well as the assumption of a BOLTZMANN population the emission coefficient of a spectral line can be written as: ε nm (λ, T (r)) = 1 hc 0 4π λ g p 0 na nm k B T (r)z(t (r)) exp ( E ) n k B T (r) (3.40) p 0 is the partial pressure of the treated atoms. By using equation 3.40 the mercury temperature T Hg (r) can be calculated. The equation is extended to take into account the undisturbed superposition of the second line. Additionally the partition function of the neutral mercury Z Hg (T ) is set to Z Hg = 1 which applies for temperatures T Hg < 8000K. ε nm = hc 0 4π [ p 0 gn,1 A nm,1 exp k B T Hg λ 1 ( E n,1 k B T Hg ) + g n,2a nm,2 λ 2 exp ( E n,2 k B T Hg )] 1 Z Hg (T ) (3.41) The nonlinear temperature dependence of this equation is solved by an iterative minimization method and T Hg is determined. The values in equation 3.41 for the statistical weight g n,i, transition probability A i and the energy for the upper energy levels E n,i are taken from [12] and shown in table 3.4. The partial pressure of mercury is calculated by a theoretical model delivered from the lamp manufacturer. The result of this model is a pressure of p 0 = 19.8bar. This pressure is estimated to be constant. Within the parameter range being used all mercury is evaporated inside the lamps and the change of the gas temperature is small compared to the absolute temperature.

77 54 3. Experimental setup λ 1 = nm g n A nm,1 = s 1 E n,1 = 8.849eV λ 2 = nm g n A nm,2 = s 1 E n,2 = 8.842eV Table 3.4: Constants used for the determination of the mercury temperature Determination of the dysprosium density The procedure for the determination of the dysprosium density is similar to the method being used for the mercury temperature. A basic requirement for the calculation of the dysprosium density is the plasma temperature. This temperature is assumed to be equal to the mercury temperature determined before. The spectral lines which are used to determine the dysprosium density are recorded together with the mercury lines. For the measurements the same setup is used, only the center wavelength position of the spectrograph is changed. In the work of Langenscheidt [35] several possibilities for a determination of the dysprosium density are discussed. In this work only the method is described which is applied. For the determination of the dysprosium density the emission coefficient ε(λ, T (r), t) of an optically thin Dy line is measured. With the help of equation 2.20 the Dy density n Dy can be calculated. In order to apply this method it has to be assured that the observed Dy line is optically thin. An extensive investigation of the spectrum of YAG lamps showed that the most appropriate atomic lines are in the wavelength region around λ = 698nm. The main focus is put on an optically thin line which is emitted with a high intensity even if the cold spot of the YAG lamp is strongly cooled. Figure 3.27 shows a spectrum where two marked lines fulfil these demands. The first line occurs at a wavelength of λ Dy = nm and the second line at λ Dy,I = nm. The line at λ Dy = nm is an optically thin line Radiance I = Wm nm sr Wavelength = nm Figure 3.27: Spectrum showing the two dy lines for the dy density calculations. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm because the lower energy state an excited state. For this line self absorption can be neglected

78 3.3. Diagnostics 55 because the lower energy level is only weakly populated. The disadvantage of this line is the strong reduction of its intensity if the cold spot of the lamp is strongly cooled. In some cases the maximum intensity of the line is close to the noise level of the camera. Therefore this is not an appropriate candidate for the dysprosium density calculation. Regarding the line intensity in the case of strong cooling the DyI nm line is better suited for the measurements. But this line is a resonance line, i.e. the lower level is the ground state of the atom. Since the ground state is strongly populated an absorption can not generally be excluded. If self-absorption is present a determination of the dysprosium density would be erroneous. Thus it must be ensured that under operating conditions self absorption can be negelected. To control this, Langenscheidt compared the profile of the resonance line DyI nm with the dysprosium line at λ 2 = nm which is optical thin without doubt. The second one does not show self adsorption since its lower energy level is far above the ground state. Both line intensities are normalized to a value of 1. For a comparison the YAG lamp is operated with the highest possible current without cooling of the cold spot. Thus the dysprosium density should be at a maximum level for which a self adsorption is most probable. The symmetry axes of the two lines are adjusted onto a common position. Now the shape of the two lines can be compared with each other. The line profiles show nearly the same shape. This indicates that the DyI nm line is optically thin for all measurement parameters. Density calculation For the determination of the dysprosium density the absolute spectral radiance I λ (y) is measured spatially resolved. For this measurement a spectrum with a center wavelength of λ = 698nm is recorded. Figure 3.28 shows a magnification of the DyI nm line. For the calculation of the spatially resolved radiance of the line I(y) the integration limits on the λ- axes are determined. Additionally the underground continuum radiation is subtracted from the spectrum. In figure 3.28 the integration limits and an additional line representing the underground continuum are indicated. Furthermore the 5% mark is inserted. It represents 5% of the difference between the intensity of the line maximum and of the underground of the right side of the line. This is necessary since the left line wing is often disturbed by a second line occurring at lower wavelength. Thus a clear determination of the left integration limit is often impossible. If the intensity at the left boundary position is above the 5% mark the right wing of the line is mirrored and substitutes the left wing. Now a complete line profile exists which is usable for a determination of the radiance I(y) of the line. Parametric studies by Langenscheidt showed that 5% is a reasonable tolerance. After I(y) is determined the radial emission coefficient ε DyI (r) is calculated applying the inverse Abel transformation. The population density N n of the upper level of the nm Dy line is given by: ε nm (r) = 1 hc 0 4π λ g na nm N n (3.42) This equation is based on equation The unknown population density N n of the dysprosium atoms can be determined with the help of the BOLTZMANN factor according to N n = N g ( n Z(T ) exp E ) n. (3.43) k B T

79 56 3. Experimental setup Radiance I = Wm nm sr Integration limits Underground continuum 5% - line Wavelength = nm Figure 3.28: Image of the Dy line with integration boundaries and indication of the underground continuum. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm λ DyI = nm λ DyII = nm g n = 15 g n = 18 A nm = s 1 A nm = s 1 E n = eV E n = eV Table 3.5: Constants used for the determination of the dysprosium atom and ion densities Z(T ) is the partition function of the dysprosium atoms. The partition function is introduced in chapter For the calculation of the partition function of dysprosium atoms the summation has to be stopped at a certain level j beyond the ionization limit. For j the sum diverges but the states near to the ionization limit can be neglected since the ionization energy is lowered due to the interaction with the plasma. The number of states being considered is uncritical as long as it is high enough. In this work 320 states are considered for the calculation of the partition function of atomic dysprosium. The data for the calculation are taken from [30]. Z(T ) is calculated in dependence on the plasma temperature T. With the help of the plasma temperature T, the measured emission coefficient ε nm (r) and the calculated partition function Z(T ), a radial distribution of the dysprosium atom density is calculated. The constants g n, A nm and E n are taken from of the Kurucz database [30]. They are listed in table 3.5. The dysprosium ion density N DyII is determined with the same procedure. For this measurement a dysprosium ion line is recorded at λ DyII = nm. This line can be estimated to be optically thin as its lower energy level is far above the ground state. Figure 3.29 shows a magnification of the dysprosium ion line cut out of the recorded spectrum. In comparison to the dysprosium atom line this line is only weakly affected by profiles of other lines. Thus the

80 3.3. Diagnostics 57 line profile serves for a determination of the density. The data for the dysprosium ion line is listed in table 3.5. The calculation results in a radial density profile of the dysprosium atom Radiance I = Wm nm sr Integration limits Underground continuum 5% - line Wavelength = nm Figure 3.29: Image of the Dy ion line with integration limits and identification of the underground continuum. Parameters: NTD1, current i = 0.8A switched-dc, electrode diameter d E = 0.36mm or ion density. In most cases the presented density values are mean values of the density profiles over a distance equal to the electrode diameter Electrical measurements The measurements of the arc voltage u arc and the arc current i arc are necessary for the evaluation of several electrode and plasma processes. In case of the model lamp both values can be measured directly at the monitoring outputs of the amplifier. If YAG lamps are observed it is necessary to use active probes for the measurements. The commutator setup does not allow grounding circuits. Thus it is impossible to use passive probes. For the measurement of the arc current an active current probe (Tektronics TM502A) or a PEARSON probe is used. The arc voltage is measured directly at the lamp socket with an active voltage probe (LECROY ADP300). For both lamp types the signals are displayed on an oscilloscope from LECROY (WAVERUN- NER LT364). Additionally the signals are digitized and stored on a PC with an analysis card from NATIONAL INSTRUMENTS (PCI-6040E). The oscilloscope is equipped with 4 channels, each with a bandwidth of 500 MS/s and an 8 bit resolution. The PC card has 8 differential A/D inputs, each with a resolution of 12 bit and a bandwidth of 250 ks/s.

81 58 3. Experimental setup Electrode sheath voltage The model lamp offers the unique possibility to measure a further important lamp parameter: the electrode sheath voltage (ESV). The ESV can be determined only within the model lamp as a result of a combined measurement of the arc voltage u arc and the arc length l arc. The possibility of a stepwise displacement of the lamp electrodes is a feature which only exists at the model lamp. Figure 2.2 shows that the arc voltage is a sum of the voltage drop along the arc column and the cathodic and anodic boundary layer, u c and u a,el. Inside the model lamp the arc column is mostly cylindrically and thus the axial electrical field is constant within the arc column E arc = const. This implies that the arc voltage is linearly depending on the arc length: u arc = u a,el + u c + E arc l arc (3.44) The distance between the electrodes can be estimated equal to the arc length for a vertical operation of the model lamp. The lamp electrodes are positioned with a gap of 30mm for a determination of the ESV. They are moved towards each other in steps of typically 2.5mm until a final distance of 10mm is reached. This procedure is illustrated in figure 3.30 a). The arc voltage and current are measured at each position. The cathodic and anodic sheaths normally are in a dimension below 2mm. Thus even for short arc length the assumption of a linear potential distribution is fulfilled. The time and phase resolved measurements of the arc voltage u arc (t, l arc ) combined with an interpolation of the arc voltage to an arc length of l arc = 0 results in a sum of the anodic and cathodic sheath voltage, the ESV. Figure 3.30 b) shows a measurement of the arc voltages for several arc lengths and the interpolated ESV(t). The ESV(t) is defined as ESV (t) = u a,el (t) + u c (t) (3.45) The arc current is monitored as a control parameter since it needs to be constant for all measured arc length. The whole procedure is automated by a LabView program which moves the stepping motors of the model lamp and measures the arc voltage. The interpolation is also automated with a Matlab program which additionally computes the electric field strength E arc Error estimations In this section estimations are presented showing the occurring measurement errors of the several diagnostic systems. Electrode temperature measurements For the error estimation concerning the electrode temperature measurement it must be distinguished between the measurement itself and the subsequent simulation. The spectroscopic measurements are quite insensitive to errors. Due to the calibration of the optical setup with a calibrated tungsten ribbon lamp errors can be excluded, apart from

82 3.3. Diagnostics U arc (measured) ESV l arc Extrapolation U = V arc u arc (t) Measurements Electrode distance = mm (a) Sketch of the ESV measurement (b) Extrapolation procedure Figure 3.30: Example for the measurement and the subsequent extrapolation of the ESV the uncertainty of the calibration lamp itself. This uncertainty is given by the calibration institute and the manufacturer of the lamp with 1.6% 2%. A further source of error may be the values for the correction of the emissivity ε(λ, T ) from DeVos [26]. For this data a statement about the accuracy is not possible. As it is mentioned in chapter a rotational symmetry is assumed for the simulation of the electrode temperature. This assumption is only valid if the arc attaches uniformly the whole electrode tip surface. The radial symmetry of the temperature distribution is no longer guaranteed if the arc attachment is constricted at a certain position on the electrode. In the region of a constricted arc attachment the electrode temperature is exaggerated. This effect only shows a minor influence on the calculation of the electrode input power if the electrode temperature measurement is not directly performed in the region of the arc attachment. In a previous investigative work of [36] it is shown that the influence of the constricted arc attachment on the temperature curve along the electrode is rather small for the same input power. Thus the values obtained for the electrode input power are trustable if the local heating of the electrode within the area of arc attachment is neglected. For the electrode tip temperature a more global temperature can be specified in the case of a constricted arc attachment. It is lower than the tip temperature for an uniform arc attachment. Hence an overall error of 5% for the electrode tip temperature and the input power is an realistic value. Spectroscopic measurements Equivalent to the electrode temperature determination the spectroscopic measurements have to be divided into two parts. The optical setup is the same as for the temperature diagnostics. Thus the error is in the order of 1.6% 2%.

83 60 3. Experimental setup For the determination of the electron density and temperature a dominant error source may be the data which are used for the evaluation of the different lines. Especially the transition probabilities A nm vary over a large range comparing different sources. Also by the Boltzmann plot errors may occur while calculating the slope of the straight line which is plotted through the values obtained from the measurements. Thus the total error can only be estimated and it is expected to be 5% 10% for this work. The error estimation is much more difficult considering the calculation of the Dy atom and ion densities. The main error may be caused by in the inverse Abel transformation. In addition, the spectral data show an influence on the results, similar to the electron temperature measurements. For the Dy data the values are even more critical than the Ar data for the electron temperature determination. For Ar much more data can be found and a better comparison is possible. In a first step the mercury temperature is determined for the determination of the Dy densities. This is an additional error source during the measurement and calculation processes. In his work, Langenscheidt [35] calculated an error for the mercury temperature T Hg,error of ±250K. This uncertainty causes an error in the subsequent Dy density calculation of 10%. Together with the missing precision of the line data the total uncertainty can only be estimated by a factor of 2. In general the order of magnitude can be considered as a trustful value but the absolute density may by doubtful by 50%. Electrical measurements The electrical measurements are the most reliable measurements. They are performed with probes directly at the lamp socket. The error of the V \I probes is given by the manufacturer in a range below 1%.

84 61 4. Measurements and results This chapter shows the results obtained by investigations of the lamps operated with various frequencies. At first the results of fundamental investigations at the Bochum model lamp are presented. At second results obtained with the YAG lamps are shown. 4.1 Fundamental research at the Bochum model lamp The Bochum model lamp is an experimental setup of an HID lamp given in The larger dimensions of the model lamp and thus the better accessibility make it a first choice for basic investigations of the electrodes. Furthermore the possibility to influence numerous of the lamp and operation parameters are very important for a fundamental investigation Optical investigations of the arc attachment (a) Diffuse (b) Spot Figure 4.1: Two different kinds of arc attachment at electrodes. Parameter: electrode diameter d E = 1.5 mm, electrode length l E = 20 mm, i = 4A DC, gas argon, pressure p = 0.26 MPa In figure 4.1 two different kinds of arc attachment are presented. Figure a) shows a diffuse mode and figure b) a spot mode. Both images are recorded at a cathode operated with a dc current. The main differences between the two kinds of arc attachment can be described as

85 62 4. Measurements and results follows. In general the diffuse mode shows a higher global electrode temperature compared to a spot mode. But the spot mode has a higher local electrode temperature in the region of the arc attachment. The current density is higher within the spot attachment than within the diffuse one. In general the spot attachment is observed at lower currents, thicker electrodes and higher pressures. A more detailed description of the cathodic arc attachment can be found in [37]. At the anode mainly a diffuse arc attachment is observed. The arc is more or less constricted depending on the operating parameters [38, 2]. The optical observation of the electrodes, particularly the arc attachment on the electrode gives a large amount of information about the whole discharge. Figure 4.2 shows the arc attachment on the upper electrode, phase resolved over one period for electrode diameters of a) d E = 0.7 mm and b) d E = 1 mm. Both upper lines of images reflect the arc attachment at a low frequency of 50 Hz while the lower lines of images are taken at a high frequency of 50 khz. The first five images are taken in the anodic phase and the last five images in the cathodic phase. For a better visualization of the plasma effects so called alternating lookup tables are used [17, 4, 39] to bridge the large differences between the radiance of the electrode and the plasma. 50 Hz 50 khz 50 Hz Anode (a) d E = 0.7mm Cathode 50 khz Anode (b) d E = 1mm Cathode Figure 4.2: Arc attachment on the upper electrode over one period for LF and RF operation, the first five pictures are in the anodic phase the last five pictures in the cathodic phase, Parameter: f = 50 Hz / 50 khz. Gas: argon, pressure p = 0.26 MPa, exposure times for 50 Hz / 50 khz : 100 µs / 2 µs a) electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with î = 1 A, b) electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with î = 2 A The thinner electrode with a diameter of d E = 0.7 mm shows a diffuse arc attachment over the whole period at low as well as at the high frequency. In case of the low frequency of f = 50

86 4.1. Fundamental research at the Bochum model lamp 63 Hz the electrode is heated up during the cathodic phase but does not change the mode of arc attachment. In contrast to the thinner electrode, at the electrode with a diameter of d E = 1 mm at a low frequency the arc attachment takes places in the spot mode during the cathodic phase while during the anodic phase the arc attachment changes to a diffuse one. The variation of arc attachment indicates that the electrode temperature strongly changes during operation. In case of the high frequency the shape of arc attachment remains diffuse during the cathodic as well as during the anodic phase. Also the electrode temperature seems to be constant during the whole period. This may be explained by the thermal time constant of the electrode which is proportional to the heat capacity (ρ M c p ) of the electrode material. Depending on the current wave form and amplitude the heating of the electrodes is lower within the anodic phase than within the cathodic phase. For low frequencies the thermal time constant of the electrodes is to low compared to the period of the sinusoidal current to keep the electrodes at a constant temperature. If the frequency is risen the time in which the electrodes can cool down is reduced. Thus the electrodes keep a nearly constant temperature over one period and consequently over time, too. This effect is of course dependent on the electrode diameter and length. The cooling effect dominates over the effect of the heat capacity for a large electrode diameter and low operation frequency. The opposite applies for a small electrode diameter and a high operation frequency as is indicated in figure 4.2 a,b frequency [khz] Figure 4.3: Arc attachment on HID electrodes during RF operation for the upper and lower electrode, Parameter: f = 15 khz / 1 MHz, Gas: argon, pressure p = 0.26 MPa, electrode diameter d E = 1 mm, electrode length l E = 20 mm Figure 4.3 shows the arc attachment for frequencies f from 15 khz up to 1 MHz. The model lamp is operated with a sinusoidal current with an amplitude of î = 2 A and a pure argon atmosphere with a pressure of p = 0.26 MPa. Both electrodes have a diameter d E = 1 mm. The exposure time amounts to t exp = 100µs, which means that the images represent averages over more than one period. The images show for all frequencies at the upper electrode a spot mode of arc attachment while at the lower electrode the arc attachment takes place in a diffuse mode. Figure 4.4 demonstrates that with rising frequency the current is reduced at which the spot mode of arc attachment is substituted by the diffuse mode. It must be mentioned that the arc attachment by a spot always occurred immediately after ignition. If the discharge only showed diffuse arc attachments after ignition an arc attachment by a spot could never be enforced by changing parameters. Only a reduction of frequency may induce a spot. An arc attachment after ignition by a spot is only found for few electrodes. The occurrence of a spot arc attachment at these high frequencies is surprising. As later considerations will show the probability of a spot shaped arc attachment will decrease with

87 64 4. Measurements and results increasing frequency. 50 khz I=1.75A I=2.0A I=2.25A I=2.5A I=2.75A I=3.0A 75 khz Pv=6.23W Ts=3033K 1427K 250 khz Figure 4.4: Images of arc attachment depending on frequency and current for the lower electrode, Parameter: f = 50 khz / 75 khz / 250 khz, Gas: argon, pressure p = 0.26 MPa, electrode diameter d E = 1 mm, electrode length l E = 20 mm Electrode temperature measurements In the previous chapter first information about the electrode temperature depending on the operating frequency are presented. To obtain a more detailed representation of the electrode temperature it is measured spectroscopically as a function of time for various frequencies as it is described in chapter For the spectroscopic measurements of the electrode temperature spectra with a center wavelength of 718nm are taken with the spectrograph. In this wavelength region only the continuum radiation of the electrode is visible. Thus a disturbance of the measurements by plasma radiation can be excluded. The electrode is imaged parallel to the entrance slit of the spectrograph to gain a spatial resolution along the electrode. After these spectra are calibrated by using a tungsten-ribbon lamp, temperature curves are calculated according to Planck s law. Figure 4.5 shows the course of the electrode tip temperature within a period for frequencies from 25 Hz to 10 khz. The electrode has a diameter of d E = 0.7 mm and a length of l E = 20 mm. The buffer gas is argon at a pressure p = 0.26 MPa and a steady gas flow of 25 sccm. The discharge was operated with sinusoidal currents at values of i RMS = 1, 2 and 3 A. The first half period in figure 4.5 is the anodic phase while the second one is the cathodic phase. For the low frequencies of 25 Hz and 50 Hz it is obvious that the electrode cools down during the anodic phase for a current of i RMS = 1 A. Then at the beginning of the cathodic phase the electrode is heated up rapidly until it cools down again at the end of the cathodic phase due to the sinusoidal current. By rising the frequency the temperature difference T between the lowest and highest temperature decreases. For a frequency of 25 Hz the temperature difference T is nearly 120 K, for a frequency of 500 Hz it decreased to

88 4.1. Fundamental research at the Bochum model lamp 65 Tip temperaure / K Hz 50Hz 100Hz 500Hz 1kHz 2kHz 5kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i RMS = 1 A Tip temperaure / K Hz 50Hz 100Hz 500Hz 1kHz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (b) i RMS = 2 A Tip temperaure / K Hz 50Hz 100Hz 500Hz 1kHz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (c) i RMS = 3 A Figure 4.5: Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1, 2 and 3A, Gas argon, pressure p = 0.26 MPa T = 5 K until the temperature is nearly constant for a frequency of 2000 Hz. Increasing the current to values of i RMS = 2 and 3 A the electrode is heated during the anodic phase for lower frequencies, too. In the region of the current zero crossing (CZC) the electrode cools down. For low frequencies the maximum temperature during the anodic phase is lower than in the cathodic phase. With increasing frequency the electrode tip temperature becomes constant over one period as it is shown before for the lower current. But now the constant tip temperature is lower than the maximum tip temperature during the cathodic phase for low frequencies. Figure 4.6 shows the tip temperature for a 1mm electrode for a sinusoidal current with i RMS = 3 and 5A. The course of the electrode tip temperatures corresponds to those measured at the thinner electrode. For the low current the electrode cools down during the anodic phase and is strongly heated during the cathodic phase. For the higher current the electrode is also heated during the anodic phase but does not reach the level of the cathode temperature. For both measurements the tip temperature approaches the maximum cathode

89 66 4. Measurements and results Tip temperaure / K Hz 25Hz 50Hz 100Hz 200Hz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i RMS = 3 A Tip temperaure / K Hz 25Hz 100Hz 500Hz 1kHz 2kHz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (b) i RMS = 5 A Figure 4.6: Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 and 5A, Gas argon, pressure p = 0.26 MPa temperature with increasing frequency. This is an indication that at higher frequencies the cathode is more dominant in the discharge. Figure 4.7 shows the electrode tip temperature for a thicker electrode with a diameter of d E = 1mm and a switched-dc current. For frequencies above 1kHz it was only possible to take less than 10 spectra within one rf period. Thus the measurement positions within one period are marked with a cross and the line length represents the exposure time of the camera. For currents of i = 3 and 4A the electrode cools down during the anodic phase and is heated up rapidly at the beginning of the cathodic phase. With increasing frequency the same effects occurs as for the operation with sinusoidal current. The electrode tip temperature becomes constant over one phase. But this happens for much lower frequencies in the range between 200 and 500 Hz. The reason can be found in the switched-dc operation since now the change of the electrode temperature over one half phase is very low compared to the operation with a sinusoidal current shown in figure 4.6. It is also visible that for the lowest current of 3A the tip temperature for high frequencies increases above the maximum temperature which is reached for low frequencies. For the current of 4A the temperature becomes constant with increasing frequency at the level of the maximum cathode temperature for the low frequencies. At these currents the electrode showed a cooling during the anodic phase and a heating during the cathodic phase. Figure 4.7 c) shows the tip temperature for a current of i = 6A. In this case the electrode is heated during the anodic phase and cools down during the cathodic phase. With increasing frequency the tip temperature becomes constant in dependence on time again. But the level at which the tip temperature converges is in the region of the temperature to which the electrode cools down during the cathodic phase. This supports the assumption that the cathode dominates at higher frequencies. In general it has to be mentioned that under ac operation an anode can be operated at much higher currents than under dc operation. In the work of Dabringhausen [40] the tip temperature of a dc anode and cathode in dependency of the arc current is shown for various electrode diameters. For an electrode diameter of 1mm the anode has a temperature of T a,dc 3400K at a current of 5A. For the same current the cathode has a temperature of

90 4.1. Fundamental research at the Bochum model lamp Tip temperaure / K Hz 25Hz 100Hz 500Hz 1kHz 2kHz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i=3 A Tip temperaure / K Hz 25Hz 50Hz 100Hz 200Hz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (b) i=4 A Tip temperaure / K Hz 25Hz 100Hz 500Hz 1kHz 2kHz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (c) i=6 A Figure 4.7: Spectroscopically measured electrode tip temperature for various frequencies. The first half period represents the anodic phase and the second half period the cathodic phase. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3, 4 and 6A, Gas argon, pressure p = 0.26 MPa T c,dc 3050K. At a current of 6A the anode temperature would have exceeded the melting temperature of tungsten. The cathode temperature would be at T c,dc = 3100K. In contrast to these values the anode temperature at i = 6A under switched-dc operation is in the range of T a,ac = 3430K for frequencies above 10 Hz. On the other hand the cathode temperature is higher than under dc operation with T c,ac = 3430K. This shows that an ac operation is possible with higher currents than for dc operation. Also remarkable is that under dc operation the current is lower for which anode and cathode have the same temperature than under ac operation lower. For dc operation the current at which this is the case is i equal,dc 3.5A. For ac operation the electrode behavior is different for switched-dc and sinusoidal operation. For the switched-dc operation the current is i equal,swdc 5A. For sinusoidal currents the current amplitude cannot be reached at which the anode exceeds the cathode temperature before the absolute electrode temperatures exceed the melting temperature. Figure 4.8 shows the electrode tip temperature as a mean value over the anodic respectively the cathodic phase as well as a mean tip temperature over a full rf period of a sinusoidal current. The mean values are calculated from the phase resolved measurements. The graphs

91 68 4. Measurements and results Tip temperature / K Mean tip temperature Mean anode tip temperature Mean cathode tip tmeperature Tip temperature / K Mean tip temperature Mean anode tip temperature Mean cathode tip tmeperature Frequency = log Hz Frequency = log Hz (a) i RMS = 1 A (b) i RMS = 2 A 3255 Tip temperature / K Mean tip temperature Mean anode tip temperature Mean cathode tip tmeperature Frequency = log Hz (c) i RMS = 3 A Figure 4.8: Mean electrode tip temperatures for the anodic and cathodic phase and over one full rf period. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1, 2 and 3A, Gas argon, pressure p = 0.26 MPa show that the mean anode tip temperature is rising with increasing frequency to the value of the cathodic mean tip temperature. Above frequencies of 2 khz the tip temperatures have obtained a constant value over one period. But also the mean tip temperature values over one period are now constant. For a current of i RMS = 1A the graph shows an increasing mean tip temperature with increasing frequency for all measured values. But for i RMS > 1A not only for higher frequencies the average temperature remains on a nearly constant level within the cathodic phase. Figure 4.9 and 4.10 show spectroscopic measurements of the electrode temperature T (z) for different phase angles ϕ within one ac period of a sin wave. In figure 4.9 the course of the temperature is shown along the electrode beginning at the electrode tip at l E = 20 mm. For the low frequency of f = 25 Hz a temperature modulation in dependence on ϕ over the whole measured electrode length of 3.5 mm is visible. For the high frequency of f = 2 khz only a very weak modulation directly at the electrode tip is left. Figure 4.10 shows a magnification of this region near the electrode tip. These observations correspond to the optical observation and confirm that the penetration depth λ pen of a sinusoidal temperature

92 4.1. Fundamental research at the Bochum model lamp 69 Electrode Temperature = K f=25 Hz f=2 khz Electrode length = mm Figure 4.9: Spectroscopically measured temperature between the electrode tip up to 3.5mm behind for 25 Hz and 2 khz. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1 A, Gas: argon, pressure p = 0.26 MPa Electrode Temperature = K anodic phase cathodic phase Electrode length = mm (a) f=25 Hz Electrode Temperature = K Electrode length = mm (b) f=2 khz Figure 4.10: Spectroscopically measured temperature between the electrode tip and a distance 0.5 mm apart from the tip for 25 Hz and 2 khz. The numbers on the right side of graphic a) indicate the position within the RF period starting with 1 at the beginning of the anodic phase at ϕ = 0 and proceeding with n = Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1 A, gas argon, pressure p = 0.26 MPa modulation at the electrode tip decreases with increasing frequency. ( ) 1 κ τ 2 λ pen = ρ M c p π (4.1) In this equation κ is the heat conductivity and c p ρ M the heat capacity of tungsten per unit

93 70 4. Measurements and results mass (ρ M is the mass density of tungsten). As τ is the time of a rf cycle it becomes clear that the penetration depth is increasing with a decreasing frequency. Calculation of the electrode power balance In chapter the time dependent heat balance equation for a periodically charged electrode is derived. With the measured electrode temperature curves T (ϕ, z) shown in the previous chapter the total input power P e,in in the electrodes are calculated using equation For the electrode with the diameter of d E = 0.7mm figure 4.11 shows the calculated input power over one ac period for various frequencies. The course of the input power mainly reflects the Input power / W Hz 50Hz 100Hz 500Hz 1kHz 2kHz 5kHz 9 0 1/2¼ ¼ 3/2¼ 2¼ Phase (a) i=1 A Input power / W Input power / W Hz 50Hz 100Hz 250Hz 500Hz 1kHz 10kHz 6 0 1/2¼ ¼ 3/2¼ 2¼ Phase 25Hz 50Hz 100Hz 250Hz 1kHz 2kHz 10kHz (b) i=2 A 6 0 1/2¼ ¼ 3/2¼ 2¼ Phase (c) i=3 A Figure 4.11: Input power into the electrode over one period for various frequencies. Parameter: electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin-wave with i=1,2 and 3 A, Gas argon, pressure p = 0.26 MPa course of the electrode tip temperature. For low frequencies there is a significant variation

94 4.1. Fundamental research at the Bochum model lamp 71 of the input power into the electrode over one rf period. With increasing frequency this variation decreases until the input power is nearly constant over one period. This mainly depends on the electrode temperature. If the electrode temperature becomes constant over one phase due to the higher frequency, the term of the heat capacity in equation 3.19 can be neglected. Thus the time dependence of the electrode vanishes and it can be treated as being in a stationary operation condition. Now the input power only consists of the radiated and the conducted power. Both terms are constant for a constant electrode temperature. Figure 4.12 shows the power input for the electrode with a diameter of d E = 1mm. For the operation with a switched-dc current the variation of the input power is small compared to the sinusoidal current. With an increasing frequency an increase of the input power can be found especially in case of the sinusoidal operation current. The reason for the increasing electrode temperature and the input power may be given by the power P input coupled into the discharge Input power / W Hz 25Hz 50Hz 100Hz 500Hz 5kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i=3 A switched-dc Input power / W Hz 25Hz 50Hz 100Hz 200Hz 2kHz 10kHz /2¼ ¼ 3/2¼ 2¼ Phase (b) i=3 A sin Figure 4.12: Input power into the electrode over one period for various frequencies. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc and sin-wave with i RMS = 3 A, Gas argon, pressure p = 0.26 MPa Electrical measurements Figure 4.13 shows the arc voltage U arc over one ac period for different frequencies corresponding to the measurements of the electrode tip temperature shown in figure 4.5. The current is kept constant for all measurements with an amplitude of i RMS = 1, 2 and 3 A. For a low current of 1 and 2 A the maximum voltage occurs directly after the current zero crossing at lower frequencies. At this moment the current is relatively low caused by its sinusoidal waveform. After the voltage has reached its maximum it decreases over the rest of the half period. With rising frequencies the voltage adopts more and more a sinusoidal waveform. Hence the maximum of the voltage is shifted towards the middle of the half period. Now the phase shift between voltage and current approaches zero. Thus the mean input power is increasing with increasing frequency. The input power is the mean value of the product from

95 72 4. Measurements and results arc V U / Hz 100Hz 500Hz 5kHz 10kHz 20kHz arc V U / Hz 100Hz 500Hz 5kHz 10kHz 20kHz /2¼ ¼ 3/2¼ 2¼ Phase /2¼ ¼ 3/2¼ 2¼ Phase (a) i=1 A (b) i=2 A 40 arc V U / Hz 100Hz 500Hz 5kHz 10kHz 20kHz /2¼ ¼ 3/2¼ 2¼ Phase (c) i=3 A Figure 4.13: Arc voltage U arc over one period for various frequencies, Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 1, 2 and 3 A, Gas: argon, pressure p = 0.26 MPa current and voltage over one rf period. With an increasing current the phase shift between voltage and current maximum is decreasing. For a current of 3 A the voltage does not show a pronounced peak after the current zero crossing. Figure 4.14 shows the mean power input over one period for frequencies from 25 Hz to 20 khz and sinusoidal currents from 1 to 3.5 A. With increasing frequency the power input is increasing, too. Figure 4.15 shows the corresponding voltage signals for a thicker electrode with a diameter of d E = 1mm. The current has a RMS value of i RMS = 3 A for both, sinusoidal and switched-dc waveform. For the sinusoidal waveform the same effect takes place as for the thinner electrode. With increasing frequency the voltage waveform adopts more and more a sinusoidal shape in phase with the current. For the switched-dc current the voltage waveform has a rectangular shape even for low frequencies. Directly after the current zero crossing a peak of the voltage signal occurs. This effect is caused by the amplifier which cannot provide the current fast enough, since the rise time of the amplifier is to slow. With increasing frequency this peak vanishes and the

96 4.1. Fundamental research at the Bochum model lamp A 1.5A 2A 2.5A 3A 3.5A 70 Input Power = W Frequency = log Hz Figure 4.14: Mean power input P input into the discharge over one period for various frequencies and current. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = A, Gas: argon, pressure p = 0.26 MPa arc V U / Hz 25Hz 100Hz 500Hz 5kHz 20kHz arc V U / Hz 25Hz 100Hz 500Hz 5kHz 20kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i = 3 A sin /2¼ ¼ 3/2¼ 2¼ Phase (b) i = 3 A switched-dc Figure 4.15: Arc voltage U arc over one period for various frequencies, Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave and switched-dc with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa voltage adopts a rectangular shape. Figure 4.16 represents the calculated input power into the discharge. It shows that for the sinusoidal current the input power increases clearly with increasing frequency until it becomes nearly constant for frequencies above 5 khz. At this frequency the voltage signal has reached a sinusoidal waveform in phase with the current. For the switched-dc current the input power is nearly constant over frequency. It slightly decreases with increasing frequency. This effect can be explained by the current signal. Fig-

97 74 4. Measurements and results sin switched-dc 90 input W P / Frequency = log Hz Figure 4.16: Mean power input P input into the discharge over one period for various frequencies. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave and switched-dc with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa ure 4.17 shows the current signal over one period for various frequencies. At high frequencies of 5 and 20 khz the current signal looses its rectangular form. This effect can again be attributed to the slow rise time of the amplifier. If the amplifier would be able to provide a clear rectangular switched-dc signal even at very high frequencies it can be estimated that the input power is constant. In case of a sinusoidal current the increasing input power affects arc A I / Hz 25Hz 100Hz 500Hz 5kHz 20kHz /2¼ ¼ 3/2¼ 2¼ Phase Figure 4.17: Current signal over one ac period for various frequencies. Parameter: f = 10 Hz - 20 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa the whole discharge. Figure 4.18 shows that both, tip temperature and input power, are rising simultaneously with increasing frequency. Thus for the model lamp the rising electrode

98 4.1. Fundamental research at the Bochum model lamp 75 temperature can be associated to the higher average power input with increasing frequency T tip P input Tip temperarue = K Input power = W Frequency = log Hz 38 Figure 4.18: Mean power input P input and tip temperature T tip into the discharge over one period for various frequencies. Parameter: f = 25 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, Gas: argon, pressure p = 0.26 MPa ESV measurements Langenscheidt et al [39] have shown that the contribution of the anodic boundary layer to the ESV(t) is only marginal, nearly constant and may be neglected compared to the voltage drop u c at the cathodic boundary layer. Therefore the course of ESV(t) over a period is an appropriate indicator for a mode change from a diffuse to a spot attachment at the cathode after current zero crossing (CZC). A monotonous increase of the ESV between CZC and current maximum indicates a diffuse mode of arc attachment. A rapid change of the ESV after the CZC from the anodic to the cathodic phase, called commutation peak (CP), represents a fast change from a diffuse to a spot attachment. The CPs occur due to a strong and rapid heating of the electrode at the beginning of the cathodic phase. Hence the CPs should vanish for an increasing frequency caused by the nearly constant electrode temperature shown in measurements in the previous chapters. In figure 4.19(a) the ESV is plotted over one period for frequencies from 10 Hz to 20 khz. The arc is operated with a sinusoidal current with i RMS = 3 A. The electrode has a diameter of d E = 1 mm. The measurements clearly show a reduction of the CP after the CZC with increasing frequency. At a frequency of 5 khz the ESV has smoothed to a clear sinusoidal form in phase with the current without a CP after the CZC. Figure 4.19 b) shows an ESV measurement for a switched-dc current at i = 3A for frequencies from 10 Hz to 20 khz for an electrode with a diameter of d E = 1 mm. For the operation with a switched-dc current a commutation peak after the current zero crossing is occurring for low frequencies, too. With increasing frequency the commutation peak vanishes. The vanishing commutation peak is also an explanation for the substitution of the spot attachment by a diffuse one. Consequently a change from a diffuse to a spot attachment

99 76 4. Measurements and results ESV / V Hz 25Hz 100Hz 500Hz 5kHz 20kHz ESV / V Hz 25Hz 100Hz 500Hz 5kHz 20kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i=3 A sin /2¼ ¼ 3/2¼ 2¼ Phase (b) i=2 A switched-dc Figure 4.19: ESV(t) over one ac period for various frequencies, Parameter: f = 10 Hz - 20 khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, switched-dc with i RMS = 2 A, Gas: argon, pressure p = 0.26 MPa during the half period, caused by an electrical breakdown of the diffuse cathodic boundary layer, seems to be impossible at higher frequencies. In figure 4.20 the ESV at ϕ = 1 π is plotted ESV / V ESV / V Frequency = log Hz (a) i=3 A sin Frequency = log Hz (b) i=2 A switched-dc Figure 4.20: ESV at the position ϕ = 1 π plotted over frequency, Parameter: f = 10 Hz khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 3 A, switched-dc with i RMS = 2 A, Gas: argon, pressure p = 0.26 MPa over frequency for the sinusoidal current and the switched-dc current. For the sinusoidal current the ESV increases at this phase position with increasing frequency. The course of the ESV adopts a sinusoidal waveform. It explains the rise of the ESV. For the switched- DC current the ESV increases with increasing frequency, too. The rise is not so pronounced as for an operation with a sinusoidal current but it is clearly visible. Thus there must be

100 4.1. Fundamental research at the Bochum model lamp 77 an additional reason for the increasing ESV. Figure 4.21 shows the ESV(t) for the thinner electrode with a diameter of d E = 0.7mm. In this case the arc was operated with sinusoidal currents of i RMS = 1, 2 and 3 A. In comparison to the thicker electrode with d E = 1 mm, a pronounced CP is not visible after the CZC even for low frequencies. According to figure 4.5 already at a frequency of 500 Hz the electrode tip temperature of the thinner electrode is elevated as well as the thermionic electron emission. It is reflected by the sinusoidal waveform of the ESV in figure But even in this case the ESV at ϕ = 1 π is increasing slightly 2 ESV=V Hz 500Hz 5kHz 20kHz 50kHz 100kHz 200kHz ESV=V Hz 100Hz 500Hz 5kHz 20kHz 50kHz 100kHz 200kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i=1 A /2¼ ¼ 3/2¼ 2¼ Phase (b) i=2 A ESV=V Hz 100Hz 500Hz 5kHz 20kHz 50kHz 100kHz 200kHz /2¼ ¼ 3/2¼ 2¼ Phase (c) i=3 A Figure 4.21: ESV(t) over one period for various frequencies, Parameter: f = 50 Hz khz, electrode diameter d E = 0.7 mm, electrode length l E = 20 mm, sin wave with i RMS = 1, 2 and 3 A, Gas: argon, pressure p = 0.26 MPa with a further increase of the frequency. Of course the ESV is not only an indicator for transitions between different modes of arc attachment, but represents also an essential contribution to the power balance of a lamp. The ESV can be treated as a loss power, since the sheaths do not produce light. Thus the ESV is also very important for the efficacy of a lamp. Taking into account the different courses of i(t) and ESV(t) at low frequencies and the adoption of both with increasing frequency the

101 78 4. Measurements and results power input into the sheaths P ESV with P ESV = T 0 seems to approach to a constant value after an initial rise. i(t) ESV (t)dt (4.2) Spectroscopic measurements The spectroscopy is used for the determination of the electron temperature and density in the model lamp. In case of a one component plasma (argon) both values can be determined by measurements of the lamp spectrum. The measurements presented in this chapter have been performed within the diploma thesis of Kristina Wolff [41]. Electron temperature and density The electron temperature and density are very important parameters in a discharge with thermionically emitting electrodes. For the characterization of the interaction between electrodes and plasma the electron temperature is very significant as it describes the enthalpy flux from the plasma sheath to the plasma in front of the electrodes. For the determination of the electron temperature the Boltzmann plot is used as it is described in chapter The electron temperature strongly depends on the kind of arc attachment and the distance at which it is measured in front of the electrode. In the work of Redwitz [4] the electron temperature is measured in front of a cathode and an anode. The main focus in the work is put on the dc operation. Typically the electron temperature is higher in front of a cathode than in front of an anode. Also the course of the electron temperature along the z-axis of the arc column differs. In front of a cathode the electron temperature decreases with an increasing distance from the cathode surface. It has to be reminded that all measurements are performed outside the cathodic sheath. A measurement inside the sheath and presheath is impossible due to the very small dimensions (several µm) and presumably the strong deviations from LTE. In front of an anode the situation is quite different. First of all the anodic boundary layer is more complex than the cathodic one. The near anode region has to be divided into two parts: the constriction zone and the anodic sheath. The anodic sheath has the dimension of several µm whereas the constriction zone may have the dimension of several mm. Measurements inside the sheath are also impossible due to the small dimensions. Within the constriction zone it is possible to determine the electron temperature if the conditions for a Boltzmann plot are fulfilled. Depending on the arc current the course of the electron temperature changes in front of the anode. For a low current a maximum of the electron temperature is measured near to the anode surface and the density decreases with increasing distance from the anode. With an increasing current the maximum is shifted away from the anode surface towards the bulk plasma. This can also be observed by images of the anodic arc attachment shown in figure 9 of [4]. The maximum radiance of the plasma is shifted away from the anode with an increasing arc current. Directly in front of the anode a dark space appears with a very low radiance. This effect can be attributed to the thermionic electron emission of the hot

102 4.1. Fundamental research at the Bochum model lamp 79 anode. Generally the electrons are accelerated towards the anode by the electric field within the constriction zone in front of the anode. It may induce an ion current which is directed towards the plasma away from the anode. The potential changes its slope in front of the anode in accordance with the potential curve shown in figure 2.2. Thus the potential curve does not have its maximum directly on the anode surface. The maximum occurs at a certain distance in front of the electrode depending on the arc current respectively the anode temperature. The counter voltage in front of the anode is generally necessary to restrict the electron current from the bulk plasma to the anode to its specified value (given by the external circuit). Without this counter voltage an electron saturation current would flow to the anode which is mostly much higher than the specified current. The electrons which are emitted thermionically by the anode have to return to the anode. The thermal energy of the reentering electrons is determined by the plasma temperature within the anodic sheath. It is higher than the thermal energy of the emitted electrons, which is given by the anode temperature. As a consequence the plasma sheath in front of the anode is cooled by the thermionically emitted electrons being demonstrated by a reduction of the electron temperature. Additionally the counter voltage in front of the anode is reduced. A more detailed description of the processes in the near anode region for dc operation can be found in [42]. Table 4.1 shows some typical electron temperatures for different currents and distances in front of a cathode and anode measured by Redwitz [4] in the case of dc operation. The Current Distance T e / K n e / m 3 Anode 1A 50µm e 21 1A 200µm e 21 1A 2000µm e 21 2A 50µm e 21 2A 200µm e 21 2A 2000µm 8500 Cathode 1.7e 21 3A 25µm e 22 4A 25µm e 22 4A 200µm e 22 4A 1200µm e 22 Table 4.1: Table of values for the electron temperature T e and density n e measured by Redwitz for a dc operated cathode and anode. Parameters: electrode diameter d E = 1mm, electrode length l E = 20mm, pure tungsten, pressure p = 0.26MPa values for the electron temperature are expected to change under ac operation. Images of the arc attachment in front of an anode no longer show a dark space. Even the radiance of the plasma is so low compared to the radiance of the anode that it is no longer visible. Figure 4.22 shows the lower electrode as an anode under switched-dc operation with an arc current of i = 3A. To suppress the thermal radiation of the electrode a filter is used which blocks radiation above λ = 890nm. The radiation of the plasma cannot be detected for this configuration. The corresponding electron temperatures and densities at several positions along the arc axis are given in figure Both curves show average values over the anodic and cathodic phase of several rf periods. The plotted values are the maximum electron tem-

103 80 4. Measurements and results Figure 4.22: Arc attachment at an anode under ac operation. Parameter: f = 50 Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa peratures and densities measured in the center of the arc. Both, electron temperature and density are monotonically decreasing with increasing distance from the electrode tip. The electron temperature decreases about 12% between a position of 62.5µm to 500µm complying with 1000K. The electron density is reduced by a factor of 2 within the same distance. In comparison with dc operation the results are within the same order of magnitude. Electron temperature and densities measured phase resolved within the anodic and cathodic phase of a switched-dc current are given in figure The measurements are performed at a position of 62.5µm in front of the electrode tip and the values are the maximum values in the center of the arc column. For the electron temperature phase resolved measurements are possible up to a frequency of 2kHz. For the electron density the intensity of the continuum radiation is too low to perform phase resolved measurements above 100Hz. For both measurements the values are higher in the cathodic phase than within the anodic phase. Radial distributions of the electron temperature and density show that in the anodic phase the arc attachment is broader than in the cathodic phase. This implies a more diffuse attachment in the anodic phase. For lower frequencies the corresponding measurements of the electrode temperature show a higher temperature at the cathode than at the anode. With increasing frequency the differences between the anodic and cathodic electron temperature and density get smaller and approach nearly the same level. It is very interesting that the electron temperature and density are almost constant in dependence on frequency in front of the anode. Only the values in front of the cathode are decreasing with increasing frequency to the level in front of the anode. For higher frequencies a statement about the behavior of the electron density is impossible as no phase resolved measurements for frequencies above 100Hz can be performed. Thus it can not be determined which phase dominates. Figure 4.25 shows a comparison between the phase averaged electron density in dependence on the distance from the electrode measured at a low (50Hz) and a high (5kHz) frequency for a sinusoidal current. It is shown that the distance from the electrode has a stronger influence on n e in the case of low frequency operation. For distances below 100µm the density is much higher for the low frequency than for the high frequency. At 100µm the density for both frequencies is at the same level and shows a monotonous decrease with a further increas-

104 4.1. Fundamental research at the Bochum model lamp T = K e Distance = ¹m (a) T e 11 x n = m e Distance = ¹m (b) n e Figure 4.23: Phase average of the electron temperature and density along the middle axis of the arc measured at several positions. Parameter: f = 50 Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 4 A, Gas: argon, pressure p = 0.26 MPa ing distance. Figure 4.26 shows a phase resolved measurement of the electron temperature for the switched-dc operation and figure 4.27 for the sinusoidal operation. The first half period represents the anodic phase and the second half the cathodic phase. For the lower frequencies the electron temperature within the cathodic phase is higher than in the anodic phase. For the switched-dc operation directly after the CZC the electron temperature shows a steep increase caused by a stronger constriction of the arc attachment in the beginning of the cathodic phase. Afterwards it adjusts to a constant temperature. For a frequency of 100Hz the temperature difference between anodic and cathodic phase becomes very small. For the sinusoidal operation the electron temperature within the cathodic phase is much

105 82 4. Measurements and results 9000 T = K e anode cathode mean value Frequency = log Hz (a) T e 1.5 x anode cathode n m e / Frequency = Hz (b) n e Figure 4.24: Anodic and cathodic electron temperature and density at a position 62.5µm in front of the electrode tip for various frequencies. For the frequency of 5 and 10 khz no phase resolution is possible. The inscribed values are average values over several ac periods. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 4 A, Gas: argon, pressure p = 0.26 MPa higher than for the switched-dc operation at the same frequency. This is caused by a higher current amplitude in case of the sinusoidal operation. Also the arc is more constricted for the sinusoidal current inducing a higher electron temperature. Generally the values for electron temperature under ac operation differ from those obtained for the dc operation. Especially for higher frequencies the temperatures in front of the cathode are much lower.

106 4.1. Fundamental research at the Bochum model lamp 83-3 n = m e x Distance = ¹m 50 Hz 5 khz Figure 4.25: Phase averaged electron density over distance in front of an ac operated electrode at a frequency of 50Hz and 5kHz. Parameter: electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i = 3 A, Gas: argon, pressure p = 0.26 MPa Electron temperature / K Hz 25Hz 50Hz 100Hz /2¼ ¼ 3/2¼ 2¼ Phase Figure 4.26: Phase resolved electron temperature over one period for various frequencies in a distance of 62.5 µm in front of the electrode. Parameter: f = 10 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, switched-dc with i = 3 A, Gas: argon, pressure p = 0.26 MPa Determination of cathode and anode fall voltage Very important parameters for the characterization of the near electrode region are the anode and cathode fall voltages. They determine the power which is coupled into the boundary

107 84 4. Measurements and results 1.8 x 104 Electron temperature / K Hz 100Hz /2¼ ¼ 3/2¼ 2¼ Phase Figure 4.27: Phase resolved electron temperature over one period for various frequencies in a distance of 62.5 µm in front of the electrode. Parameter: f = 50 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin wave with i = 3 A, Gas: argon, pressure p = 0.26 MPa layers of an electrical discharge. In case of the cathode fall voltage U c this power is responsible for the generation of ions inside the boundary layer which heat up the cathode. Generally two different ways exist to determine the fall voltages. One method are probe measurements as they are performed and described in the work of Luhmann and Lichtenberg [6, 43]. A second possibility is the determination of the cathode fall by measurements of the input power into the electrode and the electron temperature. Afterwards the electrical anode fall can be determined from the measurements of the electrode sheath voltage. In this work the second method is used. Black-Box model of the cathodic boundary layer Within the last years a comprehensive research on the cathodic boundary layer of a dc operated cathode was performed. With the help of the Bochum model lamp it is possible to determine the cathode fall voltage. By probe measurements of the plasma potential, pyrometric measurements of the input power into anode and cathode and spectroscopic measurements of the electron density and electron temperature all necessary data are obtained. Thus a so called Black-Box model of the cathodic boundary layer could be established. This model takes into account the input power into the cathode boundary layer P el = U c I arc as a product of arc current and cathode fall voltage, the enthalpy flux of the electrons from the boundary layer into the plasma ( 5 k B T e ), the power which is necessary to lift the electrons 2 e from the conduction band of the electrode to the vacuum potential φi and the input power

108 4.1. Fundamental research at the Bochum model lamp 85 into the electrode P c,in. The input power into the electrode consists of two parts, the power removed by conduction P cond and the power removed by radiation P rad. In case of an ac operation this model has to be extended to consider the time dependence of some terms of the model. In case of a time dependency the heat capacity of the electrode P hc has to be taken into account. Also the value of the electron temperature T e is now depending on time. Figure 4.28 shows the extended Black-Box model of the cathodic boundary layer for the ac operation. Thus an equation for the power balance of the cathodic boundary layer can be given as: 5 k B T i e arc 2 e iarc Á Black-Box Pel = iarcuc P c,in P loss P hc P rad P cond Figure 4.28: Time dependent Black-Box model of the cathodic boundary layer u c (t)i arc (t) = P c,in (t) + φi arc (t) k B T e (t) i arc (t). (4.3) e If this equation is divided by the arc current i arc (t) a mathematical term for the calculation of the cathode fall arises. u c (t) = P c,in(t) i arc (t) + φ + 5 k B T e (t) 2 e (4.4) Within the previous chapters measurements of all necessary values are presented to calculate values of u c (t). Determination of cathode and anode fall voltage As all input parameters for the calculation of u c are measured phase resolved it is possible to calculate a phase resolved cathode fall voltage as well. One position of special interest is the current maximum in the middle of the cathodic phase for the operation with a sinusoidal current. At this position the change of the electrode temperature is on its minimum and can be neglected in a first approach with dt = 0. Not only this position is of interest in case of a dφ switched-dc operation but now also the end of the cathodic phase is of special interest. For

109 86 4. Measurements and results the low frequency square wave operation the temperature and thus the input power reaches a constant level at the end of the half period. A further interesting position is the CZC from the anodic to the cathodic phase at which the gradient of the temperature ( dt ) has dt its maximum. Figure 4.29 shows the input power into the cathode at the before mentioned positions over frequency for an electrode with a diameter of d E = 1mm. The left figure a) represents an operation with a sinusoidal current and the right one b) with a switched-dc current. For the sinusoidal current the input power in the middle of the cathodic phase Input power / W CZC Middle cathodic phase Frequency = log Hz (a) i RMS = 3 A sin Input power / W CZC Middle cathodic phase End of cathodic phase Frequency = log Hz 10 4 (b) i = 3 A switched-dc Figure 4.29: Input power into the electrode at exposed positions within the cathodic phase, Parameter: f = 10 Hz - 10 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin and square wave with i RMS = 3A, Gas: argon, pressure p = 0.26 MPa decreases with increasing frequency and reaches a nearly constant value for high frequencies. In case of the switched-dc current the input power is nearly constant over frequency as well in the middle of the cathodic phase as at the end of the phase. Due to the small influence of the variation over time the values for the input power can be compared to those gained under DC operation. Dabringhausen [8] measured a loss power at a cathode with the same parameters of approximately 25.5W for a current of i = 3A. This value is comparable to the power calculated for the sinusoidal current. Only for very low frequencies the values are a little bit higher than 30W. For a current of i RMS = 3A the measured values for DC operation are in good agreement with the ac measured values. For the work function φ of the tungsten electrodes a value of 4.55eV can be estimated for electrodes made of AKS material. The name is derived from the additives aluminium, kalium and silicium. The amount of the additives is in the range of ppm. It reduces the dimension of the micro crystals and makes the electrodes a little bit more mechanical flexible compared to pure tungsten. The values for the electron temperature are those shown in figure 4.26 and With these values a calculation of the cathode fall voltage in the middle of the cathodic phase is possible. With the help of the measured electrode sheath voltage afterwards the electrical anode fall voltage can be calculated according to u a,el (t) = ESV (t) u c (t). (4.5)

110 4.1. Fundamental research at the Bochum model lamp 87 The results of this calculation are shown in figure The values for the calculated cathode Voltage / V Voltage / V Cathode fall middle of phase Cathode fall end of phase Anode fall middle of phase Anode fall end of phase 8 6 Cathode fall Anode fall Frequency = log Hz (a) i RMS = 3 A sin Frequency = log Hz (b) i = 3 A switched-dc Figure 4.30: Calculated cathode and anode fall voltage over frequency, Parameter: f = 10 Hz - 10 khz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin and square wave with i RMS = 3A, Gas: argon, pressure p = 0.26 MPa fall voltages seem to be nearly independent of frequency. It demonstrates that at this phase position the time dependency has only a minor influence on u c. The values of about 13V for the sinusoidal current and 14V for the switched-dc current are in the same order of magnitude as the adequate dc values (14V / 15.5V). Very remarkable is the subsequent anode fall voltage in dependence on frequency. In the work of Langenscheidt [39] the fall voltages for a switched-dc current with the same electrode parameters at a frequency of 100Hz were determined by probe measurements. The cathode fall was measured with approximately 18V and the anode fall with 2V. Thus the value of the cathode fall is higher than the one measured in this work and the anode fall is lower. The deviations may be explained in part by the different ways of measurements and the possibly occurring errors. The measurements at switched-dc show a clear increase of the anode fall voltage with increasing frequency. It reflects the increase of the ESV with increasing frequency. For the sinusoidal current this effect is even more pronounced. This increase is caused by the adjustment of the ESV to a sinusoidal waveform with increasing frequency and a unchanged cathode fall voltage which is nearly independent of frequency. In case of the switched-dc current the ESV increases only marginally. It corresponds to the less pronounced increase of the anode fall. The other interesting phase position is that at CZC for a sinusoidal operation. At this position a determination of the fall voltages is not possible. It should be zero according to the current. For a current with the value of i = 0A equation 4.6 becomes 0 = P e,in (t). (4.6) As figure 4.29 shows, the input power into the electrode does not become zero at the current zero crossing. One explanation would be erroneous measurements of the electrode temperature and the subsequent simulation of the input power. Within the temperature measurements a limitation of the phase resolution due to the minimum exposure time of the camera

111 88 4. Measurements and results is given. Thus a measurement at the CZC is always an integration over the exposure time. If these measurements are inserted into the simulation and the value for dt is calculated the dϕ resolution at the CZC is limited. This may be important as P e,in consists of the conducted power, the radiated power and the heat capacity according to P e,in = P cond + P rad + P hc, (4.7) with P hc = ω Q hc ϕ. (4.8) Q hc is the heat content of the cathode and P hc its variation with time. In case of i = 0A the variation of the heat content should compensate the terms for the radiated power and the conducted power. But even with an artificial variation of P hc, P e,in only becomes zero if the measured value for dt is increased by more than a factor of 3. Since this is much dφ more than the possible measuring error there must be another explanation for the remaining power which is coupled into the electrode during CZC. An explanation may be a power transfer from the plasma to the electrode. This implies that during the CZC the electrode is heated by the plasma. This may be possible since a certain energy is stored in the plasma respectively in the plasma sheath. This energy can be described by an additional term in the power balance of a periodically charged electrode Q c,pl for a cathode respectively Q a,pl for an anode. The following model for the cathodic and anodic boundary layer is mainly based on the model developed by Lichtenberg [7, 43]. For a cathode the power coupled from the plasma boundary layer into the cathode can be written as follows: q p = q rec + q kin + q neutral + q em + q ep + q tc. (4.9) q p denotes the total power coupled from the cathodic boundary layer into the cathode. Recombination at the electrode surface If an ion hit the electrode surface it may recombine with an electron which is released from the electrode. In that case the ionization energy E i = eu i is released. The electron which is released exhibits the negative energy eφ within the quantum well of the cathode. The energy which is transferred to the cathode is the difference between both terms: q rec = j i (U i φ) (4.10) This effect only takes place at the electrode surface. Thus it is not field enhanced and the SCHOTTKY reduction must not be considered. Kinetic energy of the ions The major part of the power flux density is carried by the ions which bombard the cathode surface. The ions are accelerated within the cathodic boundary layer towards the cathode

112 4.1. Fundamental research at the Bochum model lamp 89 and transfer their kinetic energy to the cathode if they hit the electrode surface. This energy is a loss term for the boundary layer [44, 45]. [ ( kb T e q kin = j i U kin = j i T ) ] h + U s (4.11) e T e The term proportional to T e represents the kinetic energy of the ions at the sheath edge. U s is the voltage drop within the space charge layer which additionally accelerates the ions. Thermal energy fluxes Next to the energy fluxes described above the energy fluxes caused by the thermal energy of the particles have to be considered. The neutrals produced by the recombination of ions with electrons from the electrode transport energy backwards into the sheath by diffusion. This enthalpy flux is determined by the cathode temperature T c since a contact of the neutrals with the cathode surface is assumed. q neutral = j i 2k B T c e (4.12) Electrons which are emitted thermionically from the electrode have to overcome the work function φ of the electrode material. This work function may be reduced by an amount φ caused by the SCHOTTKY effect as described in chapter The electrons which overcome the work function withdraw the energy 2k B T c /e from the cathode. ( q em = j em φ φ + 2k ) BT c (4.13) e The electrons which compose the electron back diffusion current obey reversal processes. If they enter the cathode the energy e(φ φ) is released. Additionally they transport the enthalpy 2k B T e /e to the electrode. ( q ep = j ep φ φ + 2k ) BT e (4.14) e Another energy flux which must be taken into account is the heat transfer from the heavy particles in the boundary layer to the cathode. It is represented by the temperature difference T h T c between the particles and the cathode and an empirical heat transfer coefficient α. q tc = α (T h T c ) (4.15) These terms can now be inserted into equation 4.9 together with the definition of the total current density j = j em +j i j ep. This results in the following expression for the power being coupled into the cathodic boundary layer q p = jφ + j i ( U i + U kin 2k BT c e ) 2k B T c 2k B T e + (j em j ep ) φ j em + j ep + α (T h T c ). e e (4.16) Furthermore an expression for the power balance of the electrons and heavy particles inside the boundary layer can be given. For the electrons this expression becomes (j em j ep )(U c Φ) + j em 2k B T e e = j i U i + j ep 2k B T e e + ju ee + q c,e t (4.17)

113 90 4. Measurements and results with U ee = ( n ) e kb T e 0.7 n i + n a e. (4.18) The power input into the sheath by electrons is given on the left hand side, the power loss and the increase of their energy content on the right hand side [43]. The subsequent expression for the heavy particles is j i U c + j i 2k B T c e = j i U kin + α (T h T c ) + q c,h t. (4.19) q c,e and q c,h are the terms for the heat content of the electrons and heavy particles in the boundary layer per unit of area. Both terms can now be combined to a total power balance of the boundary layer. q c,e and q c,h can be combined to one expression for the heat content of the boundary layer q c,pl. Inserting the expression for the total power balance into equation 4.16 yields In the integral form the power balance can be written as q p = j (U c φ U ee ) q c,pl t. (4.20) P c,in = i (U c φ U ee ) Q c,pl t = i (U c φ U ee ) ω Q c,pl ϕ = P rad + P cond + P hc (4.21) Now the special case of i = 0 at the current zero crossing will be considered. In this case the following assumptions are valid: j = j em + j i j ep = 0 j i = 0 u c = 0 j em = j ep With these restrictions equation 4.20 becomes q p (j = 0) = ω q c,pl ϕ = j em ( 2kB T e e 2k ) BT c + α (T h T e ) > 0 (4.22) e if equation 4.16 is taken into account. The integral form of equation 4.22 is ( 2kB T e P c,in = j em e A 2k ) BT c da + α (T h T e ) da. (4.23) e A Thus a term for the heat transfer from the cathodic plasma sheath is left. This energy is available for a heating of the electrode during the current zero crossing.

114 4.1. Fundamental research at the Bochum model lamp 91 For the anodic boundary layer an expression for the power balance in case of an ac operation can be given as well. The power flux density from the anodic boundary layer to the anode can be written according ([4], equation(16)) to the procedure at the cathode as q a =j ( Φ + 2k ) ( BT e,s + j i U i + U kin + 2k BT e,s e e ) + j em ( 2kB T e,s e 2k BT a e 2k ) BT a e + α (T h T a ) (4.24) Similar to the cathodic boundary layer a power balance for the electrons in the anodic sheath can be established according to ([4], equation(10)) j ep j em j i e ( ) ξ k B T e,s + p e + j em e 2k BT a = (j ep j em ) U a,s + j ep e 2k BT e,s + j i U i. (4.25) p e represents the additional power supply from the constriction zone to the electrons in the sheath. A rearrangement of equation 4.25 and a substitution of j ep by j yields ( j U a,s U ee + 2k ) ( BT e,s =p e j i U i + U a,s + 2k ) BT e,s e e ( 2kB T e,s + j em 2k ) BT a q a,e e e t. (4.26) The power balance for the heavy particles in the anodic sheath reads([4], equation (12)) With the definition of j i U a,s + p h + j i 2k B T a e = j i U kin + α (T h T a ) q a,h t. (4.27) p pl = p e + p h (4.28) q a,s t = q a,e t + q a,h t (4.29) equation 4.26 together with equation 4.27 can be inserted into the equation for q a. q a,s is the heat content of the anodic boundary layer per unit area. q a = j (φ + U ee U a,s ) + p pl q a,s t (4.30) is now the power input per unit area within the anodic phase into a periodically charged electrode ([4], equation (16)). The integral form of the power input can be written as P a,in = I (φ + U ee U a,s ) + P pl Q a,s. (4.31) t An alternative is obtained by an integration of equation ( P a,in = I φ + 2k ) BT e,s + P a,in (4.32) e

115 92 4. Measurements and results with P a,in = + A A j em ( 2kB T e,s e 2k ) BT a da e ( j i U i + U kin + 2k BT e,s 2k BT a e e A ) da + α (T h T a ) da. (4.33) A If now i = 0A in case of the current zero crossing the anodic power balance becomes ( 2kB T e,s P a,in = j em 2k ) BT a da + α (T h T a ) da (4.34) e e The power which is transferred to the electrode during the current zero crossing may be generated by thermionically emitted electrons from the hot anode. These electrons enter the plasma in front of the anode, are heated up and return to the electrode with an increased thermal energy. Thus the electrode is heated even during the CZC. Figure 4.31 presents a phase resolved measurement of the electrode input power. During the current zero crossing the input power into the electrode is about 9 W. This power may be transferred from the plasma boundary layer to the electrode A Input power / W Hz 50Hz 500Hz 9 0 1/2¼ ¼ 3/2¼ 2¼ Phase Figure 4.31: Input power into the electrode over one period for different frequencies. Parameter: f = 25 Hz Hz, electrode diameter d E = 1 mm, electrode length l E = 20 mm, sin-wave with i RMS = 1A, Gas: argon, pressure p = 0.26 MPa

116 4.2. YAG lamp results YAG lamp results In chapter the specifications of the YAG lamps are described and their differences from the model lamp. Especially by the addition of the several filling components their behavior is different compared to the model lamp. Also the operating parameters, e.g. pressure and current, are in another order of magnitude than in the model lamp. Thus the results obtained at the model lamp can not be transferred directly to the YAG lamps. The different operating parameters and the additional ingredients may cause other or additional effects if the operating frequency is varied. Due to the higher pressure and the smaller volume of the discharge vessel acoustic resonances occur within various frequency regions. An operation of the YAG lamps being investigated undisturbed by acoustic resonances is possible in the following frequency bands: f = Hz f = 23.2kHz f 300kHz. Operating the YAG lamps outside of these frequency regions causes instabilities of the arc attachment, arc bowing or straightening or may result in an extinguishing of the lamp. In some cases it may even cause a destruction of the lamp vessel. For frequencies of 23kHz and higher the lamps are always operated with a sinusoidal current because the setup is not able to provide a switched-dc current. This chapter describes the behavior of the YAG lamps depending on the operating frequency. A main focus is put on the influence of the frequency on the gas phase emitter effect [46, 9, 22] of dysprosium Pure Hg YAG lamps YAG lamps with a pure Hg filling without any rare earths or metal halides are preferred for a comparison with results obtained at the model lamp. In these lamps unforseen effects of the plasma should not occur which are caused by the additives. The pure Hg lamps are the most simple types of YAG lamps. Figure 4.32 shows images of the arc attachment at the upper pure Hg YAG lamp electrode. In 4.32 a) phase resolved images are presented over one period. The first five images represent the anodic phase and the last five images the cathodic phase. For the current and frequencies being chosen the arc attachment is always diffuse. For the low frequency of 50Hz a change in the intensity of the plasma can be observed in front of the electrode with polarity. In the cathodic phase the intensity in front of the electrode is higher than in the anodic phase. It may by caused by the ions which are transported towards the cathode. For the higher frequency of 1kHz the difference decreases between the intensity within the anodic and cathodic phase. This effect is even more pronounced in figure 4.32 b). The images are recorded at the end of the anodic and cathodic phase for various frequencies. No change in the kind of arc attachment can be observed for the anodic phase. Only in the cathodic phase a decrease of the intensity of the plasma is visible with increasing frequency. In contrast to the model lamp the images do not allow a conclusion on the electrode temperature. But as figure 4.33 a) implies a heating of the electrode during the anodic phase and a cooling during the

117 94 4. Measurements and results 50 Hz 1 khz anode (a) Phase resolved images cathode 1 Hz 10 Hz 25 Hz 50 Hz 100 Hz 250 Hz 500 Hz 1 khz Anode Cathode (b) Images over frequency Figure 4.32: Images of arc attachment at a pure Hg YAG lamp. a) Phase resolved images over one period at a low and a high frequency. b) Image of the anodic and cathodic arc attachment for various frequencies. Parameter: Hg, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc cathodic phase occurs. With increasing frequency the electrode temperature is fixed to a constant value independent on time for a frequency of 100Hz. As expected this frequency is lower than at the model lamp due to the smaller dimensions and lower heat capacity of the electrodes. This value is above the cathode temperature for low frequencies but clearly below the anode temperature. The results obtained at the model lamp (see figure 4.7 c))for the same operating parameters (anodic heating) show the same behavior. Thus the adjustment of the electrode temperature to a stationary value independent on time and the absolute level seem to be independent of the mercury filling, the gas mixture or pressure. This effect is even proved by the results shown in figure 4.34 for a sinusoidal current. The current signal shows a heating during anodic and cathodic phase. For the current being chosen the heating during the cathodic phase is higher than during the anodic phase. With increasing frequency the difference between the lowest and highest temperature decreases which occurs during one rf period. Additionally the mean temperature during one phase seems to increases with increasing frequency, too. A direct comparison with the results obtained at the model lamp is impossible due to the acoustic resonances which occur for frequencies 3500Hz, but the trend seems to be the same. Additionally the mercury temperature is measured spectroscopically as described in chapter Figure 4.35 shows the mercury temperature measured within one period in a distance of 125µm in front of the upper electrode for various frequencies. Measurements in the vicinity of the current zero crossing are very complicated for the sinusoidal current due to the strong decrease of the Hg line emission. With increasing frequency the intensity remains at a higher level and the results of the measurements become more trustable. However the results are generally trustable within the grey marked area. The mercury temperature is nearly unaffected by changes of the frequency within the grey marked area. Absolute temperature changes in the trustable area are smaller than the

118 4.2. YAG lamp results Tip temperature / K Hz 10Hz 25Hz 50Hz 100Hz 250Hz 500Hz 1kHz Input power / W Hz 10Hz 25Hz 50Hz 100Hz 250Hz 500Hz 1kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) Tip temperature /2¼ ¼ 3/2¼ 2¼ Phase (b) Electrode input power Figure 4.33: Electrode tip temperature and input power over one period for various frequencies. Parameter: Hg, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, i = 0.8A switched-dc Tip temperature = K Hz 250Hz 500Hz 1000Hz 2000Hz /2 ¼ ¼ 3/2 ¼ 2 ¼ Phase Figure 4.34: Electrode tip temperature of a Hg YAG lamp over one period for various frequencies. Parameters: Hg, current i = 0.8A sin wave, electrode diameter d E = 0.45mm possible measuring error. Only within the non trustable region of CZC an increasing Hg temperature occurs with increasing frequency. It should be mentioned that the mercury temperatures within the anodic and cathodic phase are nearly the same. Figure 4.36 presents the mercury temperature within one ac period for various distances z from the electrode surface for two frequencies. For the low frequency (50 Hz) a decrease of the Hg temperature is measured until a distance of 1mm is reached. For the high frequency a decrease with increasing distance is observed which is more pronounced. The change is about 500K for the low frequency and nearly 900K for the high frequency. The results obtained at the YAG lamps without any additives show a quite similar behavior compared to those obtained at the model lamp. Thus the transfer of fundamental results from the model lamp to YAG lamps is justified.

119 96 4. Measurements and results 7500 Hg temperature = K Hz 250Hz 500Hz 1000Hz 2000Hz /2 ¼ ¼ 3/2 ¼ 2 ¼ Phase Figure 4.35: Mercury temperature of a Hg YAG lamp over one period for various frequencies measured in a distance of 122µm in front of the electrode surface. Parameters: Hg, frequency f = 125 Hz - 2 khz, current i = 0.8A sin wave, electrode diameter d E = 0.45mm, electrode length l E = 5 mm Hg temperature = K z = 125 m z = 250 m 5500 z = 500 m z = 1000 m z = 2500 m /2 ¼ ¼ 3/2 ¼ 2 ¼ Phase (a) 50 Hz Hg temperature = K /2 ¼ ¼ 3/2 ¼ 2 ¼ Phase (b) 2 khz Figure 4.36: Mercury temperature of a Hg YAG lamp over one period for various distances z and two operating frequencies. Parameter: Hg, frequency f = 50 Hz / 2 khz, electrode diameter d E = 0.45 mm, electrode length l E = 5 mm, i = 0.8A sin wave YAG lamps with MH fillings Arc attachment Now YAG lamps are investigated with different kind of fillings. Similar to the model lamp the optical observations of the arc attachment show, that the spot attachment vanishes for higher operating frequencies. Figure 4.37 shows a phase resolved observation of the arc attachment at a frequency of 23kHz. For this frequency 10 pictures are recorded over one period. For more pictures the exposure time becomes too short to get enough intensity for a clear image of the arc attachment. The differences between the optical appearance of the anodic and

120 4.2. YAG lamp results 97 anode cathode Figure 4.37: Arc attachment over one rf period for a YAG lamp. First five images are taken in the anodic phase, images 6-10 in the cathodic phase. Parameters: NTD1, frequency f = 23kHz, current i = 0.6A, electrode diameter d E = 0.36mm, exposure time t exp = 4µs cathodic phase vanishes as figure 4.37 shows. Even within the anodic and cathodic phase the differences are not very pronounced between the pictures. In figure 4.38, images for a frequency series are shown with an exposure time of t exp = 10µs. The images represent the arc attachment within the frequency range from 400kHz to 1MHz. The arc attachment is always a diffuse attachment for these parameters. In general for higher frequencies the attachment tends to be diffuse. Thus the conclusion which is drawn in the case of the model lamp can be transferred to the YAG lamps even if they contain a more complex filling (NTD1). For the YAG lamps the heat capacity of the electrodes is reduced compared to the model lamp due to the smaller dimensions of the electrode. Thus the time constants for the YAG lamps should get shorter and the appearance of a spot mode becomes less improbable. Contrary to these conclusions for some measurements a spot mode occurred in YAG lamps different to the tendency at a frequency of 23kHz. This spot mode is not reproducible and can not be associated with certain lamp parameters. Up to now a systematic investigation of this spot attachment is impossible. It is clearly demonstrated in figure 4.38 that the arc attachment does not change with increasing frequency. At high frequencies, pictures are taken with an exposure time which is longer than a few periods of the rf cycle. This does not matter since it is shown before (figure 4.37) that at high frequencies the differences vanish between the anodic and cathodic arc attachment. For lower frequencies from 1Hz to 2000Hz a change of the arc attachment is visible. It does not necessarily imply a mode change from a spot to a diffuse attachment but the intensity of the arc itself and the level of constriction change. Figure 4.39 shows phase resolved images of a NTD1 lamp for various frequencies. All images are scaled consistently to an equal global minimum and maximum intensity value. Thus the intensities, represented by the color, are directly comparable. The first five images in every line show the anodic and the last five images the cathodic phase. For a frequency of 1Hz a diffuse attachment is visible in the anodic phase, covering homogenously the whole electrode tip surface. In the cathodic phase the attachment changes to a spot attachment indicated by the strong constriction and the high local intensity. With increasing frequency the arc attachment in the anodic phase remains diffuse but the constriction of the arc increases. In the cathodic

121 98 4. Measurements and results 400kHz 420kHz 440kHz 460kHz 480kHz 500kHz 520kHz 540kHz 560kHz 580kHz 600kHz 620kHz 640kHz 660kHz 680kHz 700kHz 720kHz 740kHz 760kHz 780kHz 800kHz 820kHz 840kHz 860kHz 880Hz 900kHz 920kHz 940kHz 960kHz 980kHz 1000kHz Figure 4.38: Arc attachment for a YAG lamp in a frequency range from kHz. Parameters: NTD2, current i = 0.6A, electrode diameter d E = 0.36mm, exposure time t exp = 10µs phase the arc attachment remains constricted but the intensity drops down significantly. At a frequency of 2kHz the arc attachment changes to a strongly constricted attachment in the anodic phase. It is remarkable that for frequencies above 500Hz the difference of the corresponding intensities vanishes between anodic and cathodic phase. Electrical measurements For the YAG lamps measurements of the arc voltage and current are performed with V/I probes directly at the lamp socket. In contrast to the model lamp electrical measurements of the ESV in YAG lamps are impossible as the YAG lamps are a closed system without movable electrodes. Figure 4.40 a) and 4.40 b) show the arc voltage at frequencies of 100Hz and 600kHz for various sinusoidal currents. For the low frequency the maximum of the arc voltage occurs directly after the current zero crossing. At this moment the current is relatively low. After the voltage reaches its maximum it decreases over the rest of the half period. For the higher frequency the arc voltage shows a sinusoidal wave form with a maximum at the middle of the half cycle. For both frequencies the effect of the current amplitude on the arc voltage is marginal. For the low frequency a small change in the maximum of the voltage is visible

122 4.2. YAG lamp results 99 1 Hz 10 Hz 25 Hz 50 Hz 100 Hz 250 Hz 500 Hz 1 khz 2 khz Anode Cathode Figure 4.39: Arc attachment for a YAG lamp in a frequency range from Hz. Image 1 5 represent the anodic phase, image 6 10 the cathodic phase. All images are scaled to one global minimum/maximum value. Parameters: NTD1, current i = 0.6A switched-dc, electrode diameter d E = 0.36mm after current zero crossing. For the high frequency no change occurs in the arc voltage. The different course of the arc voltage for different frequencies could be observed at the model lamp, too. It is demonstrated in chapter Figure 4.41 shows the course of the arc voltage over one period for various frequencies. With rising frequency the maximum of the arc voltage is shifted towards the middle of the half period and adopts more and more a sinusoidal waveform. Simultaneously the phase shift between voltage and current approaches zero. A comparison is interesting between the course of the arc voltage in a frequency region for 3.5kHz and 300kHz. At a frequency of 3.5kHz the course of the voltage adopts a shape which is close to a sinusoidal waveform but its maximum is not in the middle of the half period. A comparison of the amplitudes shows that the arc voltage is approximately 20V higher for the high frequency. With a constant current this implies an increase of the input power as it is observed at the model lamp, too. Figure 4.42 shows the input power in dependence on frequency. To calculate the values for the lamp input power, current and voltage of the same phase are multiplied. Afterwards absolute values of the power p(ϕ) are computed, finally a mean value of the power is derived over one ac period. It becomes visible that with increasing frequency the input power into the lamp increases until it reaches a constant level for very high frequencies. At this position the arc voltage gains a sinusoidal waveform with the maximum in the middle of the half period.

123 Measurements and results Arc voltage / V A 0.6A 0.7A 0.8A 0.9A Arc voltage / V A 0.6A 0.7A 0.8A 0.9A /2¼ ¼ Phase 3/2¼ 2¼ (a) f = 100Hz /2¼ ¼ Phase 3/2¼ 2¼ (b) f = 600kHz Figure 4.40: Arc voltage over one period for various currents. Parameter: NTD1, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, sin wave Arc voltage / V Hz 500Hz 1kHz 3.5kHz 23kHz 300kHz 600kHz Arc voltage / V Hz 500Hz 1kHz 3.5kHz 23kHz 300kHz 600kHz /2¼ ¼ 3/2¼ 2¼ Phase (a) i = 0.5A /2¼ ¼ 3/2¼ 2¼ Phase (b) i = 0.8A Figure 4.41: Arc voltage over one period for various frequencies. Parameter: NTD1, electrode diameter d E = 0.36 mm, electrode length l E = 5 mm, sin wave For a switched-dc current theses measurements are possible up to a frequency of 2000Hz. In chapter the current signal is shown and the problems which occur with increasing frequency. Since the commutator of the power supply can not provide the current fast enough the current signal reaches its amplitude only in the middle of a half period. This causes a lower input power into the discharge and affects the electrode temperature since the power is mainly determined by the arc current. Only a marginal influence on the arc voltage is observed until a frequency of 2000Hz. It can be neglected since it shows no influence on the lamp input power.

124 4.2. YAG lamp results Lamp input power / W Frequency = log Hz 0.5A 0.6A 0.7A 0.8A 0.9A Figure 4.42: Input power into a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm Electrode temperature and power investigations In the previous chapter the influence of the operating frequency is shown on the lamp input power. For the model lamp this increase could be connected with the electrode temperature and the input power into the electrodes. For the YAG lamps this is not directly possible as the following results will show. Figure 4.43 gives the mean electrode tip temperature in dependence on frequency in a frequency range from 200Hz up to 600kHz. The decrease of the average electrode tip temperature with increasing frequency up ot a value of Hz is quite remarkable. Afterwards the temperature starts to increase with a further increase of frequency. This observation is contrary to the results gained at the model lamp. At the model lamp the tip temperature continuously increases with increasing frequency. The course of the tip temperature in the frequency region below 3500Hz is also contrary to the course of the input power shown in figure For the higher frequencies the observations correlate. With increasing input power the tip temperature increases, too. The YAG lamps are a much more complex system compared to the model lamp. Therefore the reason for this different behavior can be found in one of the additional plasma processes occurring in the YAG lamps. The most probably process is the gas phase emitter effect caused by the dysprosium inside the lamp. This effect and the influence of the frequency on it is described extensively in chapter The course of the phase average input power into the electrodes in dependence on frequency is similar to the course of the phase averaged electrode tip temperature since mean temperatures distributions are used for the analysis. Figure 4.44 shows the resulting power input. For the lower currents the minimum power already occurs at a frequency of 1000Hz. Afterwards the input power starts to increase for frequencies above 3500Hz.

125 Measurements and results Tip temperature / K Frequency = log Hz 0.5A 0.6A 0.7A 0.8A 0.9A Figure 4.43: Electrode tip temperature of a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm 5 Input power / W Frequency = log Hz 0.5A 0.6A 0.7A 0.8A 0.9A Figure 4.44: Electrode input power of a NTD1 YAG lamp over frequency for various currents. Parameters: NTD1, current i = A sin wave, electrode diameter d E = 0.36mm Gas phase emitter effect The gas phase emitter effect is briefly described in chapter A more detailed description of this effect can be found in the work of Langenscheidt [9] for the ac operation and Luijks [46] for the dc operation. Both put their main focus of investigations on the emitter effect at low frequencies in the cathodic phase. The maximum frequency investigated by Langen-

126 4.2. YAG lamp results 103 scheidt is 100Hz. In this work the investigations are extended to higher frequencies and most of the measurements are performed phase resolved. Thus the investigations now include measurements within the anodic phase. In the work of Langenscheidt [9] YAG lamps with different types of fillings, mainly NTD1 and NTD2, have been used for the investigations. As the different filling components interact and thus a clear assignment of special effects to one element is impossible, now mainly lamps are investigated with a pure DyI filling. State of research For the characterization of the gas phase emitter effect it is necessary to observe the connection between the Dy atom and ion density and the electrode tip temperature respectively the input power into the electrodes. Langenscheidt did this by so called mappings of the ceramic metal halide lamps. The mappings include information about the arc attachment, tip temperature, power loss of the electrodes and the Dy atom density. Furthermore the amount of Dy in the discharge is influenced by a cooling of the cold spot of the YAG lamps. Additionally to the mappings, which were performed only in the cathodic half period, phase resolved measurements were made for frequencies up to 100Hz. The results show that in case of an ac operation the emitter effect of Dy is lower than in the case of dc operation. The formation of the atomic monolayer of Dy on the cathode surface cannot fully take place as if it is removed during the anodic phase. Also sodium with a lower ionization energy than Dy shows a strong influence on the Dy layer deposited on the electrode surface. As the mass of sodium is lower than the mass of dysprosium it is transported faster towards the cathode than dysprosium. Also the amount of Na inside the lamps is nearly 10 times higher than of Dy. These differences result in a reduced ionization of Dy and thus a lower ion current of dysprosium towards the electrode. The measurements with a cooling of the cold spot of the YAG lamp showed that for a certain Dy atom density in front of the electrode the emitter effect of Dy has an optimum degree of efficiency. This can be shown since for a distinct amount of Dy atoms the electrode gains a minimum tip temperature. For lower and higher Dy densities the electrode tip temperature starts to increase. Also the term emitter spot is introduced. The emitter spot occurs at operating parameters for which without emitter material a diffuse attachment is present. This is shown in the work of Langenscheidt [35]. But the emitter spot can not be compared with a normal spot attachment. Figure 4.45 shows three spot attachments in YAG lamps with different fillings. One lamp has a NT filling without dysprosium, the second is a NTD1 lamp and the third a lamp with a pure DyI filling. For all lamps a spot attachment is present at a frequency of 50Hz in the cathodic phase. The images are all scaled to one global maximum and minimum value for the intensity. Thus the intensities are comparable between the images. For the NT lamp the highest intensity can be observed. For the NTD1 lamp the intensity is reduced and the lowest intensity occurs for the pure DyI lamp. Thus the maximum intensity decreases with an increasing amount of dysprosium inside the lamp. The spot in the lamp with the pure DyI filling only shows half of the intensity of the spot inside the NT lamp. Different to the other examples, which show a spot on the edge, the spot is in the center of the electrode endface. The left column of images is plotted with an alternating look-up table. It visualizes

127 Measurements and results NT NTD1 DyI I max;nt I max;ntd1 I max;dyi Figure 4.45: Images of cathodic arc attachment for different YAG lamp types. The left column shows images with an alternating look-up table and the right column image which are scaled to one global minimum/maximum value. Parameters: NT, NTD1, DyI, frequency f = 50Hz, current i = 0.6A switched-dc, electrode diameter d E = 0.36mm the gradient of the intensity which is very high for the NT lamp and decreases with an increasing amount of Dy. Emitter effect in pure DyI lamps As it is mentioned in the previous section the Dy needs a certain time to create the monolayer on the electrode surface to evolve its full effect. There are several effects inside a YAG lamp