MONTE CARLO SIMULATION OF RADIATION TRAPPING IN ELECTRODELESS LAMPS: A STUDY OF COLLISIONAL BROADENERS*

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1 MONTE CARLO SIMULATION OF RADIATION TRAPPING IN ELECTRODELESS LAMPS: A STUDY OF COLLISIONAL BROADENERS* Kapil Rajaraman** and Mark J. Kushner*** **Department of Physics ***Department of Electrical and Computer Engineering Urbana, IL rajaramn@uiuc.edu mjk@uiuc.edu May 2002 * Work supported by Osram Sylvania Inc., EPRI and the NSF

2 AGENDA Radiation transport in low pressure plasmas Overview of the Hybrid Plasma Equipment Model The Monte Carlo Radiation Transport Model Base case Variation of plasma parameters and trapping factors with buffer gas Importance of resonance broadening Conclusions ICOPS02_KAPIL_01

3 ELECTRODELESS LAMPS AND TRAPPING Electrodeless gas discharges are finding increasing use in the lighting industry due to their increased lifetime. Investigations are underway to increase the efficiency of these lamps, now 25%. Typical fluorescent lamps consist of Ar/Hg 97/3. Resonance radiation from Hg (6 3 P 1 ) (254 nm) and Hg (6 1 P 1 ) (185 nm) excites phosphors which generate visible light. This resonance radiation can be absorbed and reemitted many times prior to striking the phosphor, increasing the effective lifetime of emission as viewed from outside the lamp. Control of radiation trapping is therefore an important design consideration for these lamps. ICOPS02_KAPIL_02

4 MONTE CARLO METHODS FOR RADIATION TRANSPORT Historically, characterization of trapping has been done by using analytical solutions of the Holstein equation in simplistic geometries. However, Monte Carlo methods are desirable for complex geometries where it is difficult to evaluate propagator functions. We have developed a Monte Carlo radiation transport model (MCRTM) for the radiative transitions of mercury. The model incorporates the effects of Partial Frequency Redistribution (PFR) and quenching of excitation, using a Voigt profile for emission and absorption. However, one needs a self-consistent plasma model to account for evolution of gas densities, temperatures and other plasma parameters. To address this need, the MCRTM is interfaced with the Hybrid Plasma Equipment model (HPEM) to realistically model the gas discharge. ICOPS02_KAPIL_ 03

5 HYBRID PLASMA EQUIPMENT MODEL A modular simulator addressing low temperature, low pressure plasmas. EMM: electromagnetic fields and magneto-static fields EETM: electron temperature, electron impact sources, and transport coefficients FKM: densities, momenta, and temperatures of charged and neutral plasma species; and electrostatic potentials ELECTRO-MAGNETIC MODULE (EMM) V, N E,B ELECTRON ENERGY TRANSPORT MODULE (EETM) S, Te, µ FLUID KINETICS MODULE (FKM) N, T, P, ki krad MONTE CARLO RADIATION TRANSPORT MODEL (MCRTM) ICOPS02_KAPIL_04

6 MONTE CARLO RADIATION TRANSPORT MODEL (MCRTM) Monte Carlo method is used to follow trajectories of photons from initial emission to escape from plasma. The absorption/emission lineshape function is a Voigt profile. MC photons are generated in proportion to the excited atom density at each point in the plasma. We define the trapping factor as k = τ res τ, nat where τ res is the average residence time of the photon in the plasma, and τ nat is the natural lifetime of the excited state. It can be seen that the trapping factor depends on the emitter density and absorber density profiles as well as parameters defining the Voigt profile (e.g. T gas, N broadeners ). ICOPS02_KAPIL_ 05

7 Rg + e Rg* + e Rg + e Rg + + 2e Rg* + e Rg + + 2e Rg* + e Rg + e Hg + e Hg* + e Hg + e Hg + + 2e Hg* + e Hg + e Rg* + Rg* Rg + + Rg + e Rg* + Hg Hg + + Rg + e Rg* + Hg* Hg + + Rg + e Rg + + Hg Hg + + Rg Rg + + Hg* Hg + + Rg Rg + + Rg Rg + Rg + Hg + + Hg Hg + Hg + Hg* + Hg* Hg + + Hg + e Rg* Rg + hν Hg* Hg + hν Ionization potentials: REACTION CHEMISTRY 6 1 P1 185 nm 1.33 ns Hg+ 6 3 P2 6 3 P1 6 3 P0 254 nm 125 ns 6 1 S0 He 24.5 ev Ne 21.5 ev Ar 15.7 ev Xe 12.0 ev ICOPS02_KAPIL_06

8 BASE CASE CONDITIONS Diameter 9 cm 8 Height 8 cm Initial pressure 500 mtorr Initial temperature 400 K Power 50 W Frequency 2.65 Mhz Initial rare gas mole fraction 0.98 Initial Hg mole fraction (ground state) 0.02 Height (cm) Reentrant cavity Outer wall Induction coil Ferrite core Only the 185 nm transition has been studied. ICOPS02_KAPIL_ Radius (cm)

9 ARGON The power is deposited near the antenna, leading to a maximum electron temperature near the coil, and an electron density in an annulus round the antenna. W cm -3 1 x Power density ICOPS02_KAPIL_08 1 x ev T e 5 x x cm -3 n e, [Hg+]

10 ARGON Cataphoresis and gas heating leads to a maximum of [Hg*] near the walls. cm -3 3 x x 10 8 [Ar+] cm -3 5 x x [Hg] 5 x x cm-3 [Hg*] ICOPS02_KAPIL_09

11 POWER DEPOSITION Due to the large momentum transfer cross-section of Xe, most of the power is deposited near the antenna. W cm -3 1 x Ne W cm-3 1 x Ar 1 x Xe W cm-3 ICOPS02_KAPIL_10

12 ELECTRON TEMPERATURE Xe and Ar are Ramsauer gases unlike Ne. Also, the excited state thresholds of the noble gases are different, leading to different degrees of ionization. ev Ne ICOPS02_KAPIL_11 1 x ev Ar ev Xe

13 ELECTRON DENSITY Due to the lower ionization potential for Xe (12.0 ev), the electron density is lowest for the Xe case. cm -3 1 x x Ne cm -3 9 x x Ar 3 x x cm -3 Xe ICOPS02_KAPIL_12

14 MERCURY ION DENSITY In the cases of Ne and Ar, [Hg+] maps n e, but the larger mass of Xe does not allow [Hg+] to move to the upper part of the lamp. cm -3 1 x x Ne cm-3 5 x x Ar 5 x x cm-3 Xe ICOPS02_KAPIL_13

15 MERCURY GROUND STATE DENSITY In the case of Xe, there is more depletion of Hg from the center of the column, because more power is deposited in that region. cm-3 8 x x Ne cm -3 5 x x Ar 1.5 x x cm -3 Xe ICOPS02_KAPIL_14

16 MERCURY EXCITED STATE DENSITY In cases of Ne and Xe, we do not see the peak in [Hg*] near the outer wall because of the smaller [Hg*] density in these cases. cm -3 4 x x Ne cm-3 5 x x Ar 1 x x cm-3 Xe ICOPS02_KAPIL_15

17 VOLUME AVERAGES The volume averages for some plasma parameters of the lamp are shown here Ar has the largest [Hg*] density as well as the largest [Hg*]/[Hg] ratio. ne (cm -3 ) He Ne Ar Xe [Hg*] (cm -3 ) [Hg*] / [Hg] He Ne Ar Xe 10-5 He Ne Ar Xe ICOPS02_KAPIL_16

18 TRAPPING FACTORS Even though the Xe case has a lower trapping factor, the lower emitter density in that case results in a lower radiative output. At higher pressures of 1 Torr, Ne as a buffer gas has a better radiative output as well as a lower trapping factor. However, almost all the light is emitted near the inside of the lamp, and may not be all that useful. 250 TRAPPING FACTOR Ne Ar Xe Intensity (arb. units) Ne Ar Xe PRESSURE (Torr) ν - ν 0 (GHz) ICOPS02_KAPIL_17

19 EFFECTS OF RESONANCE BROADENING The effects of Hg-Hg resonance broadening was investigated with Ar as the buffer gas, with a foreign gas broadening cross-section of cm 2. For Hg-Hg broadening cross section cm 2, resonance collisions were not found to make a significant effect on trapping. w/o collisions Intensity (arb. units) Intensity (arb. units) with collisions ν - ν 0 (GHz) Hg-Hg crosssection cm 2 Trapping factor w/o collisions 200 Trapping factor with collisions ν - ν 0 (GHz) Hg-Hg crosssection cm 2 Trapping factor w/o collisions 200 Trapping factor with collisions 160 ICOPS02_KAPIL_18

20 SUMMARY A self-consistent Monte Carlo radiation transport model has been developed which, in conjunction with a plasma equipment model, can be used to realistically model resonance radiation transport in a gas discharge, for complex geometries. Different buffer gases were investigated, and it is seen that xenon has the lowest trapping factor for pressures of interest to us. However, the emitter density profile places a restriction on the buffer gas which we can use. Ar is the most efficient buffer gas in terms of the number of emitters as well as the emitter-to-absorber ratio. Our results indicate that Ne may be a good choice as a buffer gas at pressures of 1 Torr or more. Finally, we see that for cross sections of relevance to us, resonance collisions do not play a significant role in determining exit spectra or trapping factors. ICOPS02_KAPIL_19

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