Identification of Li III lines relevant for TJ-II plasma diagnostics. Master Thesis presented by. Catalina Quirós Lara.

Transcription

1 Identification of Li III lines relevant for TJ-II plasma diagnostics Master Thesis presented by Catalina Quirós Lara Thesis Promoter Prof. José María Gómez Gómez Universidad Complutense de Madrid Thesis Supervisor Dr. Bernardo Zurro July 7th, 013

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3 Identification of Li III lines relevant for TJ-II plasma diagnostics Master Thesis presented by Catalina Quirós Lara Thesis Promoter Prof. José María Gómez Gómez Universidad Complutense de Madrid Thesis Supervisor Dr. Bernardo Zurro Erasmus Mundus Program on Nuclear Fusion Science and Engineering Physics July 7th, 013

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5 Abstract Spectroscopy is one of the most powerful techniques used to measure different plasma parameters. It is one of the least invasive methods to diagnose plasmas and it can measure different parameters found in the periphery as well as in the plasma core. It basically consists in analyzing the shape and intensity of the spectral lines emitted by atoms or ions in order to obtain information about them. Most spectroscopic methods use the radiation emitted by atoms, ions or molecules present in the plasma as impurities (passive spectroscopy) or that were intentionally added to the plasma as a diagnostic tool (active spectroscopy). The main purpose of this project is to identify, by means of passive spectroscopy, the spectrum line from Li III located at Å. This line is formed by charge exchange recombination with either the cold neutrals, whose concentration is maximum at the plasma edge, or with the fast neutrals from the Neutral Beam Injection (NBI) system, which penetrate the plasma center. Several experiments were performed in order to accomplish the objective of identifying this line. First the spectral line of interest was analyzed by examining its wavelength. The possibility of the line being contaminated with other elements will be taken into account. Additionally, the different transitions for the Li III were taken into consideration and a possible model of this line was performed. A rough estimation of the order of magnitude of the charge exchange and excitation processes was performed, with the aim of understanding better the nature of this line. Another step in analyzing this line consisted in doing a spatial resolved study of the intensity of the spectral line of interest and comparing it with others well isolated spectral lines belonging to already identified elements and their corresponding ionization stage. They were performed with discharges heated by ECRH and NBI in order to compare the behavior of this line under diverse temperature and plasma transport conditions. The results were then compared with already identified lines of elements with different ionization states such as: He I (5876 Å), B III (4487 Å), and C IV (590/ Å). Finally, the temperature and intensity evolution over time of this line were measured. These measurements were made either in the first or second order and using different heating methods. In this case, the spectral line was assumed to be only Li III, a mixture between Li III and B III or Li III and C VI or a combination between different transitions of Li III. 1

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7 Contents 1 Introduction Fusion as a future energy source Introduction Fusion as a future energy source Magnetic confinement devices Plasma heating and current drive techniques Controlling Plasma Purity: First Wall Materials and Wall Conditioning Techniques Main fusion and plasma diagnostics My thesis motivation The TJ-II Stellarator: A flexible Heliac 15.1 General Information Heating Methods: ECRH and NBI Wall Conditioning in TJ-II Overview of TJ-II Diagnostics Theoretical background and instrumental passive spectroscopy Introduction Atomic processes in fusion plasmas Ionization sequence of ions Broadening of spectral lines Spectroscopic visible and near-uv instrumentation for passive spectroscopy Wavelength analysis with spatial resolution Spatial resolved study of the line intensity Measurement of the temporal evolution Experimental Results Wavelength analysis of spectral lines Order of Magnitude Estimations NBI case ECRH case Electron excitation Study of the chord-integrated intensity profiles

8 4 Contents ECRH case NBI case Temperature analysis with time resolution ECRH case in First Order NBI case in First Order ECRH case in Second Order Conclusions 59 A Grotrian Diagrams 61 B Li III transitions 65 C Ionization Energies 67

9 Chapter 1 Introduction 1.1 Fusion as a future energy source Introduction The world s population will considerably increase over the years; thus the energy demand will quickly rise as well. Currently, most of the available energy comes from fossil fuels. A limited resource that greatly pollutes the environment and is being burnt at an increasing rate since industrialization. Renewable resources are more environment friendly, yet they are far from satisfying all of our energy demands. Nuclear fission is a good solution from the energetic point of view; nonetheless, when accidents occur in a fission power plant the consequences are disastrous. Therefore, an effective and accurate solution is promptly required. Nuclear fusion is a great alternative to solve this problem. It produces more energy than any of the known resources, the radioactive levels are very low so it does not pollute the environment in a significant way and there are not severe risks if accidents were to occur. Moreover, the resources needed to construct and operate a fusion power plant are sufficient and available all over the world. Even if achieving nuclear fusion on Earth is not an easy task, the benefits of this technology will surely raise the quality of life of all mankind. For this reason, a great effort should be devoted to this field. Hopefully, in the near future, we will all benefit from a power source that resembles the very source of energy in the Universe Fusion as a future energy source Unlike nuclear fission, where a heavy atom splits into lighter nuclei, nuclear fusion consists of two light nuclei joining and forming a heavier one. The mass of the resulting nucleus is less than the sum of the individual masses of the initial nuclei, thus a small amount of mass is lost during the process. According to Einstein s equation, E = mc, mass can be transformed into energy, 5

10 6 1. Introduction releasing high amounts of energy in the process; hence in nuclear fusion reactions large amounts of energy are released. The process of nuclear fusion is shown in Fig. 1.1 [1]. For nuclei to fuse they need to overcome the electrostatic repulsive force between them. For this to occur, the particles must have sufficient kinetic energy to overcome this Coulomb barrier. In order to obtain such a high kinetic energy, they must be heated to temperatures of millions of degrees Celsius. Once inside the barrier, the nuclear force takes over and the force becomes attractive instead of repulsive. Therefore, one of the main problems in nuclear fusion is how to heat the plasma such that the nuclei can overcome this potential barrier []. Figure 1.1: Nuclear fusion reaction where high amounts of energy are released [1]. Different isotopes can be used to achieve nuclear fusion. Fig 1. shows the different cross sections for three different fusion reactions, D-D (Deuterium- Deuterium), D-T (Deuterium-Tritium) and D- 3 He (Deuterium-Helium) reactions. It can be seen that the D-T reaction presents the highest cross section at an energy that is not unpractically high, 100keV. However, it is not necessary to heat the whole fusion fuel up to such high temperatures. The energy of the particles in a fusion reactor are spread out in a Maxwellian distribution, hence the ions in the tail of these distributions will have enough energy to fuse. The D-T reaction can be written as: 1D T 4 He(3.5MeV ) n(14.08mev ) (1.1) where deuterium and tritium fuse producing high energetic neutrons and alpha particles [3]. Obtaining tritium and deuterium is not a complicated process. Deuterium is easily found in nature, and it can even be distilled form seawater. Tritium, on the other hand, is a radioactive element with a half-life of 1.3 years and not found in nature. However, it can be produced by bombarding lithium with neutrons by means of the following reactions [1, ]: Li n 1 He T 3 (4.8Mev) (1.) Li n 1 He T n 1 (.47MeV ) (1.3)

11 1.1 Fusion as a future energy source 7 Figure 1.: Cross section for the reactions D-T, D-D and D- 3 He []. Tritium can actually be produced in a fusion reactor. The high energy neutrons released during the D-T reactions can escape the magnetic field of the reactor and impinge on the surrounding walls. If the walls contain lithium, the above mentioned reactions can occur and tritium can be produced inside the reactor itself. The breeding blanket concept is based on this an is being implemented in fusion reactors. It basically surrounds the vacuum vessel and absorbs radiation and particle fluxes from the reactor. The tritium produced in this blanket can be removed and recycled into the plasma as fuel [1]. It is clear that no material can withstand the high temperatures needed to achieve nuclear fusion. Therefore, a practical method of confinement should be developed. The sun keeps its fuel confined by gravitational forces; nevertheless, this is not possible to achieve on Earth. Therefore, other confinement methods have been developed. Magnetic confinement relies on using magnetic fields to confine the plasma, while inertial confinement heats and compresses the fuel into a pellet. The following section will focus solely in magnetic confinement and the devices developed based on this method Magnetic confinement devices Plasma is made of electrically charged particles. These particles can be confined by means of a magnetic field; however their motion will be influenced by this field. The equation of motion in an homogeneous magnetic field, given by the Lorentz force, is m d v dt = q( v B) (1.4) where m is the mass of the particle, q its charge and v its velocity. By decomposing the velocity in a component perpendicular to the magnetic field v and a parallel one v it can be seen that the parallel component is not influenced by the magnetic field and gives rise to a uniform and steady rectilinear

12 8 1. Introduction motion. The perpendicular component, on the other hand, will give rise to a circular motion with a cyclotron or Larmor radius of and with a cyclotron frequency of r c = m v qb (1.5) ω c = q B m (1.6) Given that ions and electrons have opposite charge, it can be deducted from equation (1.6) that they will move in opposite directions. Fig 1.3 shows the trajectories followed by charge particles in and homogeneous magnetic field. If, in addition to an homogeneous magnetic field, the particles are also influenced an external force, they will also experience a drift velocity from its rectilinear motion given by [] v D = F B q B (1.7) Figure 1.3: Trajectories of electrons (red) and ions (blue) in a magnetic field [3]. The optimum way of confining a plasma would therefore be in a infinite cylinder. However this is not possible and a toroidal shaped confinement is proposed. Nevertheless, the magnetic field generated by a coil winded around a torus will not be uniform; it increases towards the center of the torus. This will cause the gyroradius to change and will lead to a charge separation that will produce an electric field. This electric field will produce a drift in the particle rectilinear motion, as explained in equation (1.7) with F = qe. Another drift motion will be caused by the curvature of the magnetic field lines, which can be solved by adding a poloidal magnetic field [3]. The induction of this magnetic field has led to two different magnetic confinement types, the tokamak and the stellarator.

13 1.1 Fusion as a future energy source 9 In stellarators the poloidal field is produced by a series of helicoidal coils placed along the torus, as shown in Fig 1.4. The toroidal magnetic field is also produced by external coils and the net toroidal current is zero. This design allows for steady-state operation and does not suffer from disruptions arising from a toroidal plasma current. They are more versatile, because its external parameters can be adjusted. Nonetheless, its main disadvantage is that they present no symmetry; hence having a purely three-dimensional configuration [4, ]. Figure 1.4: Sketch of a Stellarator [5]. In tokamaks, the toroidal magnetic field is also generated by magnetic field coils. Unlike stellarators, the poloidal magnetic field is generated by external currents. This current can lead to violent disruptions and forces the reactor to work in a pulsed regime, being this its main disadvantage. Nevertheless, tokamaks have, over time, achieved the best overall performance and are the main choice for present nuclear reactors. As a matter of fact, the biggest nuclear reactor currently being built, ITER (International Thermonuclear Experimental Reactor), is based on the tokamak model. A picture of this device is shown in Fig 1.5 [1, ] Plasma heating and current drive techniques One of the main goals in current fusion reactors is to reach ignition; the point when alpha particles generated by the D-T reaction are able to heat the plasma. Before reaching this point, large power has to be injected into the plasma to raise the temperature. Furthermore, external heating sources will be also required to drive the non-inductive current in tokamaks in order to achieve steady-state operation in the reactor. In the following section, the main current drive and plasma heating techniques are discussed. Neutral Beam Injection (NBI): Consists in electrostatically accelerating either positive ions of deuterium or tritium and then taking away the extra electron so that they become neutral. The neutrals are then injected into the plasma where they propagate in a straight line, unaffected by the magnetic field, until they become ionized by collisions. Once ionized, the electrons and

14 10 1. Introduction Figure 1.5: Sketch of a Tokamak [1]. ions are held by the magnetic field. The energy of this beam must be high enough in order to reach the center and the the plasma core. The basic atomic processes that lead to the absorption of the beam are charge-exchange processes and ionization by ions and electrons [3, 6]. Radio Frequency Heating: Consists in launching high-frequency electromagnetic waves into the plasma at selected frequencies that resonate with one of the natural frequencies of the plasma; thus leading to a larger power absorption. They are classified according to their frequency. Electron Cyclotron Resonance Heating (ECRH): Electromagnetic waves are introduced in the plasma with the electron cyclotron frequency, at the order of approximately 100 GHz. The wave is launched using a RF mirroring system and the power is deposited directly into the electrons. Ion Cyclotron Resonance Heating (ICRH): As in ECRH, the waves are launched into the plasma with a selected frequency but in this case the frequency matches that of the ions, in the order of MHz. The waves are launched using an antenna placed inside the vacuum vessel and the power is deposited directly to the ions. Lower Hybrid Current drive (LHCD): Waves with a frequency that lies between the ion cyclotron and electron cyclotron ones are launched into the plasma using a waveguide array. Plasma electrons that are slightly slower than the wave can actually surf on the wave thus increasing their velocity. As a heating methods LHCD is not very efficient; nevertheless it presents a good option as a current drive technique [3, 6].

15 1.1 Fusion as a future energy source Controlling Plasma Purity: First Wall Materials and Wall Conditioning Techniques In fusion devices, the plasma facing components (PFC) are exposed to intense thermal loads, plasma disruptions and high energetic particles influx. All these factors degrade the overall performance of the materials, limit the lifetime of the PFC and have a strong influence on plasma performance. To minimize these non-desirable effects, the PFC components should meet certain requirements such as: High thermal conductivity and thermal expansion coefficient Low Z Good thermal shock resistance High melting point Low induced activation Good thermal fatigue and thermal shock resistance Low tritium retention Resistance against physical and chemical sputtering Unfortunately, there are no materials available to fulfill all of these requirements. Therefore there is an on going research in this field to find the most suitable materials for PFC. In the mean time, the most appropriate available materials are used and wall conditioning techniques are implemented to counteract the degradation caused by plasma wall interactions. A variety of wall conditioning techniques have been developed over the years to provide wall conditions that will allow a high plasma performance operation or recommissioning after vacuum leaks or major disruptions. Baking: Consists in heating the vacuum vessel at high temperatures to remove water, volatile hydrocarbons and hydrogen from first wall materials. It is the starting point for wall conditioning in fusion devices; nevertheless other conditioning techniques are needed to complement the effects obtained by this method. Metal Film gettering: Using a first wall material to passivate oxygen and other volatile impurities and thus reducing the influx of these impurities into the plasma discharge. The material used has to be compatible with the plasma, be mechanical stable and have a low hydrogen uptake. Pulsed discharge cleaning: Applying repetitively pulsed low temperature discharges to remove impurities. It has the advantage that the time between pulses allows for volatile gases to be pumped out of the vessel resulting in a high impurity removal efficiency. Glow discharge cleaning: Producing a steady state low pressure cathode glow discharge to remove oxygen and other volatile impurities such as hydrogen. Deposition of thin films: Using thin films of various materials to modify

16 1 1. Introduction the composition and surface characteristics of the plasma facing surfaces. This technique has helped in reducing the sputtering of metal impurities, reducing oxygen influx and recycling and improving confinement time in different fusion devices. Radio Frequency discharge: It is an alternative to glow or pulsed discharge cleaning methods. It still needs some optimization to have higher efficiency. In situ limiter and divertor pumping: It removes impurities such as hydrogenic particles on a steady state basis and provides recycling control. It is useful for machines with long pulses and continuous magnetic field [7] Main fusion and plasma diagnostics Plasma parameters are measured using a wide variety of diagnostic methods. In the following section different spectroscopic methods are described and categorized by the physical property of plasma that is measured. Magnetic measurements: The temperature, density and composition of the plasma can be estimated by measuring the magnitude of the electric and magnetic fields and its fluctuations. The magnetic field can be determined by using magnetic coils, internal magnetic probes, by measuring the hall effect, the Faraday effect, the current density, the Ohmic power or the conductivity. Also by using a solenoidal coils whose ends are joined forming a torus, known as a Rogowski coil. A more powerful diagnostic tool consists in measuring the plasma pressure by determining the force it exerts on the magnetic field. The local electric field can be measured by magnetic probes and edge electric field measurements. Plasma particles flux measurements: Measurements made by directly determining the flux of plasma particles using probes of various types in contact with the plasma, being the Langmuir probe the most widely known. A disadvantage of this method is that by inserting a probe to the plasma, the environment is perturbed. Plasma refractive index: Consists in inserting electromagnetic waves into the plasma and measuring the plasma refractive index; thus obtaining information about the internal properties of plasma with an acceptable spatial resolution. The main technique for performing these measurements is the interferometer, a device in which two or more waves interfere by coherent addition of electric fields. The observed intensity is modulated according to whether the systems are in phase or out of phase. Another useful method is reflectometry, when a wave propagates through a plasma and is reflected once it reaches a certain point; hence making it possible to calculate the plasma density. Electromagnetic emission from free electrons: The radiation emitted by free electrons, like cyclotron or bremsstrahlung radiation, carries important information about the temperature and electron density of the plasma [8]. Electromagnetic emission from bound electrons: Consists in measuring the transitions of electrons between the various energy levels of the atomic

17 1. My thesis motivation 13 system of ions that are not fully ionized. The radiation is in the form of narrow spectral lines, unlike the continuum of free-electron radiation. The electron processes of major importance are the radiative transitions and collisional transitions. Radiative processes include the transitions between bound states and free-bound transitions, such as recombination or photoionization. On the other hand, collisional processes include electron impact transitions, dielectronic recombination or autoionization and charge exchange processes. The emission of bound electrons can be divided in active and passive spectroscopy. Active diagnostics consists in intentionally stimulating the plasma and observing the results, whereas passive diagnostics consists in solely observing the emitted radiation [9, 8]. Scattering of electromagnetic waves: Measurements made of the radiation scattered by plasma particles when subjected to incident radiation. Neutral atom diagnostics: Consists in either injecting neutral atoms into the plasma or using the atoms emitted from the plasma in order to produce a desired diagnostic configuration. This active probing often uses other phenomena, such as line radiation, to complete the diagnosis. There are many processes that fit into this category. One of them is neutral atom diagnostics, a passive diagnostic method that uses energetic atoms emitted from the plasma core to obtain information about the plasma interior. Theses neutrons can produce ionizing collision with electrons or ions and charge exchange collisions. Another process is the active probing with neutral particles, which consists in producing intense beams of neutrals and injecting them into the plasma. This is important for charge exchange spectroscopy, in which neutral particles are injected to the plasma core, thus interacting with the fully ionized ions and forming hydrogen-like ions that emit line radiation. The atoms of the beam itself radiate as a result of their interaction with the plasma; hence beam emission spectroscopy consists in the observation of the spatial and temporal variation of the hydrogenic radiation from the beam to obtain the density perturbations [9, 8]. Fast ions and fusion products: Fusion products, highly energetic neutrons and alpha particles, along with other fast ions emitted from the plasma carry important diagnostic information about the plasma. This is important for neutron diagnostics in which nuclear reactions that occur within the plasma are used for diagnostics. Another type is the charged particle diagnostics that consists in observing the thermal-energy ions that overcome the potential barrier and are found outside the plasma. This can be done as well by injecting charged particle beams into the plasma [8]. 1. My thesis motivation Spectroscopic measurements are widely used to measure different plasma parameters. Most spectroscopic methods use the radiation emitted by atoms, ions or molecules present in plasma as impurities or being intentionally added

18 14 1. Introduction for specific purposes such as heating, radiation cooling or diagnostics. By using different diagnostic methods, several parameters like the ion and electron temperature and density can be measured. Well diagnosed plasmas allow the verification of theoretical atomic data as well as the measurement of plasma parameters not yet accessible by other techniques. This information plays a major role in the nuclear fusion research and the improvement of fusion reactors. On the other hand, plasma facing components (PFC) play a key role in maintaining the plasma purity and achieving good confinement. Different characteristics such as high Z, bad thermal conductivity or high induced activation can negatively influence the lifetime of fusion plasmas. Throughout the years, many PFC have been used in fusion reactors without finding a suitable one. Therefore, different materials are currently being used around the globe and consequently different ions and impurities are used to conduct plasma diagnostics. TJ-II is not exempt from this, and over the years its PFC have changed. During the first years, it had mostly stainless steel walls and afterwards it was boronized. Eventually, on top of this boron film a lithium one was added. These changes have made the identification on new lines for plasma diagnostics a crucial task. In the near future, the carbon tiles are expected to be changed; hence the lines used to conduct plasma diagnostics should be changed as well. Unfortunately, the identification of new lines for diagnostics purposes is not an easy task. There are many lines that can contaminate the relevant one and many atomic processes that can interfere as well. Additionally, the useful lines for spectroscopic measurements should be very intense and well isolated, making this process even more difficult. The main focus of this work is to identify the line located at Å, which could be the Li III line formed by charge exchange recombination. The difficulty relies on the fact that this line can be contaminated by B III, C VI or by another Li III line formed by excitation and recombination. To identify this line, several experiments will be performed and different hypothesis will be made in order to fulfill this objective.

19 Chapter The TJ-II Stellarator: A flexible Heliac.1 General Information TJ-II is a four period low magnetic shear medium size heliac type stellarator located in Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT) in Madrid, Spain. It was done in collaboration with the Oak Ridge National Laboratory (ORLN) in the United States and IPP in Garching, Germany. A schematic representation of the TJ-II stellarator is shown in Fig..1 [10, 11]. Figure.1: Schematic Representation of TJ-II stellerator [5]. It consists of 3 toroidal magnetic field coils that create the magnetic field required to confine the plasma. Additionally, it has a central conductor made up of two coils: a pure horizontal circular one and a helical winding wrapped around the circular one. Finally, the position of the plasma is controlled by four vertical field coils. The combined action of the magnetic fields created by these coils generates bean-shaped magnetic surfaces and by changing the values of the currents that circulate through the coils a wide range of magnetic 15

20 16. The TJ-II Stellarator: A flexible Heliac configurations can be achieved, as shown in Fig. [1]. The main parameters of TJ-II are summarized in Tab.1. Figure.: Sketch of the plasma cross-section for three different magnetic configurations [10]. Parameter Value Major Radius R 1.5m Average minor radius < a > 0.m Magnetic field B o Electron temperature T e Ion temperature T i Electron density (ECRH) n e Electron density (NBI) n e Rotational transform < 1 T Plasma Volume V 1m 3 Working gas kev 150 ev m m ι π. Hydrogen, Deuterium Table.1: Typical plasma parameters of TJ-II.. Heating Methods: ECRH and NBI TJ-II is equipped with two heating methods: Electron Cyclotron Resonance Heating (ECRH) and Neutral Beam Injection (NBI), being the first heliac device to use NBI. NBI: Consists of two independent tangential injectors in the co-counter configuration. The beams obtained are of 30 kev and 50 A at the ion source. It has a flexible, scalable and distributed control system that ensures the operation and integration of the NBI and associated facilities. Additionally, the timing system has been synchronized with the TJ-II plasma pulses [13].

21 .3 Wall Conditioning in TJ-II 17 ECRH:This system is equipped with two 300 kw gyrotrons at a frequency of 53. GHz. They are coupled to the plasma through two quasi optical transmission lines, placed at two symmetric positions of TJ-II and equipped with an internal steerable mirror. They are fed by a common high voltage power supply that reaches 80 kv and 50 A during a maximum pulse length of 1 s [14, 15]..3 Wall Conditioning in TJ-II The behavior of TJ-II plasmas is greatly influenced by the desorbed impurities during the discharge. The reasons for this are the close coupling between the vacuum vessel, made entirely of stainless steel, and the plasma periphery and the small plasma volume in contrast with a great vacuum area. Therefore, wall conditioning in TJ-II is of paramount importance in order to have good conditioned discharges [16, 17]. The first wall conditioning technique performed in TJ-II consisted in baking the vacuum vessel at 150 C in a thermal cycle that lasted 30 hours. This helped with the removal of water and thus contributed in achieving a decrease of the total base pressure. To complement the benefits obtained with baking, other wall conditioning methods must be used. In order to remove the hydrogen implanted on the wall during the plasma discharges and to produce an activated surface with a typical wall pumping behavior an Helium Glow Discharge (He GDC) cleaning is performed. This discharge is done half hour previous to the power discharges. However, to control the amount of desorbed Helium during the discharge, a short Argon Glow Discharge is performed after the daily He GDC [16, 17]. The introduction of the NBI heating brought new challenges for the TJ-II wall condition techniques since the injected atoms that are not absorbed in the plasma hit the graphite tiles located in the opposite side of the injection system. Therefore, to reduce the amount of metallic sputtering a boronization of the walls was performed. This material was chosen due to its low Z and its gettering effects. Nonetheless, with these conditions the injected power of the NBI could not reach the desired level because of the inadequate control of recycling associated with the saturation of the film by hydrogen. Hence, a lithium coating was applied due to its low Z and its strong H retention as well as strong O getter activity. It was performed by using ovens to evaporate the Li and then it was homogenized by the plasma itself [16]. The lithium coating presented important changes in the overall plasma performance. The edge radiation was lowered, which avoids the power imbalance that produces the low radiation collapse. Furthermore, the density limit of the NBI plasmas has increased reaching values of m 3 and T e ev, with peaked density, rather than flat T e profiles and higher ion temperatures up to 150 ev. The lithium coating led to an improvement in the plasma density control by external puffing and increase in particle control [18].

22 18. The TJ-II Stellarator: A flexible Heliac.4 Overview of TJ-II Diagnostics TJ-II is equipped with numerous diagnostics systems (see Fig..3) which are in charge of obtaining information from the plasma in order to analyze the main parameters and characterize the discharges. They are divided in passive and active diagnostics [5]. Passive Diagnostics Figure.3: Diagnostics present in TJ-II [5]. Magnetics: They include Rogowski coils, Minorv coils and diamagnetic loops. H alpha monitors: TJ-II has various H α monitors located in different parts of the vacuum chamber. Electron Cyclotron Emission (ECE): This system measures electron temperature profiles by a 16 channel heterodyne radiometer covering the frequency range Hz. Soft X-rays: It consists of 5 cameras with 16 channels each. Then, using a numerical code a tomographic reconstruction of the plasma emissions is made. Bolometry: The total energy losses due to radiation is measured using three 0-channel pinhole cameras, three 16-channel cameras and six global bolometry monitors. Spectroscopy: TJ-II is equipped with various high and low resolution spectrometers that cover the visible and UV region.

23 .4 Overview of TJ-II Diagnostics 19 Compact Neutral Particle Analyzer: Consists of 16 channels at fixed energy in charge of studying the high energy tails during NBI. Fast ion loss probe: It is a mobile luminescent probe that detects fast ion losses and suprathermal ions escaping from the plasma. Fast camera: Several cameras are in charge of plasma imaging. Active diagnostics Charge exchange spectroscopy: This diagnostic system has spatial resolution and it is used to measure ion temperature profiles and poloidal velocities. Interferometry: It is used to measure the line-integrated electron density during a discharge. Reflectrometry: TJ-II has various reflectometers in charge of measuring electron density profiles, the velocity of the shear layer and its radial position of origin and the plasma density fluctuation velocities and their wave number spectra. Heavy Ion Beam Probe: TJ-II has two heavy ion beam probes that measure the plasma electric potential, the electron density and poloidal magnetic field component. Also, a multiple cell array detector is in charge of studying the spatial structure of plasma turbulence. Langmuir Probes: They are used to obtain information about the electron density, electric potential, and electron temperature of the plasma. Thomson Scattering: It provides information about the electron temperature, density, and pressure profiles at a single time in the discharge. Diagnostic neutral beam: It is used to perform spatially resolved charge exchange recombination spectroscopy and neutral particle analysis measurements. Helium and Lithium Beam: It measures the electron temperature and density profiles in the edge and scrape-off layer.

24 0. The TJ-II Stellarator: A flexible Heliac

25 Chapter 3 Theoretical background and instrumental passive spectroscopy in TJ-II 3.1 Introduction Spectroscopy is one of the most powerful techniques used to measure different plasma parameters, such as temperature, rotation velocity, density and transport of impurities in fusion plasmas. It is one of the least invasive methods used to diagnose plasmas and it can measure different parameters found in the periphery as well as in the plasma core. It basically consists in analyzing the shape and intensity of spectral lines emitted by atoms or ions in order to obtain information about them. The plasma parameters can be measured by using information about the intensity, width and displacement of the spectral line. Most spectroscopic methods use the radiation emitted by atoms, ions or molecules present in the plasma as impurities or that were intentionally added to the plasma as a diagnostic tool. This technique is divided into two main groups: passive and active. Passive spectroscopy consists in measuring the plasma emission without injecting any external impurity. The measurements are integrated along the line of sight and due to the nature of this technique, it is not possible to acquire local information about fully stripped ions. Active spectroscopy, on the other hand, relies on the injection of external elements, such as neutral beams, to obtain information about different plasma parameters. This is a very efficient method to obatin information about fully stripped ions; nevertheless it is a more invasive technique than passive spectroscopy. In this work, we are going to perform measurements using passive spectroscopy techniques in order to identify spectral lines located in the visible spectrum [19, 9]. 1

26 3. Theoretical background and instrumental passive spectroscopy 3. Atomic processes in fusion plasmas The population of atomic, molecular, and ionic levels changes due to collisions with different elements present in the plasma. A spectral line is emitted by the transitions of excited atoms or ions. Therefore, spectroscopic measurements are based on these atomic transitions [0]. This section will include the different atomic processes that can take place in the ions present in the plasma. Collisional Excitation and Ionization: When an electron collides with an ion, energy is transfered to one of the bound electrons. If this energy is high enough, the electron can gain sufficient energy to leave the ion. If the energy is not high enough to free the electron, this electron can move to a higher energy level. These processes can be illustrated as follows [19, 9]: I (Z 1)+ + e I Z+ + e (3.1) I Z+ (n) + e I Z+ (n > n) + e (3.) These two processes can have an inverse one as well. After a collision there can also be a deexcitation process, that is, when a bound electron decays to a lower energy level. Additionally, two electrons (or an ion and an electron) interacting near an ion may result in the recombination of one electron and the remaining particle will carry away the resulting energy. These processes can be visualized as follows [0]: I Z+ (n) + e I Z+ (n < n) + e (3.3) I Z+ (n) + e I Z 1 + e (3.4) Radiative recombination: Occurs when a free electron is captured into bound state of an ion or atom. A photon, with energy equal to the kinetic energy of the free electron and the ionization potential of the bound state, is emitted in this transition. It can be visualized as follows [9, 1]: I z+ + e I (Z 1)+ + hν (3.5) Spontaneous Emission: A bound electron in an excited state can spontaneously move to a lower energy level. A photon is emitted during this transition. Spontaneous emission can be illustrated as [9]: I Z+ (n) I Z+ (n < n) + hν (3.6) Charge Exchange: Occurs when a fast or cold neutral particle collides with an ion, this ion will attract the atomic electrons and eventually the atom may transfer an electron to an excited energy level of the ion. This electron will then decay to a lower energy level emitting a photon. It is better visualized as follows [9, 0]:

27 3.3 Ionization sequence of ions 3 I Z+ + H 0 (I (z 1)+ ) + H + I (Z 1)+ + H + + hν (3.7) The cross section values for these reactions vary according to the plasma region where they occur. In the low energy region the cross section is quite high and shows little energy dependence. In higher energy regions, the cross section quickly decreases with increasing energy. These reactions offer a great possibility to obtain information about completely ionized ions [9, 0]. 3.3 Ionization sequence of ions Due to its high temperatures, fusion plasmas are always made up of ions with high ionization degrees. Also, as explained in the previous section, one of the main atomic processes in fusion plasmas is the collisional ionization or excitation by electrons. Therefore, the ionization degree of a given ion will highly depend on its temperature. Due to the fact that temperature in a fusion plasma is not constant in space, the ionization degree of ions is also related to the position they have in the plasma. In this work we will study the presence of boron and lithium; therefore it is important to have a simulation of the different ionization degrees with respect to their temperature. Fig 3.1 and 3. show the fractional abundance n(z) of B and Li respectively as function n(el) of the their temperature. These calculations were made taking into account a Maxwellian distribution function and assuming equilibrium B + B + B 3 + B 4 + B 5 + n Z /n T e (ev) Figure 3.1: Fractional abundances of B ions n(z) B 0 n(el) as functions of temperature.

28 4 3. Theoretical background and instrumental passive spectroscopy 10 0 Li + Li + Li 3 + n Z /n T e (ev) Figure 3.: Fractional abundances of Li ions n(z) n(el) as functions of temperature. 3.4 Broadening of spectral lines There are many processes that can affect the shape and width of the spectral line. The following section focuses on the main factors that can cause broadening of the spectral lines. Natural Broadening: Quantum states of an atom do not have a single energy, but a small spread in energy that causes a small and negligible broadening of the line. According to Heisenberg s uncertainty principle, there is an uncertainty in the measurement of the energy E of any atomic system when measured along with the half-life of that level, in other words E t. Therefore, due to the finite lifetime of the levels, these spread of the energy level of excited levels can be calculated [9, 8]. Doppler Broadening: The particles that make up the plasma have different temperatures Li and velocities. This motion of the particles give rise to a 0 broadening of the spectral line, named Doppler broadening. In the case of a Maxwellian velocity distribution, the ionic temperature is related to the width of the line by the following formula T i = A i ( δλ λ 0 ) (3.8)

29 3.5 Spectroscopic visible and near-uv instrumentation for passive spectroscopy5 where λ 0 is the rest wavelength of the spectral line, A i is the mass of the ion and the temperature is expressed in ev [1]. Zeeman and Stark effect: The spectroscopic measurements can be affected by the magnetic field (or electric field in case of the Stark effect). The atoms and ions present in the plasma have a direct interaction with the magnetic field, which may cause the spectral lines to separate into different components; hence causing a broadening of the total spectral line [9, 1]. Pressure broadening: Arises from the influence of nearby particles upon the emitting atom. Ideally, the atom would radiate undisturbed; nevertheless in a fusion plasma there are collisions between particles that interrupt this emission. This broadenning may be related to the Stark broadening when the nature of this perturbation is due to an electric field [8]. 3.5 Spectroscopic visible and near-uv instrumentation for passive spectroscopy In order to accurately identify spectral lines, several experiments and analysis need to be performed. In the present work different approaches were used to analyze the behavior of the spectral line under different circumstances. The spectral line was analyzed by its wavelength, its spatial profile behavior and the temporal evolution of its temperature and intensity. In the present section, the different systems used to perform these measurements are described Wavelength analysis with spatial resolution In order to perform a wavelength analysis a high resolution multi-channel spectrometer was used to obtain the data. This system uses fiber guides to view the plasma perpendicular to the magnetic field. It consists of 9 channels separated by 5 mm and distributed along different plasma chords that cover most of the plasma cross-section. Each channel is 1 mm in diameter and they can be independently focused onto the plasma by a quartz lens. Fig. 3.3 illustrates this system: (a) shows the position of the spectrometer with respect to the NBI heating system while (b) shows the distribution of the 9 channels and their position in a typical TJ-II plasma shape. The geometry of this system is quite flexible. The support of the 9 channels can be displaced upwards or downwards as a complete unit by about 30 mm and each channel head can be tilted [, 3]. The system is equipped with a Czerney-Turner image-corrected spectrometer with different gratings that cover a broad wavelength range with a good response. In this work we used a grating of 100 grooves. The signal is recorded mm into a pixel charged coupled device (CCD) array (model OMA IV by EG&G) with a pixel size of 19 µm [3].

30 6 3. Theoretical background and instrumental passive spectroscopy Figure 3.3: (a) Position of the spectrometer with respect to the NBI heating system. (b) Position of the 9 channels of the spectrometer and their observation geometry on a typical TJ-II plasma shape [] Spatial resolved study of the line intensity The system used to do a spatial study of the intensity of the spectral line is depicted in Fig. 3.4 The system used reflects plasma emissions using a fast rotating hexagonal mirror. This reflection goes to a 1 meter monochromator with a turret grating mounting (two of 100 grooves and a holographic one of mm 400 grooves ) that selects the radiation wavelength from Å with a mm spectral width of about 5 Å and.5 Å respectively. The radiation wavelength and spectral width depend on the input slit and grating used; usually the input slit is kept constant and the gratings are changed. After leaving the monochromator the light is registered using a photomultiplier tube (Model H by Hamamatsu) and recorded on a PXI data acquisition system using a single ended input. This spectrometry system is positioned near the NBI 1 heating system and it acquires a plasma emission profile of approximately 1 ms every 8 ms. The profile is obtained starting from the upper side until it reaches the lower side; the NBI-plasma interaction can be seen in the lower part (see Fig. 3.4 (b)) [4, 5]. Figure 3.4: (a) Sketch of the experimental set-up [4]. (b) Position of the spectrometer with respect to the NBI heating system. (c) Sketch of the plasma scan done by the system.

31 3.5 Spectroscopic visible and near-uv instrumentation for passive spectroscopy Measurement of the temporal evolution The apparatus used to perform the measurements of the temporal evolution of the intensity and temperature of the spectral line is the spectrometer system depicted in Fig 3.5. First, the plasma emission goes through a fused-quartz window then, via a 5 mm diameter lens and m long-branch fiber made of 1 mm diameter fused silica, is transferred into the spectrometer. This fiber length should be kept small in order to obtain a better light collection; therefore improving the system sensitivity. To calibrate the system several pen lamps were used given that they provide prominent spectral lines and are very flexible to use. The signal is analyzed using a 1 m focal length Czerny Turner spectrometer (model 051 by McPherson) and equipped with a 100 lines grating that resulted in a dispersion of approximately 8 Å. Additionally, the focal mm mm plane has an intensified silicon photodiode array (OMAIII, model 140, provided by EG&G), sensitive over a range of nm, with 700 active pixels, 5 µm wide by.5 mm high for recording the spectral emission lines. This spectrometer has a single spatial channel that collects light perpendicular to the TJ-II toroidal field and its line of sight can be varied shot to shot [6, 7], although for this work we have used mainly a chord whose line of sight is directed towards the plasma center. Figure 3.5: Sketch of the system used to obtain the data and its position with respect to the NBI heating system.

32 8 3. Theoretical background and instrumental passive spectroscopy

33 Chapter 4 Experimental Results The main purpose of this work is to identify the spectrum line from Li III located at Å. This line is formed by charge exchange recombination with either the cold neutrals, whose concentration is maximum at the plasma edge, or with the fast neutrals from the Neutral Beam Injection (NBI) system which penetrate the plasma center, as follows Li 3+ + H 0 (Li ()+ ) + H + Li + + H + + hν (4.1) where (Li + ) is in an excited state (n,l). At this moment, it is important to point out that the spectroscopic notation for ions will be mostly used. In this notation, a neutral Li ion will correspond to Li I, a singly ionized Li ion will be written as Li II and so on; needless to say this notation also applies to all other ions besides Li. Several experiments were performed in order to accomplish the objective of identifying this line. A wavelength analysis was done, followed by an order of magnitude estimation of the intensities for charge exchange and electron impact excitation. Additionally, a study of the spatial variation of the intensity of different lines was performed, in other to compare them with the line of interest. Finally, by making several hypothesis, the temporal evolution of the intensity and temperature of this line was studied. These experiments will be further explained in the present chapter. 4.1 Wavelength analysis of spectral lines In this section, the spectral line of interest will be analyzed by examining its wavelength; then it will be compared with the information available on different databases, mainly the National Institute of Standards and Technology (NIST) database [8] and the Atomic data and analysis structure (ADAS) database [9]. Afterwards, with the information obtained some analysis and hypothesis will be made. The possibility of the line being contaminated with other elements will be taken into account. Additionally, the different transitions for the Li III will be taken into consideration and a possible model of 9

34 30 4. Experimental Results this line will be made. All this is done with the aim of finding a reasonable argument, which will help in the process of identifying the line. By using the system described in section the raw spectrum in Fig 4.1 was obtained on a TJ-II plasma heated by the NBI- heating system, with a exposure time of 400 ms. The horizontal axis is given by the charge couple device CCD detector pixel number for one of the nine fiber channels available for this experiment. This data was taken from the third channel, as can be seen from the figure. Figure 4.1: Spectrum obtained in a TJ-II plasma heated by Neutral Beam Injection. The most prominent line in this spectrum is the line we are primarily interested in identifying. In addition to this line the other ones present in the spectrum are shown in Tab The approximate wavelength for the main prominent lines can be determined by using nominal parameters for the central wavelength and linear dispersion. These lines might also be second order diffraction lines, so their corresponding second order wavelength is also shown in Tab The approximate wavelength values for these unidentified spectral lines are given in the second column and in the third. These values were calculated using the following formula: λ n (c x) p ld (4.) Where λ n is the nominal wavelength, in this case 4500 Å. c is the center of the focal plane to which we assign the nominal wavelength values of 4500 Å. x is the location of the line whose wavelength we want to calculate.

35 4.1 Wavelength analysis of spectral lines 31 p is the separation between pixels. In this case mm. in first order diffrac- ld is the linear dispersion of the instrument in Å (7.9 A mm tion). mm Pixel Nominal Lambda (Å) Second order lambda (Å) Table 4.1: Lines obtained from Fig. 4.1 arranged from left to right and their corresponding wavelength in first and second order. In order to obtain a precisely wavelength-calibrated scale we have recorded, in the wavelength range of interest, the spectra of several standard calibration lamps: Ne, Ar, Kr and the He emission from the TJ-II glow discharge. These lines are plotted in Fig. 4. (a) along with the plasma spectrum whose wavelength we want to identify with the maximum accuracy. Using the wavelength of these calibration lines, a relationship between pixel number and wavelength is calculated. This relation is inferred to be linear as shown in Fig. 4. (b) and is used to calculate a precisely calibrated wavelength scale. The spectrum with the calibrated scale is shown in Fig. 4. (c). The values of the wavelengths obtained will be analyzed using the NIST and Open-ADAS database. The elements selected from the database to analyze this spectrum are those that are likely to be present in TJ-II plasmas. Hydrogen, the gas used for the discharge, is always going to be present; nonetheless, there are only a few H lines and they are easily distinguished. The first wall of TJ-II is made up of stainless steel with a B and Li coating, hence Fe, C, Cr, Li and B lines are expected to be present. Carbon lines might also be found because the NBI neutrals may hit the graphite tile protection that is located in the opposite wall of the neutral beam injection system. Helium is likely to be found due to the glow discharge cleaning applied daily to TJ-II. Additionally, there is Cs and W found in certain probes, F and C in Teflon, as well as Cu in the antennas. These elements are very localized but still might be present in the spectrum. Finally, if there is a leak in the vacuum chamber N and O lines might be found. Taking into account the former elements, the wavelengths for the lines obtained in the spectrum were compared with the information found on the databases. Lines having a low relative intensity in the database were not taken into ac-

36 3 4. Experimental Results Figure 4.: Normalized Kr, He, Ne and Ar calibration lines along with the spectrum obtained on a TJ-II plasma heated by Neutral Beam Injection. (b) Linear relation between pixel number and wavelength of the calibration lamps. This relation was used to obtain a precisely calibrated wavelength scale. (c) Spectrum obtained on TJ-II plasma heated by Neutral Beam Injection with its corresponding wavelength. count. Also if the strongest line of a certain element is not present in the spectrum, it is not taken into account. For certain wavelengths, more than one element was found to be a possible candidate, as shown in Tab. 4.. The spectral line located at Å was successfully identified as B III. Other lines show many possibilities; hence further experiments and analysis should be performed. We are mainly interested in the peak corresponding to Å, which could be either B III (n = 5 n = 4 λ = Å), Li III (n = 5 n = 4 corresponding to many wavelengths), C VI (n = 10 n = 8 λ = Å) or a mixture between those elements. The Grotrian Diagrams with the allowed transitions for B III, C VI and Li III can be seen in Appendix. A. To analyze the presence of B III in the Å peak, we rely on the information obtained from the Å peak already identified as B III. According to the NIST database [8], this peak corresponds to two different transitions of B III, n = 5 j = 7 n = 4 j = 3 with and n = 5 j = 7 n = 4 j = 5, both having the same wavelength at Å and relative intensity of 1900 a.u; whereas the intensity for the B III line located at Å has a relative intensity of 1700 a.u. Assuming that B III is present in the line of interest we compare both intensities of B III, as shown in Fig As can be seen, if B III were present in this line, its intensity would be very low.

37 4.1 Wavelength analysis of spectral lines 33 Pixel Lambda (Å) Possible ions First order He I Å Second Order B III Å B III Å B III 34.6 Å First order Å B III Å Second order First order B III Å Second order C VI Å Li III several wavelengths between Å and Å 64.6 First order Cs II Å Second order Cu I Å Fe I Å Cs II Å 91. First order N III Å Second order Cu II Å First order Cs III Å Second order W I 45. Å Cs III Å Table 4.: Lines obtained from Fig. 4.1, arranged from left to right, with their corresponding wavelength in first and second order. The third column shows the possible ions that make up the line.

38 34 4. Experimental Results Figure 4.3: Two peaks from TJ-II spectrum; the first one already identified as B III and the second one is the unidentified line corresponding to a wavelength of Å. The blue squares correspond to the relative intensity of B III supposedly present in each line. Another hypothesis concerning this spectral line is that it is made entirely of different Li III transitions. According to the information found on the NIST and ADAS databases [8, 9], this line could be influenced by many transitions located around Å formed by charge exchange and by the line formed by excitation and recombination located at Å, shown in Appendix B. Additionally, the transitions for the charge exchange processes are shown in Fig The next step will consist in plotting the Gaussians for each transition, analyzing their sum and comparing it with the Gaussian formed at Å by excitation and recombination. In order to analyze the different Li III transitions it was necessary to make some assumptions. First, it was assumed that the charge exchange processes were mostly taking place in the plasma core and the excitation and recombination process were assumed to be taking place in the plasma periphery; as in the case of a plasma with NBI heating. Hence the temperature for Li undergoing charge exchange was assumed to be 150 ev while the temperature for Li III undergoing excitation and recombination was estimated as 50 ev. The transitions for charge exchange were summed and plotted along with the one obtained for excitation and recombination, as shown in Fig.4.5 (a). According to the databases [30], the intensity for all the charge exchange transitions with high energy neutrals was assumed to be higher than for the excitation and recombination transitions. It can be seen that in the case the temperature of the Li III ions undergoing charge exchange is very high, is not possible to measure the 4500 Å line for excitation and recombination. Therefore another assumption was made, in which the Li III ions undergoing charge exchange

39 4.1 Wavelength analysis of spectral lines 35 Figure 4.4: Estimated Gaussians for Li III ions undergoing charge exchange processes with a wavelength close to Å. have a lower temperature, 100 ev. The Li III ions undergoing excitation and recombination were assumed to have the same temperature as in the previous case, 50 ev. The results for this case are shown in Fig. 4.5 (b). It can be seen that in this case both peaks still blend. Therefore, if all the transitions of Li III are occurring at an equal rate, the two peaks will not be easily distinguished in a NBI heated plasma. The case for ECRH plasma is also analyzed. In this case, the density of neutrals in the plasma core is negligible and the charge exchange processes are assumed to be occurring mainly with cold neutrals in the plasma periphery. Therefore, two cases are assumed. The first scenario consists of the recombination and excitation processes occurring closer to the plasma core and in the other case they occur in the plasma periphery. These two cases are plotted in Fig 4.6 (a) and (b) respectively. It can be seen that when the excitation and recombination processes are taking place closer to the plasma center, the line can be easily distinguished from the Å one. On the other hand, when both processes are occurring in the plasma periphery, the excitation and recombination line blends with the charge exchange line.

40 36 4. Experimental Results Figure 4.5: (a) Gaussian calculated from the sum of all the possible transitions (n = 5 n = 4) for Li III formed by charge exchange located around Å (red) and the Gaussian formed by the transition (n = 5 n = 4) for excitation and recombination located at 4500 Å (blue); assuming the temperature the Li III ions undergoing charge exchange is 150 ev whereas the one for Li III ions undergoing excitation and recombination is 50 ev. (b) Gaussian calculated from the sum of all the possible transitions (n = 5 n = 4) for Li III formed by charge exchange located around Å (red) and the Gaussian formed by the transition (n = 5 n = 4) for excitation and recombination located at 4500 Å; assuming the temperature for Li III ions undergoing charge exchange is 100 ev whereas the one for Li III ions undergoing excitation and recombination is 50 ev.

41 4.1 Wavelength analysis of spectral lines 37 Figure 4.6: (a) Gaussian calculated from the sum of all the possible transitions (n = 5 n = 4) for Li III formed by charge exchange located around Å (red) and the Gaussian formed by the transition (n = 5 n = 4) for excitation and recombination located at 4500 Å (blue); assuming the temperature the Li III ions undergoing charge exchange is 50 ev whereas the one for Li III ions undergoing excitation and recombination is 100 ev. (b) Gaussian calculated from the sum of all the possible transitions (n = 5 n = 4) for Li III formed by charge exchange located around Å (red) and the Gaussian formed by the transition (n = 5 n = 4) for excitation and recombination located at 4500 Å; assuming the temperature for all Li III ions is 50 ev.

42 38 4. Experimental Results 4. Order of magnitude estimations of the intensities for charge exchange recombination and electron impact excitation In the following section, the intensities for charge exchange, with either high energetic neutrals from the plasma core or cold neutrals found in the plasma periphery, and electron impact excitation occurring on the plasma periphery are going to be calculated based on theoretical formulas and values obtained from different databases [30, 31, 0]. This calculation will be done in a very simplified manner, with the aim of estimating the order of magnitude for each process. It will be divided in 3 sections: Charge exchange with and without NBI and electron excitation. To begin with, the definition of spectral line should be well understood. Basically, a spectral line is emitted when a bound electron undergoes a transition from a higher energy level to a lower energy one. During these transitions photons with certain energy are emitted. These photons are subsequently detected and the spectral line can be seen in the resulting spectrum. The intensity of this line can be measured by its emission coefficient, which is the number of photons emitted in a given solid angle by a given population density of a certain species taking into account the probability of the measured transition. Therefore, the emission coefficient ɛ, in following formula [3]: photons m 3 s sterad, may be calculated by the ɛ(p q) = 1 A(p q)n z (p) (4.3) 4π A(p, r) where p is the higher energy level. q is the lower energy level. A(p q) is the atomic transition probability or Einstein coefficient (s 1 ). n z (p) is the population density of the excited states of the atomic species (m 3 ). A(p, r) is the sum of al the transition probabilities (s 1 ) from the energy level p to a lower energy level r Charge Exchange Recombination with high energy neutrals In this section, we are primarily interested in the charge exchange recombination process between high energetic neutrals from the NBI and a doubly ionized lithium ion explained in eq 4.1. If it is assumed that this charge exchange process is not interfered by any other processes, then the population density of the excited states of the atomic species can be calculated as follows [3]:

43 4. Order of Magnitude Estimations 39 n p (z) = n h n + < σv > cx (4.4) where n h is the density of neutral hydrogen in the beam (m 3 ). n + is the density of fully stripped Li 3+ ions (m 3 ). < σv > cx is the charge exchange reaction rate (m 1 s 1 ). Therefore, eq. 4.3 can be written as ɛ(p q) = n hn + 4π < σv > cx A(p q) A(p, r) (4.5) where n h is the density of neutral hydrogen in the beam (m 3 ). n + is the density of fully stripped Li 3+ ions (m 3 ). A(p q) is the atomic transition probability or Einstein coefficient (s 1 ). < σv > cx is the charge exchange reaction rate (m 1 s 1 ). A(p, r) is the sum of al the transition probabilities (s 1 ) from the energy level p to a lower energy level r. The present calculation is done with the aim of comparing the intensities for charge exchange recombination and excitation of lithium ions. Specifically, the transition from n = 5 n = 4. Given that the term A(p, r) will be the same for either case it can be neglected and the values for each intensity can still be compared. The first case that will be calculated is the charge exchange recombination with high energetic neutrals from the NBI heating. The density of neutrals in the NBI beam can be calculated by knowing that the intensity of the beam is 50 A, its energy 30 kev and the diameter of the circular cross section is 0 10 m. The current density is defined as electric current per unit area; therefore it can be easily estimated by dividing the current and the area of the circular cross section [33] J = I A = 50A m = A m (4.6) To obtain the density of neutrals in the beam, we first have to know that the electric current can also be explained in terms of the charge density and the drift velocity of the particles [33] J(r, t) = ρ(r, t)v d (r, t) (4.7) So, in order to obtain the density of neutral we need the drift velocity and the charge of individual particles. The charge can be easily obtained by recalling that this beam was accelerated using negative ions of hydrogen. Therefore,

44 40 4. Experimental Results the charge of the beam is equal to the charge of an electron. The drift velocity is readily calculated from the kinetic energy, E = 1 mv. Therefore, where V = E m = m s (4.8) m is the mass of the particle. In this case the particle is hydrogen with m = 1 amu = kg. E is the energy of the particle. In this case 30 kev or in S.I units J. Using eq. 4.7 along with the values for the drift velocity, the current density and the charge of the beam we can calculate the density of neutrals as follows: n = J qv d = m 3 (4.9) On the other hand, the density of Li 3+ ions can be easily estimated. We assume the density of these ions is approximately 1% of the electron density; hence for TJ-II plasmas the density of Li 3+ ions would be in the order of m 3. According to the databases, there are many possible transitions between the n = 5 n = 4 energy levels of Li. Consequently, a assumption should be made in order to calculate the value for the intensity of charge exchange and compare it with the one for excitation. All of these transitions have different cross sections depending on their principal and angular quantum number. Given that all of these transitions occur within the same principal quantum number n = 5 n = 4 we are going to focus solely on the angular quantum number. The relationship between the cross section and the angular quantum number, for a collision energy close to 30 ev shows that the highest cross amu section corresponds to l = [30]. Therefore, we focused on the transitions occurring from d level to a lower one. For a energy close to 30 kev the cross section has a value of 10 1 m [31]. The atomic transition probability was also chosen from the databases by taking into account the relationship between the cross section and the angular quantum number. According to the NIST databases, the highest transition probability for l = corresponds to a value s 1 [8]. The particle velocity corresponds to the velocity of the incident fast neutrals. This value was previously calculated in eq 4.8 and corresponds to m s. Therefore, substituting these values in eq.4.5 the emission coefficient is approximated to a value of photons m 3 s sterad.

45 4. Order of Magnitude Estimations Charge Exchange Recombination with cold neutrals In this case, the neutrals are mainly located in the plasma periphery; thus having a lower temperature than the neutral beam. The value for the atomic transition probability remain the same as in the previous case for NBI. Nevertheless, in this case the density of Li +3 ions is going to be lower due to the lower temperature of the plasma edge. Hence, we assume that the density of these ions is 0.1% of the electron density, that is m 3. The velocity can be calculated from eq. 4.8 with an energy of J (corresponding to a temperature of 50 ev) and the hydrogen mass ( kg). Therefore, the velocity for cold hydrogen atoms located in the plasma periphery is m s. The neutral hydrogen density should be higher than the Li density but still not high enough as the electron density; hence it is estimated as being 10% of the electron density, which corresponds to a value of m 3. Following the same assumptions as in the previous section, the cross section can be obtained and corresponds to a value of 10 9 m [30, 31]. Substituting all these values in eq. 4.5 the emission coefficient for this case is estimated as having a value of photons 4..3 Electron excitation m 3 s sterad. The last step is to calculate the emission coefficient of the electron impact excitation. This reaction happens when an electron collides with an ion, in this case Li +, and excites one of the electrons of the ion. This excited electron will then decay into a lower energy level. Li + (nl) + e Li + (n l ) Li + (nl) + hν (4.10) Where Li + (nl) is a doubly excited Li ion in a lower energy level and Li + (n l ) is a doubly excited Li ion in an excited energy level. The emission coefficient for the electron excitation process can be easily calculated by using the following eq Assuming that this electron excitation process is not interfered by any other processes, then the population density of the excited states of the atomic species can be calculated as follows [3] where n e is the density electrons in m 3. n g is the density of ground state Li atoms. n p (z) = n e n g < σv > exc (4.11)

46 4 4. Experimental Results < σv > exc is the excitation reaction rate in m 1 s 1. Therefore, eq. 4.3 can be written as: ɛ(p q) = n en g 4π A(p q) < σv > exc A(p, r) (4.1) where n e is the density of electrons in m 3. n g is the ground state of Li atoms m 3. A(p q) is the atomic transition probability or Einstein coefficient in s 1. < σv > exc is the reaction rate in m 1 s 1. A(p, r) is the sum of al the transition probabilities in s 1 from the energy level p to a lower energy level r. As in the charge exchange case, this calculation is performed with the aim of comparing the intensities for charge exchange recombination and electron excitation of lithium ions. Specifically, the transition from n = 5 n = 4. Given that the term A(p, r) will be the same for either case it can be neglected and the values for each intensity can still be compared. The electron excitation processes can occur either in the plasma periphery or in the core. In this case, we are going to focus in the excitation processes occurring at the plasma periphery, where there is a greater probability of finding neutral Li atoms. Therefore, the electron density should be lower than in the core and therefore it is assumed that it has an approximate value in the order of m 3. The density population of ground state Li atoms can be estimated as being lower that the population of Li ions. Therefore, for order of magnitude purposes we assume that the population of Li atoms is 0.01% of the electron density, which corresponds to an order of m 3. Additionally, the most probable atomic transition is in the order of 10 8 s 1 [30, 8]. The cross section has a value of m [0]. The velocity is calculated from eq. 4.8 assuming the electrons have an energy of J (1000 ev) and using the electron mass kg. This velocity has a value of m s. So finally, by substituting these values in eq. for the emission coefficient is photons. m 3 s sterad 4.1, the approximate value It is important to notice that this exercise was performed in the most simplified way possible. An accurate collisional radiate model can be found in literature [30] and was not the main objective of this thesis work.

47 4.3 Study of the chord-integrated intensity profiles Study of the chord-integrated intensity profiles The main objective of the following section is to do a spatial resolved study of the intensity of the Å spectral line and compare it with other well isolated spectral lines belonging to already identified elements or ions. The measurements were performed with discharges heated by ECRH and NBI; in order to compare the behavior of this line under diverse temperature and plasma transport conditions. The results were then compared with already identified lines of elements with different ionization states such as: He I (5876 Å), B III (4487 Å), and C IV (590/ Å). The study of the spatial behavior of the intensity will provide us with new information that may help us in the assessment of the line of interest ECRH case It was assumed that the Å was formed mainly by charge exchange with highly energetic neutrals found in the plasma core or with cold neutrals located mostly in the plasma periphery. Therefore, the ECRH case presents an interesting scenario because there are no energetic neutrals being injected into the plasma. Hence, any charge exchange reactions should be taking place close to the plasma periphery, where there is a higher concentration of cold neutrals. Otherwise excitation and recombination of Li 3+ might be the working mechanism; although not at the very edge where the electron temperature (10-0 ev) is not high enough to produce that ionization stage. It should also be clear that there can be a non-negligible concentration of Li 3+ ions at the plasma periphery caused by drift losses. Measurements were taken for two previously identified lines, He I and B III, and they were compared with the line of interest. The lines compared correspond to the different shots shown in Fig This figure also shows the spatial measurements for He I, B III and the 4498 Å spectral line. It can be seen that the density remains fairly constant with time throughout all the discharges; the highest density is from the pulse 34413, shown in Fig. 4.7 (c), that reaches a value beyond m 3. The bolometer and X-ray intensity do not show any major change in any discharge; the lowest intensity for these traces is found in Fig. 4.7 (b), due to its lower density. The electron cyclotron emission trace is a bit higher for the shot shown in Fig Finally, Fig. 4.7 (a) also shows the spatial study of the behavior of He I. The intensity for this element is increasing throughout the discharge. Fig. 4.7 (b) displays the spatial study of the behavior of the Å spectral line; which remains somehow constant throughout the discharge. The spatial behavior of B III is depicted in Fig 4.7 (c) where it can be seen how the overall intensity remains rather constant, with a few isolated high peaks, during the entire discharge. A more detailed study will be done taking into consideration the form of some individual traces at a given time in order to perform a proper comparison.

48 44 4. Experimental Results Figure 4.7: Traces of TJ-II pulses analyzed to do a spatial resolved analysis of the intensity of the spectral line. The line integrated electron density along with the heating methods used during this shot, in this case solely ECRH. The bolometer, X-ray, gas puffing intensity, electron cyclotron emission and CV traces are also shown. These traces confirm that none of the shots show any abnormal behavior. (a) Spatial behavior of He I. The overall intensity increases throughout the discharge. (b) Spatial behavior of the Å. The overall intensity remains rather constant, with a small increase after 1150 ms (s). (b) Spatial behavior of B III. The overall intensity remains somewhat constant.

49 4.3 Study of the chord-integrated intensity profiles 45 Individual peaks from He I and B III were analyzed at different times and their shape was compared with the shape of the line of interest; the results are shown in Fig He I was chosen to do this comparison because is a neutral element that defines well the plasma edge, since it is mostly found in the plasma periphery. As explained in the experimental set-up section, this system maps the plasma from the upper side of the periphery to the lower side of the border. In the He I case, the intensity in the central chords is lower because the concentration of this element in the plasma core is negligible. This is the typical shape for an ions that lies in the plasma periphery. The B III spatial evolution shows a somehow similar behavior as He I in Fig. 4.8 (a); nevertheless, its trace is narrower that the He I trace, giving a clue that this element is peaking more inside the plasma not as close to the periphery as He I. Fig. 4.8 (b) shows that at time 1149 ms BIII is more evenly distributed in the plasma; whereas Fig. 4.8 (c) show that at time 100 ms it is closer to the plasma periphery, but still peaking more to the center than He I. Fig 4.8 also shows the comparison between these two traces and the Å trace. In Figs. 4.8 (a) and (b) it can be seen that this ion lies closer to the plasma core, and is mainly found in the lower part of the plasma. Fig. 4.8 (c) shows that towards the end of the discharge this ion is more evenly spread across the plasma. It is expected that, if this peak were Li III formed by charge exchange, in the case of ECRH the reactions should not take place in the plasma core. In this case, the ion is not in the outermost part of the plasma periphery but is not in the plasma core either. This fact also suggests that excitation and recombination rather than charge-exchange must be the responsible mechanisms dominating this emission line when operating in ECRH plasmas. This scanning system is operated with a spectral resolution of either 5 Å (gratings of 100 g ) or.5 Å for the holographic one (gratings mm of 400 g ); therefore it is not a high resolution system and hence this trace mm can also be from the Å line formed by excitation and recombination.

50 46 4. Experimental Results Figure 4.8: Spatial resolved study of He I (5486 Å) (red), B III (4487 Å) (blue) and the Å (green) spectral line at approximately (a) 1100 ms (b) 1150ms (c) 100 ms NBI case This case is of special interest, because fast energy neutrals are being injected to the plasma. These highly energetic neutrals interact with the ions found in the plasma, being Li III one of these ions. This high-energy beam is the source of charge exchange reactions between stripped ions and fast energetic neutrals. If the high-energy neutral beam crosses the observation zone, as in this case, we will be able to detect this the effect of the NBI. The shots analyzed have a short ECRH phase followed by a longer NBI heating phase, as can be seen in Fig In each case, the density behaves in a similar way, increasing after the NBI starts. The gas puffing trace shows that during NBI operation gas is injected only in the ECRH phase because the own NBI provides enough gas to fuel the plasma during this phase. The C V is depicted to illustrate the effect of the NBI. The carbon tiles are located in the opposite side of the injection system, and when the NBI is injected the high energetic neutrals collide with these tiles, therefore the intensity of C is likely to increase after the NBI is injected. Fig. 4.9 (a) shows the overall spatial resolved trace of C VI. It is clear that this trace increases shortly after the NBI is injected due to the positioning of the C tiles. Fig 4.9 (b) shows the overall spatial and temporal evolution of the intensity of the Å spectral line. This trace increases throughout the discharge. This increase in intensity starts to be noticeable at 1100 ms, when the NBI is injected. On the other hand, as seen in Fig. 4.9 (c), the B III trace does not seem to be highly affected by the NBI.

51 4.3 Study of the chord-integrated intensity profiles 47 Figure 4.9: Traces of TJ-II pulses analyzed to highlight the space-time resolved analysis of the intensity of the Å spectral line. The line integrated electron density along with the heating methods used during this shot. The bolometer, X-ray and gas puffing intensity are also shown. The CV trace is depicted a representation of the effect of the NBI. The carbon tiles are located in the opposite side of the injection system; therefore when the high energetic neutrals impinge into the tiles, carbon is sputtered. (a) Spatial behavior of C VI. The overall intensity increases after the NBI is injected. (b) Spatial behavior of the Å line. The overall intensity increases throughout the discharge (s). (b) Spatial behavior of B III. The overall intensity does not seem to be highly affected by the NBI injection.