! ELECTRON!DENSITY!IN!A!HELIUM!DISCHARGE! PLASMA! ! ! BACHELOR!THESIS! ! SUBMITTED!BY! ! CHRISTIAN!KÜCHLER! ! DECEMBER!2013!! ! ! ! ! ! ! ! ! ! ! ! PRIMARY!EXMINER:!PROF.!DR.!JOACHIM!JACOBY! SECONDARY!EXAMINER:!PROF.!DAVID!Q.!HWANG,!PHD! ! ! ! ! ! ! ! Contents Abstract 4 Chapter 1. Introduction 5 Chapter 2. Theory of discharge plasma and their diagnostics 7 2.1. DefinitionofPlasmaandimportantProperties 7 2.2. IonizationandRecombinationinaDischargePlasma 8 2.3. Breakdown Condition for a Discharge Plasma 9 2.4. Interferometry 11 Chapter 3. Experimental setup 14 3.1. Interferometer 14 3.2. Plasma source 17 3.3. Vacuum system 19 Chapter 4. Data Processing and Analysis 21 4.1. Reconstruction of line-integrated densities 21 4.2. Abel Inversion 24 4.3. EstimationandEvaluationofUncertainties 29 Chapter 5. Results and Evaluation 32 5.1. Reproducibility 32 5.2. ResultsandEvaluationofAbelInversion 34 5.2.1.Densityprofile 35 5.2.2. Electron density over time 37 5.3. Interpretation and Evaluation of Experimental Results 41 Chapter 6. Outlook 43 Chapter 7. Acknowledgements 45 Bibliography 46 Erklärung/Declaration 48 3 Abstract The thesis at hand describes the experimental investigation of the electron den- sity in a plasma source. The source has been developed to study the current drive by crossing two lasers within a plasma. The plasma is created by a helium discharge within a small vacuum chamber containing the two spherically shaped electrodes (about 1 cm apart). The energy of 11.3 J necessary is stored in a capacitor of ca- pacity 0.15 µF. The electron density was measured at pressure in the range between 500 Pa and 1350 Pa. To investigate the electron density a heterodyne Michelson- interferometer is used, which gives the line-integrated density along the interferome- ter beam. To reconstruct the density as a function of time and position, the process of Abel inversion is used. The overall goal is to find a time and position at which 15 3 the density is most likely to be in the range of (2 0.2) 10 cm− . ± · The plasma was found to form at a different position at each discharge in contrast to initial expectations. Therefore the results can only show the average density profile of the source over many discharges. This effect also causes a moderate reproducibility at the center of the setup and a low reproducibility at the outer positions of the setup. In most cases the electron density had a peak between 0.5 and 1.5 cm away from the center of he source. Nevertheless some conclusions about radial density profile over time can be drawn and suggestions on the adjustment of the experimental setup are made. 4 CHAPTER 1 Introduction A plasma is a partially or fully ionized gas. Plasma are a integral part of our daily lives, yet mostly hidden in natural phenomena or everyday products. A major part of the world’s artificial lighting is based on gas-discharge plasma, and the earth’s major natural source of light, the sun, is a burning plasma by itself. While these plasma are completely different in their physical properties, they are important for much of plasma-related research. The social, environmental and economic impact of modern energy production is becoming larger due to the fading supply of fossil fuels and the effects of global warming. Nuclear fusion - the physical effect that drives the energy production in the center of the sun - could be the basis of a future energy source. Current research in fusion science can be separated into two groups. In magnetic confinement fusion (MCF) a plasma of more than 10 keV is confined using external magnetic fields. In inertial fusion the conditions necessary for such a process are created by compressing a plasma very quickly and thereby creating very high densities and temperatures. A somewhat intermediate approach is the so-called magneto-inertial fusion. This method is based on inertial fusion, but exploits magnetic fields to increase confine- ment efficiency and thereby requires less extreme conditions. One method to achieve this could be to spherically distribute several plasma guns around a plasma target. When ignited, the plasma guns accelerate a plasma jet to about 200 km/s. When these jets merge, they form a shell around the initial target, which collapses quickly, ideally to fusion conditions. Confining the initial target by a magnetic field reduces losses due to heat and decreases the implosion velocity needed, leading to a higher target mass and therefore higher energy gains [1]. The magnetic fields have to be very strong ( 103 T), which cannot be created directly from the outside of a po- ⇠ tential fusion reactor. A possible solution is to use the compression of the target itself to increase an initial seed magnetic field. If magnetic fields are compressed adiabatically, the magnetic flux is conserved, leading to the expression [2] φ = B~ dS~ = const., (1.0.1) · ZS where S~ is a plasma surface area and B~ denotes the magnetic flux density through that surface. For the sake of simplicity the magnetic field has been estimated to be constant over the area. Decreasing the area A by a large amount will therefore result 5 1. INTRODUCTION 6 in an increase of the magnetic flux density B. It has been shown [3]thatupto3kT can be achieved using this technique. The initial magnetic field can be formed by driving a current with a plasma wave. This current may be created by exploiting the phenomenon of Landau damping. It is based on the motion of charged particles due to the field of an electromagnetic wave. When the energy transfer by the electromagnetic wave δW is averaged over initial positions and a distribution of initial velocities f (v) in the collisionless limit, the expression ⇡q2E2 ! @f(v) ! δW = (1.0.2) − 2m k k @v k | | ⇣ ⌘ can be derived [4], where E is the electric field amplitude, q the particle charge, m their mass and ! and k the waves’ frequency and wave vector, respectively. The term @f/@v is essential for the current drive due to Landau damping. If the initial velocity of a particle is smaller than !/k, the particle will gain energy; if it is larger, energy will be lost. The ratio !/k can therefore determine the number of particles gaining energy and is responsible for driving the desired current. One way to create such a wave exploits the phenomenon of beating, i.e. the interference of two electromagnetic waves of different frequencies. If the difference between those frequencies is approximately equal to the plasma frequency, Landau damping can cause a resonant excitation of the plasma and thus create a current and consequently a magnetic field. The experiment described in this thesis was carried out on a plasma source created to study this method of distant magnetic field creation. It is described in [5] and summarized as follows: Two CO2 lasers are crossed inside the plasma at a pre-defined point. The lasers may have a frequency difference of 30 GHz to 3.6 THz, 13 3 17 3 which can excite plasma with densities of 10 cm− to 10 cm− . In order to study 15 3 the beatwave process, a density of 2 10 cm− has been chosen, corresponding to · a plasma frequency of 2.5 THz. As the lasers have to be crossed at a pre-defined position and time within the plasma source, it is essential to know the time-resolved density distribution. The aim of this thesis is to experimentally investigate the electron density within a newly developed plasma source, ending with a conclusion as to which conditions, positions and times are suitable for studying the beat-wave process. CHAPTER 2 Theory of discharge plasma and their diagnostics This chapter will introduce the concept of plasma in a general sense and give a definition of the term. This definition will cover an extremely broad range of physical conditions that need to be characterized by certain parameters. Within a plasma several atomic processes take place and the most important of them are discussed briefly in the second part of this chapter. In the final part the condition necessary for a breakdown in a gas is derived, as the experiment treated in this thesis is based on a gas discharge. 2.1. Definition of Plasma and important Properties A plasma is most commonly defined as an ionized gas, i.e. a gas consisting of free electrons and ions, but without an overall charge (quasi-neutrality). This 4 includes partially and fully ionized plasma, but a degree of ionization of 10− is regarded as the minimum amount of ionization [6]. This definition covers a very wide range of physical conditions. In nature, the most fundamental plasma properties, 6 39 3 electron density and electron temperature may have values of (10− -10 ) cm− and (104 -108) K, respectively. Owing to this large range of values, it is essential to introduce additional parameters to characterize the physical conditions present within a plasma. In a plasma every charge carrier is surrounded by several charge carriers of op- posite charge, resulting in a shielding of the initial charge and in a quasi-neutral plasma. The distance from a charge carrier at which the electron thermal energy Wth equals the electric potential energy W pot is defined as Debye length λD.From 2 2 Poisson’s equation V (r)= nee/"0 and V (r) E~ (r) /r, where E~ (r) represents r − r ' the electric field vector, it follows that nee E~ (λD) = λD. (2.1.1) | | "0 λD Using the condition Wpot = Wth and Wpot = e 0 E (e) dr = neeλD/(2"0) [7], R "0kBT λD = . (2.1.2) n e2 r e A plasma of dimensions L is considered as quasi-neutral, if the condition λD L is ⌧ satisfied [7].