! 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]