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Investigations of Runaway Electron Generation, Transport, and Stability in the DIII-D Tokamak

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Investigations of Runaway Electron Generation, Transport, and Stability in the DIII-D Tokamak UNIVERSITY OF CALIFORNIA, SAN DIEGO Investigations of runaway electron generation, transport, and stability in the DIII-D tokamak A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Engineering Science (Engineering Physics) by Alexander Nevil Tronchin-James Committee in charge: George Tynan, Chair C. Fred Driscoll Eric Hollmann Stefan Llewellyn Smith Richard Moyer Thomas O'Neil 2011 Copyright Alexander Nevil Tronchin-James, 2011 All rights reserved. The dissertation of Alexander Nevil Tronchin-James is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California, San Diego 2011 iii DEDICATION Dedicated to all the people who have treated me like family and made me feel at home, wherever I am. Also dedicated to the pursuit of flying motorcycles. iv EPIGRAPH Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. {Mark Twain v TABLE OF CONTENTS Signature Page.......................................... iii Dedication............................................ iv Epigraph.............................................v Table of Contents........................................ vi List of Figures.......................................... ix List of Tables........................................... xiii Acknowledgements........................................ xiv Vita................................................ xvi Abstract of the Dissertation................................... xvii Chapter 1 Introduction....................................1 1.1 Energy in modern civilization.......................1 1.2 Nuclear Fusion...............................2 1.2.1 Natural reactors..........................2 1.2.2 Manmade reactors.........................2 1.2.2.1 Inertial confinement...................3 1.2.2.2 Magnetic confinement..................3 1.3 Runaway electrons.............................4 1.3.1 Basic theory of runaway generation................4 1.3.2 Natural occurrence.........................5 1.3.3 Laboratory occurrence.......................5 1.4 Tokamak Disruptions............................6 1.4.1 Causative factors..........................6 1.4.2 Thermal Quench..........................6 1.4.3 Current Quench..........................6 1.4.4 Runaway plateau..........................7 1.4.5 Runaway termination.......................7 Chapter 2 A brief history of runaway electron studies...................8 2.1 Theory....................................8 2.1.1 Generation.............................8 2.1.1.1 Dreicer generation....................8 2.1.1.2 Hot-tail generation.................... 10 2.1.1.3 Avalanche generation.................. 10 2.1.2 Energy limit and energy distribution............... 11 2.1.3 Transport, equilibrium, and stability............... 12 2.1.3.1 Diffusion......................... 12 2.1.3.2 Force equilibrium.................... 13 2.2 Prior Experiments............................. 14 vi Chapter 3 Experimental techniques for studying runaway electrons in tokamak disruptions 17 3.1 Argon killer pellet injection and plasma shaping to generate runaway electrons................................... 17 3.2 Diagnostics for studying rapid shutdowns and runaway electrons... 18 3.3 Hard x-ray sensing scintillators...................... 21 3.3.1 Motivation............................. 21 3.3.2 Modelling bremsstrahlung from runaway electrons....... 21 3.3.3 Detector design........................... 21 3.3.3.1 Scintillator selection................... 24 3.3.3.2 Amplifier and electronics................ 24 3.3.3.3 Electromagnetic shielding................ 26 3.3.4 Array arrangement......................... 26 3.3.5 Runaway energy resolution.................... 27 3.3.5.1 Photo-neutron signals.................. 30 3.3.5.2 Radiation damage to silicon detectors......... 32 3.4 Magnetic diagnostics............................ 32 3.5 Bolometer and soft x-ray arrays...................... 33 3.6 Interferometers............................... 36 3.6.1 Fringe skips, and corrections................... 37 3.7 Electron cyclotron emission........................ 39 3.7.1 ECE cutoff............................. 39 3.8 Other diagnostics.............................. 41 3.8.1 Fast visible camera......................... 41 3.8.2 Reflectometers........................... 41 3.8.3 EUV Spectroscopy......................... 41 3.8.4 Other spectroscopy......................... 42 3.9 Flux function reconstructions....................... 42 3.9.1 EFIT................................ 42 3.9.2 JFIT................................. 43 Chapter 4 Hard x-ray emission from runaway electrons in DIII-D............ 47 4.1 Experimental findings........................... 47 4.2 Discussion and Analysis.......................... 51 4.2.1 Limitations of thermal quench measurements.......... 51 4.2.2 Prompt-loss phenomena...................... 51 4.2.3 Plateau phenomena........................ 52 4.2.4 Termination phenomena...................... 57 4.2.5 NIMROD modeling........................ 61 4.2.6 RE energy and loop voltages................... 63 4.2.7 Bremsstrahlung from runaways.................. 63 4.3 Conclusions................................. 65 Chapter 5 Interaction between runaways and injected pellets.............. 67 5.1 Motivation................................. 67 5.2 Impurity pellet injection.......................... 67 5.3 Visible Imaging............................... 69 5.4 Observed cyclotron emission........................ 70 5.5 Discussion of cyclotron emission in the relativistic limit........ 72 5.6 Pellet heating and breakdown by runaways............... 72 5.7 Conclusions................................. 74 vii Chapter 6 Determining loop voltages during tokamak rapid shutdowns......... 76 6.1 Review of voltage sources in a cooling plasma.............. 77 6.1.1 Spitzer resistivity and hyper-resistivity.............. 77 6.1.2 Models of radiative cooling and killer pellet ablation...... 78 6.1.2.1 Radiative cooling modelled by KPRAD........ 78 6.1.2.2 Killer pellet models................... 79 6.2 Thermal quench timing with bolometer tomography.......... 79 6.3 Inferring the loop voltage using magnetic diagnostics.......... 82 6.3.1 Derivation of loop voltage for changing current from Faraday's equation............................... 82 6.3.2 Limitations of magnetic diagnostics................ 83 6.3.3 Inverse techniques for inspecting loop voltages before the current quench................................ 85 6.4 Conclusions................................. 88 Chapter 7 Conclusions and outlook............................. 89 Appendix A Table of symbols................................. 91 Appendix B History of runaway electron observation in DIII-D.............. 93 Appendix C Pellet injector................................... 96 C.1 Repairs................................... 96 C.2 Modifications................................ 97 C.3 Pellet material selection.......................... 100 Appendix D Comparison of various techniques for calculating runaway current due to avalanche..................................... 102 D.1 Empirical techniques............................ 102 D.2 Coupled inductor model.......................... 103 D.3 Calculation of runaway electron seed current.............. 105 Bibliography........................................... 107 viii LIST OF FIGURES Figure 0.1: The DIII-D Team................................. xiv Figure 1.1: A cartoon of the DIII-D tokamak operated at General Atomics in San Diego.3 Figure 2.1: A 3D rendering of the DIII-D tokamak. From the outside in are: toroidal field coils (black), poloidal field/shaping coils (red), center solenoid windings (green), the Inconel vacuum vessel (grey), and graphite limiting surfaces (black). 16 Figure 3.1: A histogram of plateau phase runaway current plotted for the two different experimental shapes showing increased frequency of runaway plateau for the limited shape.................................... 18 Figure 3.2: Histograms of the initial a) electron temperature, b) electron density, c) stored thermal energy, and d) edge safety factor..................... 19 Figure 3.3: Diagnostic and hardware arrangement for the experiments discussed..... 20 Figure 3.4: A cartoon of the EGSnrc geometry used for modelling x-ray spectra from run- aways striking the DIII-D wall, and a series of those spectra observed outside the DIII-D vessel. Each curve terminates at approximately the incident RE energy........................................ 22 Figure 3.5: A cartoon of the EGSnrc geometry used for modelling x-ray fluence (color) vs. angle of incidence α and energy (radius) from runaways impacting a 2mm × 2mm carbon pellet, and a series of the resulting fluences for three different energy incident electrons.............................. 23 Figure 3.6: Drawing of detector assembly with a) side view and b) rear view....... 24 Figure 3.7: A detailed drawing of the scintillator detector design.............. 25 Figure 3.8: Spatial arrangement of a) midplane toroidal and b) poloidal scintillator arrays. 27 Figure 3.9: Scintillator array signals in a disruption with a) significant runaway electron current Ir (measured by subtracting a fitted L/R current decay IL=R from the total measured current Im), b) time traces from the poloidal array at 90 de- grees with detectors above,
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