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Effects of Charged Particle Heating on the Hydrodynamics of Inertially Confined Plasmas

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Effects of Charged Particle Heating on the Hydrodynamics of Inertially Confined Plasmas Effects of Charged Particle Heating on the Hydrodynamics of Inertially Confined Plasmas by Alison Christopherson In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Department of Mechanical Engineering University of Rochester 2020 ii POWER!! UNLIMITED POWER!! Emperor Palpatine iii I dedicate this thesis to the anonymous referees of my Physical Review E paper for their insight in pointing out how harmful and manipulative my work was to the field of inertial confinement fusion. iv TABLE OF CONTENTS Biographical Sketch . xi Acknowledgments . xvi Abstract . xxi Contributors and Funding Sources . xxi List of Tables . xxii List of Figures . xxiv Chapter 1: Introduction . 1 Chapter 2: A comprehensive alpha-heating model for the deceleration phase . 8 2.1 Basic physics of alpha heating and ignition . 9 2.2 Implosion simulation database . 17 2.3 One dimensional dynamic hot-spot and shell model . 19 2.3.1 Hot-spot pressure . 25 2.3.2 Shocked-shell velocity . 27 2.3.3 Shock position in shell . 29 v 2.3.4 Hot-spot energy . 30 2.3.5 Hot-spot mass . 35 2.3.6 Shocked-shell mass . 41 2.3.7 Shocked shell momentum balance . 43 2.3.8 Solution of the model . 45 2.4 Conclusions . 48 2.5 Appendix A . 50 Chapter 3: 1D Theory of alpha heating and burning plasmas for inertially con- fined plasmas . 54 3.1 Analysis of measurable alpha-heating metrics . 57 3.1.1 Definition of fα ............................ 57 3.1.2 Inferring fα experimentally . 60 3.1.3 Relation between fα and χα ..................... 63 3.2 Yield amplification curves and comparisons with compressible shell model . 67 3.3 Burning-plasma metrics . 70 3.3.1 First burning-plasma regime . 70 3.3.2 Second burning-plasma regime . 77 3.4 Burning-plasma regimes in high-foot implosions . 85 3.5 Conclusions . 90 3.6 Appendix A . 92 vi Chapter 4: 1D theory of ignition and burn propagation for inertially confined plasmas . 96 4.1 History of ignition criterion . 97 4.2 Burn propagation model for inertial confinement fusion . 116 4.2.1 Solution of the model . 131 4.3 Transition from alpha-heating to burn propagation . 132 4.3.1 Yield amplification - fα curve . 132 4.3.2 Effect of the alpha particle range . 137 4.3.3 Burn profile shift . 138 4.3.4 Transition out of the subsonic regime . 144 4.4 Fusion yield output required for ignition . 146 4.5 Conclusions . 148 Chapter 5: Modifications to alpha-heating, burning plasma, and ignition theory in the presence of implosion nonuniformities . 150 5.1 Impact of asymmetries on the definition of ignition . 150 5.1.1 Comparison of fα with other metrics . 155 5.2 Effect of asymmetries on the burning plasma condition . 158 5.3 Conclusions . 162 Chapter 6: Direct measurements of hot electron preheat in inertially confined plasmas . 163 6.1 Analysis of hard x-rays . 168 6.1.1 DT Preheat formula . 170 vii 6.1.2 Dependence of fuel areal density on preheat energy . 178 6.2 Experimental setup and results . 181 6.3 Preheat Analysis . 189 6.4 Analysis of α ∼ 4 DT-layered implosions . 191 6.5 Conclusions . 193 6.6 Appendix A: pinhole camera images . 194 6.7 Appendix B: The effect of Aluminum coatings on the hard x-ray analysis . 195 6.7.1 The DT preheat formula (including Aluminum) . 195 6.7.2 The χ2 analysis of experimental data (including Aluminum) . 196 6.7.3 Analysis of DT-layered implosions including the effect of Aluminum198 6.8 Appendix C: scaling of areal density with adiabat . 198 Chapter 7: Conclusions . 203 7.1 Alpha-heating metrics and theory of burning plasmas and ignition . 203 7.2 Hot electron preheat measurements . 204 References . 235 Appendix A: Basic physics of nuclear energy . 238 A.1 Nuclear reaction kinematics and binding energy . 239 A.2 Quantum tunneling and barrier penetration . 244 A.3 Nuclear cross sections and reactivity . 247 Appendix B: Plasma physics . 253 viii B.1 Definition of a plasma . 253 B.2 Coulomb collisions . 255 B.2.1 Charged particle stopping powers in a material . 264 B.2.2 Charged particle collision frequencies . 266 B.2.3 Alpha particle slowing down in ICF plasmas . 270 B.2.4 Energetic electron slowing down in ICF plasmas . 274 B.2.5 Hard x-ray emission from energetic electrons . 278 B.3 Fokker Planck description of plasmas . 292 B.3.1 Dynamical friction vector . 294 B.3.2 The diffusion tensor . 297 B.3.3 Evaluation of the collision operator for electron-ion collisions . 299 B.4 Moments of the Boltzmann equation . 300 B.4.1 Zeroth moment (conservation of mass) . 304 B.4.2 First moment (conservation of momentum) . 305 B.4.3 Second moment (conservation of energy) . 307 B.4.4 Equation of state for closure . 310 B.4.5 Coupling between ions and electrons . 311 B.4.6 The one-fluid description of a plasma . 311 B.5 Plasma waves . 312 B.5.1 Electron plasma waves . 314 B.5.2 Collisional damping of electron plasma waves . 317 ix B.5.3 Landau damping of electron plasma waves . 318 B.5.4 Ion acoustic waves . 331 B.5.5 Electromagnetic waves . 332 B.5.6 Collisional damping of light waves . 334 B.5.7 Collisional absorption of light waves by plasmas . 335 B.5.8 Nonlinear ponderomotive force . 339 B.6 Parametric instabilities . 341 B.6.1 Two Plasmon Decay . 344 B.6.2 Stimulated Raman Scattering instability . 345 B.6.3 Crossed Beam Energy Transfer . 345 Appendix C: Inertial confinement fusion physics . 347 C.1 Laser driven ablation fronts . 348 C.2 The shock timing phase of implosions . 357 C.3 The acceleration phase of implosions . 361 C.4 The deceleration phase of implosions . 369 C.5 Scaling of stagnation conditions with design parameters . 372 C.6 Rayleigh Taylor Instability . 378 C.6.1 Classical RTI . 379 C.6.2 Ablative RTI . 384 Appendix D: ICF capsule engineering . 388 x D.1 Direct drive designs . 391 D.1.1 Shock ignition . 393 D.1.2 Fast ignition . 395 D.2 Indirect drive design . 395 Appendix E: History of the United States inertial confinement fusion program . 401 E.1 Nuclear weapons . 402 E.1.1 The Manhattan project . 402 E.1.2 Development of the “Super” . 405 E.1.3 Stockpile Stewardship . 407 E.2 Laboratory nuclear fusion . 408 E.3 The development of the laser . 412 E.4 Inertial fusion research at KMS fusion . 415 E.5 Inertial fusion research at Lawrence Livermore National Laboratory . ..
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