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Direct Drive Inertial Confinement Fusion Direct Drive Inertial Confinement Fusion: Analysis of the Implosion Core by Arijit Bose Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Supervised by Professor Riccardo Betti Department of Physics and Astronomy Arts, Sciences and Engineering School of Arts and Sciences University of Rochester Rochester, New York 2017 ii Table of Contents Biographical Sketch vii Acknowledgments xi Abstract xv Contributors and Funding Sources xviii List of Tables xix List of Figures xx 1 Introduction1 1.1 Inertial Confinement Fusion: A Brief Overview...........1 1.1.1 Nuclear Fusion: The Fundamentals.............1 1.1.2 Motivation for Fusion Research...............4 1.1.3 Challenges for Laboratory Fusion..............5 1.1.4 Complementary Approaches: Direct- and Indirect-Drive..7 1.1.5 Current Status and Future Endeavors............ 11 1.2 Thesis Outline............................. 14 Bibliography................................ 17 TABLE OF CONTENTS iii 2 Compression of the Fusion Fuel 20 2.1 Hot Spot dynamics: A Theoretical Model.............. 23 2.1.1 Energy of the Hot Spot.................... 24 2.1.2 Temperature of The Hot-Spot................ 27 2.1.3 Momentum of the Imploding Shell............. 28 Trajectory of the Return Shock in the Shell........ 29 Mass of the Shocked Shell.................. 31 Momentum of the Shocked Shell............... 31 2.1.4 Solution of the Simplified Model............... 32 2.2 Monitoring Progress towards Ignition in Steps........... 38 2.2.1 Simplest Model for Alpha Heating.............. 39 2.2.2 The Burning Plasma Regime................. 41 2.2.3 Implosion Performance Metric................ 44 2.3 Summary............................... 45 Bibliography................................ 47 3 Simulations of Core Asymmetries 49 3.1 Rayleigh Taylor Instability (RTI): A Brief Summary........ 49 3.1.1 Classical RTI (Linear Theory)................ 50 3.1.2 Stabilization of the RTI................... 54 Effect of a Diffused Density Profile at the Interface.... 54 Effect of Ablation Velocity at the Interface......... 56 3.2 Simulations of the Deceleration-Phase RTI............. 58 3.2.1 A Brief Description of DEC2D ............... 59 TABLE OF CONTENTS iv 3.3 Summary............................... 66 Bibliography................................ 67 4 Nonlinear RTI induced Asymmetries of the Hot Spot 70 4.1 Nonlinear RTI of ICF Implosion Core................ 71 4.2 Simulations of the Deceleration Phase................ 75 4.3 Effect of Asymmetries on the Implosion Hydrodynamics...... 78 4.4 Comparison of Neutron-Averaged and Hot-Spot{Averaged Quantities 86 4.5 Model for Compression of an Asymmetric Hot Spot........ 93 4.5.1 Flow Correction to Adiabatic Compression......... 93 4.5.2 Relating Pressure Degradation and Total Residual Energy 100 4.6 Effect of Asymmetries on the Implosion Energetics........ 106 4.7 Conclusions.............................. 113 4.8 Appendix: Other Shapes Represent a Gradual Transition from Low- to Mid- Mode Effects............................. 115 Bibliography................................ 117 5 Asymmetry Trends in Experiments 123 5.1 Outline................................. 123 5.2 Trends in Cryogenic Implosion Experiments............ 124 5.3 The Reconstruction Technique and its Application......... 128 5.3.1 Inferred Hot-Spot Pressure.................. 132 5.3.2 Estimation of the Hot-Spot Size: Using Time-Gated Self- Emission Images....................... 135 TABLE OF CONTENTS v 5.3.3 Shape Analysis of Time-Integrated Self-Emission Images. 139 5.3.4 Neutron-Averaged Ion Temperature............. 143 5.3.5 Implosion Areal Density................... 146 5.3.6 Burnwidth and Bang Time.................. 147 5.4 Summary and Future Work..................... 151 Bibliography................................ 153 6 Scaling of the Implosion Core 156 6.1 Introduction.............................. 156 6.2 Hydro-Equivalent Scaling of the Deceleration Phase........ 158 6.3 Scaling of the no-α Yield Over Clean................ 161 6.4 Hydro-Equivalent Implosion Design and Simulations of Deceleration- Phase RTI............................... 163 6.5 Non-Hydro-Equivalent Physics of the Deceleration Phase..... 167 6.5.1 Effect of Thermal Conduction: Vabl=Vimp Scaling...... 168 6.5.2 Effect of Radiation Transport: Lmin=Rh Scaling...... 174 6.6 Scaling of the no-α Ignition Condition............... 176 6.7 Conclusions.............................. 179 Bibliography................................ 181 7 Fusion Yield Extrapolation to Larger Drivers 183 7.1 Outline................................. 184 7.2 Conditions for Scaling to Ignition Relevant Laser Energies.... 185 7.3 The Theory for Alpha Heating Extrapolation............ 187 vi 7.4 Consolidation with Simulations................... 192 7.5 Summary and Future Directions................... 195 Bibliography................................ 198 8 Conclusion 202 Bibliography................................ 207 vii Biographical Sketch The author was born in the city of Udaipur in Rajasthan, India in 1988, and was brought up in Asansol and Kolkata, West Bengal. He attended the Chen- nai Mathematical Institute from 2007 to 2010 and graduated with a Bachelor of Science degree with honors in Physics. Following his graduation, he enrolled in the Department of Physics and Astronomy at the University of Rochester. Ar- ijit designed and instructed an undergraduate course on Classical Mechanics at the University of Rochester for which he received the Graduate Student Teaching Award in 2012. He received a Master of Arts degree in Physics in 2012 and started research at the Laboratory for Laser Energetics (LLE), to pursue a Doctoral de- gree on plasma physics and inertial confinement fusion under the supervision of Professor Riccardo Betti. Arijit received the Frank J. Horton Graduate Research Fellowship awarded by the LLE. BIOGRAPHICAL SKETCH viii List of Publications 1. A. Bose et al.,\Analysis of trends in implosion observables for direct- drive cryogenic implosions on OMEGA", manuscript in preparation, Phys. Plasmas (2017) 2. A. Bose, R. Betti, D. Shvarts, and K. M. Woo, \The physics of long- and intermediate-wavelength asymmetries of the hot spot: Compression hy- drodynamics and energetics", Phys. Plasmas, 24, 102704 (2017). DOI: 10.1063/1.4995250 3. A. Bose, K. M. Woo, R. Betti, E. M. Campbell, D. Mangino, A. R. Christo- pherson, R. L. McCrory, R. Nora, S. P. Regan, V. N. Goncharov, T. C. Sangster, C. J. Forrest, J. Frenje, M. Gatu Johnson, V. Yu. Glebov, J. P. Knauer, F. J. Marshall, C. Stoeckl, and W. Theobald, \Core conditions for alpha heating attained in direct-drive inertial confinement fusion", Phys. Rev. E 94, 011201(R) (2016). DOI: 10.1103/PhysRevE.94.011201 4. A. Bose, K. M. Woo, R. Nora, and R. Betti, \Hydrodynamic scaling of the deceleration-phase Rayleigh{Taylor instability", Phys. Plasmas 22, 072702 (2015). DOI: 10.1063/1.4923438 5. W. Theobald, A. Bose, R. Yan, R. Betti, M. Lafon, D. Mangino, A. Christo- pherson, C. Stoeckl, W. Seka, W. Shang, D. T. Michel, C. Ren, R. Nora, A. Casner, J. Peebles, F. N. Beg, X. Ribeyre, E. L. Aisa, A. Colaitis, V. T. Tikhonchuk, and M. Wei, \Enhanced Hot-Electron Production and Strong- Shock Generation in Hydrogen-Rich Ablators for Shock Ignition", accepted, Phys. Plasmas Lett. (2017) BIOGRAPHICAL SKETCH ix 6. A. R. Christopherson, R. Betti, A. Bose, J. A. Howard, K. M. Woo, E. Campbell, J. R. Sanz, and B. K. Spears, \A comprehensive alpha heat- ing model for inertial confinement fusion", under review, Phys. Plasmas (2017) 7. R. Betti, A. R. Christopherson, B. K. Spears, R. Nora, A. Bose, J. Howard, K. M. Woo, M. J. Edwards, and J. Sanz, \Alpha Heating and Burning Plasmas in Inertial Confinement Fusion", Phys. Rev. Lett. 114, 255003. DOI: 10.1103/PhysRevLett.114.255003 8. R. Nora, R. Betti, K. S. Anderson, A. Shvydky, A. Bose, K. M. Woo, A. Christopherson, J. A. Marozas, T. J. B. Collins, P. B. Radha, S. Hu, R. Epstein, F. J. Marshall, R. McCrory, T. C. Sangster, and D. Meyerhofer, \Theory of Hydro-Equivalent Ignition for Inertial Fusion and Its Applica- tions to OMEGA and the National Ignition Facility, Phys. Plasmas 21, 056316 (2014). DOI: 10.1063/1.4875331 9. S. P. Regan, V. N. Goncharov, I. V. Igumenshchev, T. C. Sangster, R. Betti, A. Bose, T. R. Boehly, M. J. Bonino, E. M. Campbell, D. Cao, T. J. B. Collins, R. S. Craxton, A. K. Davis, J. A. Delettrez, D. H. Edgell, R. Epstein, C. J. Forrest, J. A. Frenje, D. H. Froula, M. Gatu Johnson, V. Yu. Glebov, D. R. Harding, M. Hohenberger, S. X. Hu, D. Jacobs-Perkins, R. Janezic, M. Karasik, R. L. Keck, J. H. Kelly, T. J. Kessler, J. P. Knauer, T. Z. Kosc, S. J. Loucks, J. A. Marozas, F. J. Marshall, R. L. McCrory, P.W. McKenty, D. D. Meyerhofer, D. T. Michel, J. F. Myatt, S. P. Obenschain, R. D. Petrasso, P. B. Radha, B. Rice, M. J. Rosenberg, A. J. Schmitt, M. J. Schmitt, W. Seka, W. T. Shmayda, M. J. Shoup III, A. Shvydky, S. Skupsky, A. A. Solodov, C. Stoeckl, W. Theobald, J. Ulreich, M. D. Wittman, K. BIOGRAPHICAL SKETCH x M. Woo, B. Yaakobi, and J. D. Zuegel, \Demonstration of Fuel Hot-Spot Pressure in Excess of 50 Gbar for Direct-Drive, Layered Deuterium-Tritium Implosions on OMEGA", Phys. Rev. Lett. 117, 059903 (2016). DOI: 10.1103/PhysRevLett.117.025001 10. W. L. Shang, R. Betti, S. X. Hu, K. Woo, L. Hao, C. Ren, A. R. Christopher- son, A. Bose, and W. Theobald, \Electron shock ignition of inertial fusion targets", Phys. Rev. Lett. 119, 195001 (2017). DOI: 10.1103/Phys- RevLett.119.195001 11. E. L. Aisa, X. Ribeyre, G. Duchateau, T. H. Nguyen-Bui,
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