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/content/aip/journal/pop/22/5/10.1063/1.4918953
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74. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-Value Problems, 2nd ed. ( Interscience Publishers, a division of John Wiley & Sons, Inc., 1967), pp. 311320.
75.
75.Note that within the liner region, we do not attempt to radially resolve thermal conduction, radiation transport, or ohmic dissipation. Doing so would significantly increase the complexity of our model, while not significantly improving the accuracy, since our model already captures the overall dynamics of a liner implosion (i.e., compression, bulk heating, and acceleration) very well relative to full 1D radiation magnetohydrodynamics simulations.
76.
76. R. P. Drake, High Energy Density Physics: Fundamentals, Inertial Fusion, and Experimental Astrophysics, 1st ed. ( Springer, 2006), p. 70.
77.
77.Atomic, molecular, and optical physics; ionization potentials of atoms and atomic ions,” in CRC Handbook of Chemistry and Physics, 84th ed., edited by D. R. Lide ( CRC Press, 2003), Chap. 10.
78.
78. Y. B. Zel'dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, edited by W. D. Hayes and R. F. Probstein ( Dover Publications, Inc., 2002), p. 131.
79.
79. F. F. Chen, Introduction to Plasma Physics and Controlled Fusion, 2nd ed. ( Plenum Press, 1984), pp. 6768.
80.
80. J. D. Callen, Fundamentals of Plasma Physics (unpublished, 2014), Chap. 2, preprint available from http://homepages.cae.wisc.edu/~callen/book.html.
81.
81. M. Geissel, personal communication (2014).
82.
82. M. Geissel and A. J. Harvey-Thompson, personal communication (2014).
83.
83. M. Geissel, L. E. Ruggles, I. C. Smith, J. E. Shores, C. S. Speas, and J. L. Porter, Bull. Am. Phys. Soc. 59, 75 (2014).
84.
84.Note that if the entire fuel region is preheated uniformly, i.e., from r = 0 to rg(tph), then only the hot spot region will exist.
85.
85.Note that our radiation model is a bremsstrahlung model that accounts for dopants and/or contaminants mixed into the fuel. However, this radiation model does not account for line radiation, which can be substantial for dopants and/or contaminants with mid to high atomic numbers.
86.
86.The bisection method is a robust technique that is simple to program and simple to explain. However, the method is also computationally inefficient. For our radiation loss model, we have found that the number of iterations required to meet a given solution accuracy can be substantially reduced by supplementing the bisection algorithm with various “best guess” techniques that make use of the fact that the ratios and rh/rg change relatively slowly from one time step to the next. However, a detailed description of our efforts in this regard is beyond the scope of this paper.
87.
87. E. M. Epperlein and M. G. Haines, Phys. Fluids 29, 1029 (1986).
http://dx.doi.org/10.1063/1.865901
88.
88. S. I. Braginskii, Reviews of Plasma Physics ( Consultants Bureau, New York, 1965), Vol. 1, p. 205.
89.
89.Note that this axial energy loss is due solely to mass flow out of the imploding region. Our model does not account for energy losses due to other axially directed transport processes, e.g., axial thermal conduction.
90.
90. A. L. Velikovich, personal communication (2014).
91.
91. A. A. Harms, K. F. Schoepf, G. H. Miley, and D. R. Kingdon, Principles of Fusion Energy, 1st ed. ( World Scientific Publishing Co. Pte. Ltd., 2000), p. 26.
92.
92. H.-S. Bosch and G. M. Hale, Nucl. Fusion 32, 611 (1992).
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93.
93. S. Atzeni and J. M. ter Vehn, The Physics of Inertial Fusion, 1st ed. ( Oxford University Press, 2004), p. 19.
94.
94. J. R. McNally, K. E. Roth, and R. D. Sharp, Technical Report No. ORNL/TM-6914, Oak Ridge National Laboratory, Oak Ridge, TN, 1979.
95.
95.We have shifted the plots of the normalized magnetic field strengths by +0.2 so that the lines for the case without the Nernst effect can be seen. Since our model assumes Bz(r)/ρg(r) = const., the normalized Bz(r) would fall directly on top of the normalized ρg(r) without this shift.
96.
96. S. A. Slutz, personal communication (2015).
97.
97. W. A. Stygar, personal communication (2015).
http://aip.metastore.ingenta.com/content/aip/journal/pop/22/5/10.1063/1.4918953
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/content/aip/journal/pop/22/5/10.1063/1.4918953
2015-05-21
2016-10-01

Abstract

Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end losses; (9) enhanced losses due to prescribed dopant concentrations and contaminant mix; (10) deuterium-deuterium and deuterium-tritium primary fusion reactions for arbitrary deuterium to tritium fuel ratios; and (11) magnetized -particle fuel heating. We show that this simplified model, with its transparent and accessible physics, can be used to reproduce the general 1D behavior presented throughout the original MagLIF paper [S. A. Slutz ., Phys. Plasmas , 056303 (2010)]. We also discuss some important physics insights gained as a result of developing this model, such as the dependence of radiative loss rates on the radial fraction of the fuel that is preheated.

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