On the efficacy of imploding plasma liners for magnetized fusion target compression

摘要

A new theoretical model is formulated to study the idea of merging a spherical array of converging plasma jets to form a "plasma liner" that further converges to compress a magnetized plasma target to fusion conditions [Y. C. F. Thio , "Magnetized target fusion in a spheroidal geometry with standoff drivers," Current Trends in International Fusion Research II, edited by E. Panarella (National Research Council Canada, Ottawa, Canada, 1999)]. For a spherically imploding plasma liner shell with high initial Mach number (M=liner speed/sound speed) the rise in liner density with decreasing radius r goes as rho similar to 1/r(2), for any constant adiabatic index gamma=d ln p/d ln rho. Accordingly, spherical convergence amplifies the ram pressure of the liner on target by the factor A similar to C-2, indicating strong coupling to its radial convergence C=r(m)/R, where r(m)(R)=jet merging radius (compressed target radius), and A=compressed target pressure/initial liner ram pressure. Deuterium-tritium (DT) plasma liners with initial velocity similar to 100 km/s and gamma=5/3, need to be hypersonic M similar to 60 and thus cold in order to realize values of A similar to 10(4) necessary for target ignition. For optically thick DT liners, T < 2 eV, n>10(19)-10(20) cm(-3), blackbody radiative cooling is appreciable and may counteract compressional heating during the later stages of the implosion. The fluid then behaves as if the adiabatic index were depressed below 5/3, which in turn means that the same amplification A=1.6x10(4) can be accomplished with a reduced initial Mach number M approximate to 12.7(gamma-0.3)(4.86), valid in the range (10 < M < 60). Analytical calculations indicate that the hydrodynamic efficiency for plasma liners assembled by current and anticipated plasma jets is < 4%. A new similarity model for fusion alpha-particle heating of the collapsed liner indicates that "spark" ignition of the DT liner fuel does not appear to be possible for magnetized fusion targets with typical threshold values of areal density rho R < 0.02 g cm(-2). (c) 2008 American Institute of Physics.