Self-similar implosions and explosions of radiatively cooling gaseous masses

Abstract

A self-similar solution of the gas dynamics equations with heat conduction, which describes homologous contraction and expansion of gaseous masses with a free external boundary, is investigated in detail. As a primary application, implosion of deuterium-tritium (DT) fuel in inertial confinement fusion targets is considered. For strongly non-adiabatic implosions the self-similar solution predicts that the flow pattern should approach an asymptotical regime in which it ceases to depend on the initial entropy. For DT masses relevant to inertial confinement fusion (ICF) this regime begins to dominate at αUim≳6 × 108 cm/s, where α=p/pdeg is the fuel isentrope parameter, and Uim, is its implosion velocity. The solution has also a branch which describes an asymptotical regime of explosive expansion after an ultra-fast initial heating to a strongly radiating state. © 1998 American Institute of Physics.