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Scaling laws governing implosions of thin shells in converging flows are established by analyzing the implosion trajectories in the A, M≫ parametric plane, where A is the in-flight aspect ratio, and M is the implosion Mach number. Three asymptotic branches, corresponding to three implosion phases, are identified for each trajectory in the limit of A, M≫1. It is shown that there exists a critical value γcr = 1 + 2/ν (ν= 1, 2 for, respectively, cylindrical and spherical flows) of the adiabatic index gamma, which separates two qualitatively different patterns of the density buildup in the last phase of implosion. The scaling of the stagnation density ρs and pressure Ps with the peak value M0 of the Mach number is obtained. ©2002 The American Physical Society
