A necessary condition for adiabatic explosion behind a shock of arbitrary dynamics

We present a solution to the problem of the induction of an adiabatic explo sion by a shock of arbitrary dynamics. We obtain a general expression for t he induction time as a function of the velocity, acceleration and total cur vature of the shock. We derive a necessary condition for explosion that ens ures bounded values of the induction time. The method is illustrated by det ermining conditions for initiation by impact of a piston, and it is validat ed by means of direct numerical simulations. (C) Academie des sciences/Else vier, Paris.