Self‐similar solutions of ion‐beam‐driven plasma expansion

Self‐similar solutions of ion‐beam‐driven plasma expansions, separating in mass and time coordinates, are presented. Model equations are derived for the general class of separable flows with prescribed energy source. Their solutions show, representatively, the transition from an initial heating to an asymptotic expansion regime described by constant energy ratios. The dependence of the asymptotic energy ratios on the temporal form of the beam pulse is examined and maximum heating is found for exponentially growing pulses. The spatial flow profiles are discussed for uniform and nonuniform energy deposition with application to a realistic energy loss formula that is Bragg peaked. Comparison with numerical simulations suggests a general asymptotic validity of the present similarity results.