Self-similar plasma expansion of a limited mass into vacuum

Abstract

A new self-similar solution is presented which describes non-relativistic expansion of a finite plasma mass into vacuum with a full account of charge separation effects. The solution exists only when the ratio A = R/λ D of the plasma scale length R to the Debye length λ D is invariant, i.e. under the condition T e α [n e (t)] 1-2/v , where v = 1, 2, and 3 corresponds, respectively, to the planar, cylindrical, and spherical geometries. For A >> 1 the position of the ion front and the maximum energy E i,max of accelerated ions are calculated analytically: in particular, for v = 3 one finds E i,max = 2ZT e0 W(A 2 /2), where T e0 is the initial electron temperature, Z is the ion charge, and W is the Lambert W-function. It is argued that, when properly formulated, the results for E i,max can be applied more generally than the self-similar solution itself.