Self-similar expansion of a plasma into a vacuum

Abstract

The Boltzmann equilibrium for electrons has been an ad-hoc assumption of previous work about self-similar plasma expansion in vacuum. Using Boltzmann’s relation, one finds a linear electrostatic potential as a solution of the self-similar expansion. It is first shown that in such a potential, the electron behavior is exactly solvable. As a result, one finds that the exact electron density differs substantially from the Boltzmann equilibrium for moderate values of the self-similar parameter. The complete calculations of the self-similar expansion, without any assumption about the equation of state of the electrons, is presented. It is shown, in particular, that half the electron density depletion in logarithmic units is compensated for by the self-consistent modification of the electric potential. Finally, the effect is analyzed in terms of energy exchange between the electrons and the ions in the expansion.