Collisionless plasma expansion into a vacuum

Particle simulations of the expansion of a collisionless plasma into vacuum are presented. The cases of a single-electron-temperature plasma and of a two-electron-temperature plasma are considered. The results confirm the existence of an ion front and verify the general features of self-similar solutions behind this front. A cold electron front is clearly observed in the two-electron-temperatures case. The computations also show that for a finite electron-to-ion mass ratio, m_e/m_i, the electron thermal velocity in the expansion region is not constant, but decreases approximately linearly with ξ=x/t, where x is distance and t is time. A self-similar solution, derived from the relation T_en^1-γ_e=const, where T_e is the electron temperature, n_e is the electron density, and γ is a constant (instead of the isothermal assumption made in earlier theories), yields a linearly decreasing ion acoustic speed, c≃c₀-(γ-1) ξ/2, and comparison with computer simulation results show that the constant γ-1 is proportional to (Zm_e/m_i)^1/2, where Z is the ion charge number.