Structure of Evolving Ion-Acoustic Fronts in Collisionless Plasmas

Exact analytic solutions are obtained to the linearized, two-species Maxwell-Vlasov equations for the evolution of an initial step-function density discontinuity in an initially neutral, collisionless plasma. These solutions have been evaluated numerically for hydrogen plasmas with starting temperature ratios 0 ≤ θ = Te/Ti ≤ 30, for times 0 ≤ τ = ωpit ≤ 100, and over distances into the original low-density region 0 ≤ η = x/Ait ≤ 12, where Ai is the mean thermal speed of ions. For τ ≪ 1 both species simply free stream. By late times (τ ≳ 30) quasineutrality of the perturbation has been established, and it is found that: (1) the ion profiles for θ ≲ 1 exhibit the appearance of free streaming at an enhanced ion temperature, suggesting that the strong Landau damping usually attributed to the low-θ limit might better be termed “ambipolar free streaming,” (2) for θ ≃ 5 they are self-similar and monotonic with a steep leading edge near η = θ1/2 followed by a broad, arched trailing edge accounting for half the density rise, and (3) for θ ≳ 30 they have a steep but spreading leading edge near θ1/2 and general resemblance to the integrated Airy function profile obtainable through a moment equation treatment retaining only the last damped collective mode.