We show that, for a test ion moving in a collisionless single-species electron plasma, exact analytical solutions can be obtained for certain anisotropic velocity distributions of the electron plasma. By comparing the analytical formula with the numerical results calculated for the more realistic Maxwellian plasma, we demonstrate that plasmas with three different velocity distributions behave similarly for ions moving with velocity smaller than the velocity spread of the electrons. Furthermore, we show that the response of the electron density to a rest ion decays exponentially with distance, provided the anisotropic velocity distribution exhibits elliptical symmetry.

• Received 3 April 2008

DOI:https://doi.org/10.1103/PhysRevE.78.026413