Reflection of ion acoustic waves by the plasma sheath

Abstract

The reflection coefficient R for linear monochromatic ion acoustic waves incident on the transonic layer and sheath from the plasma interior is calculated. The treatment differs from previous analyses in that (1) the exact zero-order ion density and velocity profiles for a planar, bounded plasma are used, and the zero-order charge separation is not neglected, and (2) the first-order quantities near the transonic layer are considered in detail, including first-order charge separation, whereby it is found that no coupling to the beam modes exists, and that the functional form of the first-order solution is completely determined. It is shown that the upper bound for ‖R‖ is (1)/(3) . The largest reflection occurs for frequencies which are small compared with the ionization frequency, and generally decreases with increasing frequency. By Fourier superposition, the reflection of a pulse is computed. For a narrow incident pulse, the reflected pulse is greatly distorted and is small compared with the incident pulse. For a broad pulse, the reflected pulse is similar in shape to the incident pulse, and has a magnitude which is approximately (1)/(3) of the incident pulse.