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.

Bending of solitons in weak and slowly varying inhomogeneous plasma

“…Kuehl investigated theoretically the reflection of ion acoustic soliton, and showed that a shelf develops behind the soliton and the reflected wave is small compared with both trailing shelf and soliton amplitude decrease due to energy transfer to the shelf [17][18][19]. Then after, many authors took the problem of soliton propagation in inhomogeneous plasma in different physical situations like plasma with finite ion temperature [20,21], with negative ions [22][23][24][25], with dust [26] and trapped electrons [27], in magnetic field [28,29], with non isothermal electrons [30], with ionization [31,32], with electron inertia contribution [33] and also in other contexts [16,34,35].…”

Simulations of ion heating due to ion-acoustic instabilities in the presheath

“…Other works also suggest that ion-acoustic waves reflect from sheaths. [37][38][39][40] Recently, Hood et al 22 measured fluctuations in an ion presheath at conditions where ion-acoustic instabilities were expected to be excited near the sheath edge. The measurements showed evidence of ion-acoustic fluctuations near the sheath edge, but also further into the plasma in the region predicted by linear theory to be stable 22 .…”