Echo in a Semi-Bounded Plasma

Abstract

Plasma echo theory is revisited and reviewed to apply it to a semi-bounded plasma. Spatial echoes in a semi- bounded plasma are investigated by calculating the electric field produced by external charges and satisfying the boundary conditions at the interface. We show that echoes can occur at various spots. The diversity of echo occurrence spots is due to the boundary terms. x ik e  or ) / ( v x t i e   . This modulation is called free streaming term since x = vt is the characteristic line of a free particle. This term makes the modulation of the distribution function more and more oscillatory as t or x increases, and consequently,  fdv will become vanishingly small due to almost complete cancelations (phase-mixing). Therefore, the free streaming term yields no appreciable effect on macroscopic variable such as density perturbation.