On the Existence and Stability of Trapped Langmuir Modes in a Double Layer

摘要

The stability problem of the double layer (electrostatic shock) is investigated using a simple model of the plasma. It is shown that local Penrose stability in general is insufficient for global stability due to the existence of linearly unstable trapped Langmuir modes in the density cavity. An additional requirement for stability is that the thickness of the layer must be smaller than a critical value, which in the case of a strong layer, and for the particular model being used, is shown. Various qualitative features of the instability mechanism are discussed in terms of normal mode coupling and quantitative results such as mode frequencies, growth rates, etc., are obtained by means of a conventional perturbation approach which in addition to the results expected from coupled mode theory also shows the existence of two purely decaying modes appearing for a sufficiently thin, stable layer. The double layer formation process is briefly commented on and some distinguishing features of the instability in this regard are pointed out.