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On the existence and stability of trapped Langmuir modes in a double layer

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, owing to the existence of linerly 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 (eΔπ/κTe ≫ 1). and for the particular model being used, is of the order (eΔπ/κTe)½ λD. 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.