A sufficient condition for instability of BGK type waves in both unmagnetized and magnetized plasmas

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Abstract
This paper investigates the general problem of stability of Bernstein—Greene— Kruskal type waves. By investigating perturbations perpendicular to the wave, we obtain a general sufficient condition for instability. This is then extended to the case of magnetized plasmas with a uniform magnetic field in the direction of the BGK wave. New perturbed modes, having no counterpart in linear theory, are also found. Various special cases are considered and previous, more particular results confirmed.