Abstract
The stability of Bernstein–Greene–Kruskal (BGK) modes is investigated in the limit of small electric potential (weak inhomogeneity). It is proven that one-hole BGK modes can be unstable, contrarily to what was observed in previous numerical simulations. A simple stability criterion is derived. In particular, it is proven that the velocity distribution must have at least three maxima for instability to occur. Numerical simulations confirm the analytical results, and extend them to the nonlinear and strongly inhomogeneous regimes. In particular, it is shown that a strong inhomogeneity has a stabilizing effect.
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