Unstable BGK solitary waves and collisionless shocks
The Penrose condition for linearized instability is generalized to the relativistic case for a collisionless neutral plasma. A general one-dimensional equilibrium (a BGK wave) is considered that is either a collisionless shock or a solitary wave. The electric potential is then allowed to undergo a transition from one constant value to another as \(x\) changes from \(-\infty\) to \(\infty\). It is proved that if one of these constants satisfies the relativistic version of the Penrose condition, then the BGK wave is nonlinearly unstable. Periodic relativistic BGK waves of small amplitude are also considered and shown to be nonlinearly unstable.
scientific article; zbMATH DE number 1294602