One-Dimensional Simulation of Relativistic Streaming Instabilities

A relativistic version of the one-dimensional cloud-in-cell model for plasma simulation is developed. The model is physically self-consistent despite the omission of transverse, electromagnetic waves. The conditions for the onset of relativistic electrostatic instabilities between two electron beams and between two identical counterstreaming plasmas are derived for the case in which the one-dimensional and three-dimensional results are identical. In particular, the ion-ion instability can occur only for extremely high electron temperatures. Collisional effects in the model are discussed. Supraluminous waves are shown to be generated both by collisional effects and by nonlinear interactions in unstable plasmas. The results of the simulation of the instabilities are consistent with the theory. With the exception of the behavior of vortexes in position-momentum phase space, the relativistic results correspond reasonably well to the nonrelativistic ones.

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