Collisional effects in the ion Weibel instability for two counter-propagating plasma streams

Abstract

Experiments directed towards the study of the collisionless interaction between two counter-streaming plasma flows generated by high-power lasers are designed in such a way as to make collisions between the ions of the two flows negligibly rare. This is reached by making flow velocities v as high as possible and thereby exploiting the 1/v4 dependence of the Rutherford cross-section. At the same time, the plasma temperature of each flow may be relatively low so that collisional mean-free paths for the intra-stream particle collisions may be much smaller than the characteristic spatial scale of the unstable modes required for the shock formation. The corresponding effects are studied in this paper for the case of the ion Weibel (filamentation) instability. Dispersion relations for the case of strong intra-stream collisions are derived. It is shown that the growth-rates become significantly smaller than those stemming from a collisionless model. The underlying physics is mostly related to the increase of the electron stabilizing term. Additional effects are an increased “stiffness” of the collisional ion gas and the ion viscous dissipation. A parameter domain where collisions are important is identified.