Numerical study of ion acoustic instability

We studied the linear saturation and nonlinear evolution of a collisionless ion acoustic unstable plasma using a Vlasov-Poisson code. We apply a weak constant external electric field that accelerates electrons and ions and causes ion acoustic instability. The preliminary result shows ion acoustic instability saturates through quasi-linear relaxation of electron distribution. Ion acoustic turbulence (IAT) creates a sharp peak of anomalous resistivity, which is close to that predicted by quasi-linear theory rather than Sagdeev resistivity, when the instability saturates. The increase of current does not come to a stop through IAT itself as anomalous resistivity gradually decreases back to zero after the saturation. During this process, the ion acoustic instability further relaxes through a combination of a reduction of the temperature ratio and a quasi-linear relaxation of the background distribution functions to a stable non-Maxwellian configuration. Run-away electrons are not observed in the simulation. We investigate whether saturation of the system will ultimately occur through the transition to other streaming instabilities.