Theory of nonlinear ion-electron instability

A nonlinear theory describing the interaction of ion and electron ’’clumps’’ in a turbulent Vlasov plasma is presented. Numerical and analytical solutions predict that, in the presence of a drift vd of the average electron distribution, a spectrum driven by such fluctuations will be unstable to drifts which are appreciably below those required for the onset of a linear instability. The instability exists over a large range of the parameter space vd and Te/Ti (the electron to ion temperature ratio); moreover, the growth rate is amplitude dependent being approximately proportional to the trapping time. These results are in good agreement with recent computer simulations.