Nonlinear development of the ExB-instability in the adiabatic approximation

The nonlinear development of the ExB-instability in a weakly ionized plasma is governed by an infinite set of coupled ordinary nonlinear differential equations for the amplitudes of the modes of the system. The solution of these equations are investigated in the adiabatic approximation by setting the time derivative of linearly stable modes equal to zero. Approximate analytical solutions for the time development of the different modes, in good agreement with previous numerical results, have been obtained for control parameters fifteen times the critical value. The results clearly indicate the possible existence of a cascading process, where the amplitudes of the linearly most stable modes have the highest nonlinear growth rates. (orig.)