On the nonlinear damping of a plasma mode

We present a theory of the nonlinear damping of a plasma mode based on a solution of the Vlasov-Poisson system. The formulation is exempt from the objectionable separation of the particles into ‘resonant’ and ‘nonresonant’, and is valid for ion as well as for electron modes. The effect of the damping of the mode on particle motion is taken in account. In particular, we evaluate numerically the damping of an ion mode for a temperature ratio T_e/T_i = 16. We also obtain a number of small new shifts in the damping of a plasma mode in general, including contributions from the second derivative of the stationary distribution function.