Saturation of nonlinear Landau damping by cascading

It is shown that a heating wave in a plasma (say lower hybrid) that decays by a nonlinear Landau damping process can saturate by cascading. No matter how small the (linear) damping rates are the instability saturates without piling up great amounts of energy in the last mode. In the presence of source terms the wave energies approach their equilibrium values. A formal analogy is shown to exist between the present problem and that of interacting animal populations first investigated by Volterra