Non-linear saturation of a single wave by particle trapping

A new method is presented for determining the amplitude at which a single unstable wave in a collisionless plasma saturates due to particle trapping. A non-linear dispersion relation for a small-amplitude test wave, with the same frequency and wavenumber as the main large-amplitude wave, is obtained. The solution of this dispersion equation gives the saturation condition ωsub(t) approximately γsub(l), which is in good agreement with the results of the recent numerical simulations. (U.K.)