Nonlinear oscillations and the capture of particles by waves in a plasma

A study is made of the influence that capture of particles by plasma waves has on the dispersion properties of the waves. Specifically, periodic waves of finite amplitude are studied for the ease of arbitrarily many interpenetrating cold electron and ion streams. A dispersion equation relates the frequency and wavelength of the oscillations to the wave amplitude, and it is shown that trapping of particles may stabilize plasma oscillations. If there is a single species of trapped particles, it is necessary and sufficient for the density of the trapped particles to decrease when their potential energy increases for thi s to happen. Nonlinear periodic charge-density waves are investigated in a dielectric medium through which a stream of charged particles passes, and it is shown that the trapping of these particles by the waves earl also stabilize growing waves.