Nonlinear longitudinal oscillations of relativistic plasma

The investigation has been made of nonlinear forced longitudinal oscillations of a relativistic plasma. It was demonstrated that: a) the nonlinear terms (v▽)p arising in the equations of motion do not restrict the electron oscillation amplitude increase in the region of plasma resonance; b) the nonlinear terms due to the relativistic nature of oscillations, firstly, limit the oscillation amplitude in the resonance region and, secondly, lead to the development of a parametric instability. The harmonic, sub- and ultraharmonic oscillations turned out to be unstable. The conditions for the instability as well as expressions for the growth rates of unstable oscillations were obtained.