Parametric instabilities below the electron plasma frequency due to relativistic corrections

Abstract
We present a model which describes the interaction of a cold homogeneous plasma with a strong linearly polarized external electromagnetic wave, taking into account relativistic terms. Instabilities appear for transverse and longitudinal waves when the pump-field frequency is at the same time below the electron plasma frequency and above but very near the cutoff frequency obtained by Kaw and Dawson with a nonlinear relativistic theory.