Parametric Instabilities in Strongly Relativistic, Plane-Polarized Electromagnetic Waves

We investigate the stability of long-wavelength, plane-polarized electromagnetic waves when the oscillatory energy of the electrons exceeds their rest energy. The strong electron-mass variation destabilizes electron modes polarized along the electric field of the pump ${\overrightarrow{\mathrm{E}}}_0$. The electron and ion modes decouple in the presence of such an intense pump and hence the ions do not strongly influence the instability.