Parametric Excitation of Transverse and Longitudinal Waves near the Plasma Frequency

Intense laser light with frequency ${\omega }_0$ near the plasma frequency excites transverse waves with real frequency components 0 and $\pm 2{\omega }_0$ and longitudinal plasma oscillations at $\pm {\omega }_0$. The resonant coupling is due to the $\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}}$ forces and relativistic mass corrections. The maximum growth rate is $\frac{{\omega }_0{v}_0^2}{16c^2}$, where $v_0$ is the maximum electron velocity in the incident laser light.