Surface instabilities in over-dense and under-dense plasmas excited by external high frequency fields

Plasma surface waves are excited by a high-frequency field in a semi-infinite plasma with a plane boundary when $\omega_0 - \omega_p$ .simeq. $\pm$($\omega_p\sqrt{2}$) and $\omega_0$ - $\omega_p$ $\pm$($\omega_p\sqrt{2}$) – $\omega_0$ ($\omega_0$ being the frequency of the high frequency field and $\omega_p$ the plasma frequency). The instabilities, in effect, take place at ($n_c/n_0$) = 3, 8.5 * $10^{-2}$, 0.72 and 2* $10^{-2}$, where $n_c$ and $n_0$ are the critical and the particle densities respectively. Threshold conditions are derived for plasmas with and without a low-d. electron beam. In the absence of the beam the thresholds are more than the relativistic limit, while its presence reduces the thresholds considerably under certain conditions