Saturation Amplitude of Nonlinearly Excited Plasma Waves

The saturation amplitude of a nonlinearly excited plasma oscillation is calculated, taking into account both the frequency-mismatch effect due to relativistic correction and the effect of collision damping. It is explicitly shown, even in cases where the collision frequency $\nu$ may be considered extremely small, how the inclusion of $\nu =0^{+}$ leads to a qualitative change in the asymptotic behavior of the system.