Wave Damping in Plasma due to Scattering by Ion Sound Waves

When high-frequency waves in a plasma are scattered by an enhanced spectrum of low-frequency waves, they lose energy if the resulting secondary waves are Landau damped. Such a nonlinear energy loss of longitudinal waves was calculated hydrodynamically by Sturrock. However, the Vlasov equation gives a more intense scattering. Thus, a wide spectrum of ion sound waves prevents a weak two-stream instability of electron plasma waves more easily than according to the hydrodynamic calculation. If the wave vectors of the ion sound waves are shorter than the width of the instability, the scattering of secondary waves becomes decisive: Electron plasma waves diffuse in $\overrightarrow{\mathrm{k}}$ space and the nonlinear stabilizing effect is reduced. Also, transverse high-frequency waves are nonlinearly damped, but less so by a relativistic order at least.