Modulational Instability and Its Consequences for the Beat-Wave Accelerator

Abstract

The modulation instability caused by the coupling of a Langmuir wave to the ion motion is investigated in the domain of large $\frac{v_{\mathrm{L}}}{v_{\mathrm{te}}}>1\mathrm{}$ ratios, where $v_{\mathrm{L}}$ and $v_{\mathrm{te}}$ denote the pump Langmuir-wave quiver velocity and the electron thermal velocity, respectively. A convenient approximate expression for the growth rate is given for $\frac{v_{\mathrm{L}}}{v_{\mathrm{te}}}<50\mathrm{}{\left(\frac{A}{Z}\right)}^{\frac{1}{6}}$. The limitation of the beat plasmon growth due to the modulational instability is studied in the context of plasma beat-wave experiments and the maximum beat plasmon amplitude is determined numerically.