Plasma-wave generation in the beat-wave accelerator.

We analytically study the generation of longitudinal plasma waves in an underdense plasma by two electromagnetic waves with frequency difference approximately equal to the plasma frequency, as envisioned in the plasma beat-wave accelerator concept of Tajima and Dawson. The relativistic electron fluid equations describing driven electron oscillations with phase velocities near the speed of light in a cold, collisionless plasma are reduced to a single, approximate ordinary differential equation of a parametrically excited nonlinear oscillator. We give amplitude-phase equations describing the asymptotic solutions to this equation valid for plasma wave amplitudes below wave-breaking. We numerically compare the behavior of the asymptotic equations with that of the original equation and with particle simulation results. -.