1 J ul 1 99 9 Amplification of External EM - wave by Nonlinear Wake Wavesin Cold Plasma

1 Abstract Interaction of external monochromatic, linearly polorized plane EM-wave with nonlinear one-dimensional wake wave, generated by relativistic electron bunch moving in cold plasma, is considered. At definite conditions on parameters of plasma and bunch, nonlinear wake wave can have a pronounced spikes, where plasma electron density has its maximum value and plasma electron velocities are nearing wave breaking limit, i.e. velocity of the rigid driving bunch [1]-[5]. Presented calculations show, that external EM-wave, propagating through plasma, normal to the bunch velocity, at such a conditions can be amplified inside the spikes, due to interaction with the plasma electrons. EM-wave, Thomson scattered on spikes, is also amplified. Amplification factors are obtained for the both cases at different conditions on EM-wave-plasma-electron bunch system parameters. An additional amplification takes place, when the frequency of EM-wave is nearing to the spike plasma frequency. Results are obtained in the perturbative approach, when dimensionless external EM-wave amplitude is used as a small parameter. The exact one-dimensional solution of the problem of nonlinear wake wave generation in cold plasma by relativistic electron bunch, obtained previously in [4], [5], is taken as a zero order approximation.