Amplification of External EM-wave by Nonlinear Wake Waves in Cold Plasma

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. 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.