ACCELERATION OF A RELATIVISTIC ELECTRON BUNCH IN LINEAR AND NONLINEARPLASMA-WAVES

A method is developed for studying the acceleration of a relativistic electron bunch in a plasma wave with a potential of arbitrary profile. The dependence of the energy spectrum of the accelerated electrons on the interaction length is considered. It is shown that, for a linear wave, the maximum of the spectral density lies near the maximum energy of the accelerated electrons. For acceleration in a nonlinear plasma wave, the spectrum is shown to become broader, so that the relative nu mber of electrons of highest energy is less than that in the linear ca se.