Interaction of an Electron Beam with a Collisionless Plasma

The growth of electrostatic wave excitation in a collisionless plasma, interacting with an electron beam of finite length, as well as the simultaneous modification of the beam are studied for weakly unstable situations. Using quasi-linear theory, explicit results as a function of space, of time, and of the plasma and beam parameters are obtained for the surface layer where the relaxation of the beam effectively takes place. The effect on the beam of both unstable modes and resonant stable modes of thermal excitation is considered.