Theory of wakefield effects of relativistic electron beams

A brief theoretical description of the wakefield effects is presented. In terms of the plasma density and beam parameters, this basic theory determines several critical wakefield quantities, including the oscillation frequency, the wavelength, the radial profile of the induced axial electric field, and its strength. The phase velocity of the wakefield waves is shown to be the same as the beam velocity. Thus, the perturbation created by the wakefield is a standing wave in the frame of reference moving with the electron beam. The axial electric field at the beam is also a standing wave in the beam frame, thereby removing energy from the beam in one half of the wavelength and adding energy to the beam in the other half. This mechanism modulates beam energy along the beam pulse, which is easily measurable. After a long range propagation, the portion of the beam which loses energy eventually loses its equilibrium condition and beam electrons in this portion are lost. This effect will break the beam into a train of small beam segments with length πβc/ω