Theory of wake-field effects of a relativistic electron beam propagating in a plasma

A theoretical description of the wake-field effects is presented for a relativistic electron beam propagating through a tenuous background plasma. When the electron beam enters the plasma chamber, it expels plasma electrons from its vicinity leaving ions behind. The plasma electrons move out to the charge neutralization radius and oscillate near the radius, producing wake-field effects. In terms of plasma density, beam current, beam current rise time, and a geometrical factor of the system, the theory determines several critically important wake-field quantities, including the oscillation frequency, the wavelength, the radial profile of the induced axial electric field, and its strength. A particle simulation study of the wake-field effects is also carried out by two-dimensional particle-in-cell codes, and the simulation results are compared with the theoretical predictions. The simulation data agree remarkably well with the theoretical values. It is found from the theory and the simulation that the strength of the wake-field effects increases with beam current and plasma density. However, the wake-field strength decreases significantly as the beam current rise time increases.