Transverse equilibrium and stability of the primary beam in the plasma wake-field accelerator

The primary electron beam in the plasma wake-field accelerator is studied, using multidimensional particle simulation, for cases in which a shaped electron beam is used, with length L≳λp, where λp is the plasma wavelength. Excellent agreement is found between radial equilibrium conditions and simulation results. Wake amplitudes are significantly reduced when the beam is initialized in a nonequilibrium state. The electron-hose and the transverse two-stream instabilities are observed to cause transverse deflections of the beam, with the transverse two-stream instability having a lower growth rate. Operation in the electron-hose regime can be avoided by reducing the beam density.