INSTABILITY OF LONG DRIVING BEAMS IN PLASMA WAKEFIELD ACCELERATORS

In plasma wakefield accelerators, long (as compared to the wakefield period) driving beams are subject to the vig-orous transverse two-stream instability, the nonlinear stage of which is numerically studied. If only one mode of the instability grows up in the system (as in the case of a sharp beam front), then the beam quickly gets modulated, the in-stability saturates, and the generated wakefield increases; further propagation of the modulated beam is stable. Si-multaneous growth of several unstable modes (which is the case for a smooth beam front) completely destroys the beam in the time of several betatron oscillations. The trains of short bunches are stable.