THERMAL LIMITS ON WAVE AMPLITUDE IN THE PLASMA WAKE-FIELD ACCELERATOR

We discuss the nonlinear regime of the Plasma Wakefield Ac-celerator and its potential advantages over linear operation, and de-scribe the general behavior of the plasmaelectron phase space in large amplitude plasma waves. We develop a Hamiltonian formalism for calculating the trapping of thermal electrons from the background plasma, and derive approximate limits on plasma wave amplitude due to loading by trapped electrons and other thermal effects. &roduction The one-dimensional nonlinear theory of the Plasma Wakefield “J ’ Accelerator (PWFA), developed recently by Rosenzweig, Ruth et al. “I and Amatuni et al. i ” predicts certain advantages the extremely nonlinear regime. It has been shown that the transformer ratio, the ratio of the maximum decelerating field inside the driving electron bunch to the maximum accelerating field found in the wake of th