Limitations on plasma acceleration due to synchrotron losses

In this letter we consider the effect of synchrotron radiation losses due t o the betatron motion of the electron beam in its self-induced magnetic fie ld in a plasma acclerator taking into account the charge neutralization fac tor. The most favorable case is where the plasma density is smaller than th e beam density. The contrary regime is strongly disfavored by the synchrotr on radiation loss for beams with characteristics for TeV energies. In both cases we find that upon increasing the plasma density the synchrotron losse s kill the acceleration process, so that there are limitations on the maxim um allowable plasma density. (C) 1999 Elsevier Science B.V. All rights rese rved.