The nonlinear interaction of a continuous electron beam with a traveling electromagnetic wave in the cyclotron resonance laser (CRL) accelerator is analyzed. It is found that the maximum beam energy gain and acceleration distance obey certain scaling laws for optimized systems, and that the maximum energy gain is limited primarily by the degree of wave dispersion and is almost independent of the wave amplitude. As an example, design studies of a 33-GHz, high-current, CRL accelerator based on three- dimensional, self-consistent, multiparticle simulations are presented.
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