In this work, we analyze the effects produced by the inclusion of space-charge waves in a Hamiltonian model for a cyclotron resonant accelerator. We find that space charges impose limits on acceleration and that these limits appear as bounding curves on the appropriate stroboscopic phase spaces. In addition, space charges create nonlinearly locked states which undergo not only the period doubling bifurcations preceding chaos, but saddle-node inverse bifurcations as well.
Physical Review. E, Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics. New York. Vol. 54, no. 4 (Oct. 1996), p. 4202-4210