Application of a Localized Chaos Generated by RF-Phase Modulations in   Phase-Space Dilution
  Physics of chaos in a localized phase-space region is exploited to produce a longitudinally uniformly distributed beam. Theoretical study and %numerical simulations are used to study its origin and applicability in phase-space dilution of beam bunch. Through phase modulation to a double-rf system, a central region of localized chaos bounded by invariant tori are generated by overlapping parametric resonances. Condition and stability of the chaos will be analyzed. Applications include high-power beam, beam distribution uniformization, and industrial beam irradiation. 
S.Y. Lee, K.Y. Ng
physics.acc-ph