Production of Enhanced Beam Halos via Collective Modes and Colored Noise
  We investigate how collective modes and colored noise conspire to produce a beam halo with much larger amplitude than could be generated by either phenomenon separately. The collective modes are lowest-order radial eigenmodes calculated self-consistently for a configuration corresponding to a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium. The colored noise arises from unavoidable machine errors and influences the internal space-charge force. Its presence quickly launches statistically rare particles to ever-growing amplitudes by continually kicking them back into phase with the collective-mode oscillations. The halo amplitude is essentially the same for purely radial orbits as for orbits that are initially purely azimuthal; orbital angular momentum has no statistically significant impact. Factors that do have an impact include the amplitudes of the collective modes and the strength and autocorrelation time of the colored noise. The underlying dynamics ensues because the noise breaks the Kolmogorov-Arnol'd-Moser tori that otherwise would confine the beam. These tori are fragile; even very weak noise will eventually break them, though the time scale for their disintegration depends on the noise strength. Both collective modes and noise are therefore centrally important to the dynamics of halo formation in real beams. 
Ioannis V. Sideris and Courtlandt L. Bohn