MOE11 Emittance Growth from the Thermalization of Space-Charge   Nonuniformities
  Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). In this paper, we employ a simple kinetic model of a continuous focusing channel and build on previous work that applied system energy and charge conservation quantify emittance growth associated with the collective thermalization of an initial azimuthally symmetric, rms matched beam with a radial density profile that is hollowed or peaked. This emittance growth is shown to be surprisingly modest even for high beam intensities with significant radial structure in the initial density profile. 
Steven M. Lund, John J. Barnard, and Edward P. Lee