Simulations of beam emittance growth from the collective relaxation of space-charge nonuniformities

Abstract

Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. For unbunched beams with high space-charge intensity propagating in linear focusing channels, Debye screening of the self-field interaction between particles tends to make the transverse density profile flat. An injected particle distribution with a large systematic charge nonuniformity will generally be far from an equilibrium of the focusing channel and the initial condition will launch a broad spectrum of collective modes. These modes can phase-mix and experience nonlinear interactions which result in an effective relaxation to a more thermal-equilibrium-like distribution characterized by a uniform density profile. This relaxation transfers self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). Here we employ two-dimensional electrostatic particle-in-cell (PIC) simulations to investigate the effects of initial transverse space-charge nonuniformities on the statistical emittance growth of beams with high space-charge intensity propagating in a continuous focusing channel. Results are compared to theoretical bounds of emittance growth developed in previous studies. Consistent with earlier theory, it is found that a high degree of initial distribution nonuniformity can be tolerated with only modest emittance growth and that beam control can be maintained. The simulations also provide information not addressed by the theory on the rate of relaxation and characteristic levels of fluctuations in the relaxed states. This research suggests that a surprising degree of initial space-charge nonuniformity can be tolerated in practical intense beam experiments.