A core-particle model for periodically focused ion beams with intense space-charge

A core-particle (CP) model is derived to analyze transverse orbits of test-particles evolving in the presence of a core ion beam that has uniform density within an elliptical cross-section. The model can be applied to both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image-charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image-charge nonlinearities. Transformations are employed in diagnostics to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied-focusing forces. Diagnostics for particle trajectories, Poincaré phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The CP model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms-envelope matched beam in a periodic quadrupole focusing-channel [S.M. Lund, S.R. Chawla, Nucl. Instr. and Meth. A 561 (2006) 203]. Further characteristics of these processes are presented here.