A core-particle 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 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, Poincare 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 core-particle model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms matched beam in a periodic quadrupole focusing channel. Further characteristics of these processes are presented here
