This paper presents the results of calculations of the transverse effects of space charge of coasting beams in rings for three globally comparable lattice configurations: uniform focusing, FODO, and doublet. The parameters of the lattice and theH−beam are chosen similar to those of the SNS accumulator ring. Three models for space charge are considered: 1) a particle core model based on rms beam parameters, 2) a self-consistent particle-in-cell (PIC) model, and 3) a phase-averaged PIC model. In all cases both matched and mismatched K-V distributions are considered by randomly initializing, and then tracking, collections of macroparticles representing the beam. In the particle core model the initial rms values of the macroparticle distributions are used as initial values for solving the envelope equations, including space charge forces and dispersion effects. For matched beams the calculations, performed using a modified version of the injection and tracking code, ACCSIM, reveal only a slight emittance growth and no halo generation with the particle core model. However, the self-consistent PIC model yields greater emittance growth and halo generation, particularly for the doublet lattice in the vertical plane. When the calculations are performed with the phase-averaged particle-in-cell (PIC) model, the results agree substantially with the particle core model, suggesting that the observed self-consistent PIC results are not a consequence of numerical truncation. As further confirmation, we have performed numerical convergence studies using the doublet lattice, and have observed the behavior of the self-consistent PIC model to persist. The tendency for emittance growth and halo generation in the doublet lattice is not surprising, as the fluctuations in beam area, which are an excellent indicator of space charge forces, are larger and more rapid than for the other lattices. For mismatched beams, only the particle core model has been applied at present, and good beam transport is obtained with up to 25&percent; envelope oscillation amplitudes for all three lattices. ©1998 American Institute of Physics.