Smooth approximation model of dispersion with strong space charge for continuous beams

We apply the Venturini-Reiser (V-R) envelope-dispersion equations [M. Venturini and M. Reiser, Phys. Rev. Lett. 81, 96 (1998)] to a continuous beam in a uniform focusing/bending lattice to study the combined effects of linear dispersion and space charge. Within this simple model we investigate the scaling of average dispersion and the effects on beam dimensions and show that the V-R equations lead to the correct zero-current limits. We also introduce a generalization of the space charge intensity parameter and apply it to the University of Maryland Electron Ring and other machines. In addition, we present results of calculations to test the smooth approximation by solving the V-R original equations and also through simulations with the matrix code ELEGANT.