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A computer program which models the behavior of an intense beam of charged particles in a periodic focusing system is described. The program solves for electrostatic fields in two dimensions, i.e., the x-y coordinates of a typical electrostatic quadrupole lens, including space-charge fields due to the presence of an array of macroparticles. Adjacent drift sections and quadrupoles are defined by "hard edges", i.e., no fringing fields. However, longitudinal changes in electrostatic potential are used to calculate applied axial fields. Particles are tracked through short segments for which Poisson's equation is solved to update the self-fields. Examples shown include the transport of an intense (space charge limited) beam in a periodic structure and the optics of a matching system between ion source and transport system. The program is equally applicable to magnetic or electrostatic focusing. In either case it accounts for space-charge image field effects which are frequently ignored in other treatments of this problem.