Three-Dimensional Model for Green´s Function Charged-Particle-Beam Simulations in Cylindrical Geometry

We develop a completely 3-D model for Green´s function simulations of nonrelativistic charged-particle beams in cylindrical geometry, which explicitly takes into account the surface-charge density induced by the beam itself on the drift-tube walls. The beam is represented as a collection of pointlike charged macroparticles of equal charge. The approach essentially uses the Kirchhoff formula, allowing us to separate analytically the singular part of irrotational (potential) part of self-electric (space-charge) field induced by the moving charged macroparticles. A useful representation of the nonsingular part of the self-electric field possessing only fast convergent series is given. The adequacy of such a model is verified by considering the fall on the wall of infinite grounded cylindrical drift tube of charged macroparticles injected asymmetrically along the tube axis and the dynamics of uniform distribution, on the perimeter of a small circle, of a set of identical pointlike charged macroparticles, imitating an off-axis hollow beam.