Green's function description of space-charge in intense charged-particle beams

We present two- and three-dimensional models of space charge in intense charged-particle beams using Green's functions. In particular, we compute the electrostatic Green's function for a periodic collinear distribution of point charges located inside of a perfectly conducting drift tube. As applications of the Green's function description, we analyze the matching and transport of an initially axisymmetric beam into a quadrupole channel and the interaction of a particle with its induced surface charge.