Modeling of space charge effects in intense electron beams using two and three dimensional Green's function

Green's functions for Maxwell equations can provide a powerful technique for the modeling of high-intensity particle accelerators. The authors present both, two-and three-dimensional models of space charge in intense charged particle beams. Specifically, they compute the Green's function for a point charge located inside of a perfectly conducting drift tube with periodic boundary conditions. As an application of the two-dimensional Greens's function, they study the effect of current oscillations and associated envelope oscillations on inducing beam halos in intense relativistic electron beams in periodic permanent magnet focusing and uniform solenoidal focusing klystrons. For system parameters corresponding to the SLAC PPM Klystron experiment, the authors find that a sizeable initial envelope mismatch produces halo particles with a maximum radius extending to several core radii at the output section. An eigenfunction expansion technique is utilized for the computation of the three-dimensional Green's function. The authors show the agreement of the function with electrostatic potential that can be computed exactly, i.e. potential due to an on axis distribution with infinite conductor radius. Results from multi-particle simulations obtained from this function are presented