Calculation of particle motions at the head and tail of a bunch for the University of Maryland electron ring

The end effect in a bunched beam is caused by the space-charge forces, which accelerate particles at the bunch head and decelerate particles at the bunch tail. It occurs in high-current linear accelerators and rings. In the University of Maryland Electron Ring (UMER) project, the energy of particles at the very ends of a rectangular bunch is 15% different from that of the main part of the bunch. Assuming a negligible transverse space charge effect at the edge of the bunch, one dimensional single particle calculation is performed by a matrix formalism to estimate the ratio of particle loss due to the end effect. Two possible cases are examined: with no induction gap, and with three induction gaps. If three induction modules are used, for a small number of turns, the particle loss is less than 0.15%, which is small enough to be acceptable. Simulation by code CIRCE is in progress.