The Effect Of Induced Charge At Boundaries On Transverse Dynamics Of A Space-Charge-Dominated Beam

A particle simulation code has been used to study the effect on transverse beam dynamics of charge induced on focusing electrodes. A linear transport system was assumed. The initial particle distribution was taken to be that of a uniform elliptical beam with a Gaussian velocity distribution. For misaligned, highly space-charge-dominated beams (betatron phase advance per lattice period -< lo"), a large oscillation of the rms emittance occurred in a beat pattern. Linearized Vlasov analysis shows the oscillation to be a sextupole oscillation, driven by the beam coherent betatron motion. Emittance growth accompanied the oscillation. Preliminary experimental results from the Single Beam Transport Experiment (SBTE) are consistent with the code results. Addition of a dodecapole nonlinearity to the computational focusing field greatly reduces the oscillation amplitude. Introduction and Description of the Model We report here the results of a theoretical study of the transverse dynamics of a space-charge-dominated charged particle beam subject to forces due to charge induced by the beam on conducting boundaries. We find that these nonlinear "image" forces can cause a collective oscillation of the transverse rms emittance. We have investigated this phenomenon using computer simulation, and explained the results analytically. We assume a single species charged particle beam in a linear alternating-gradient transport system. The beam is assumed to enter the transport channel with uniform density and elliptical cross-section, with major and minor radii matched to the focusing system. The initial velocity distribution is locally Maxwellian with a unique temperature throughout the beam. Four conducting cylinders, whose axes are parallel to the transport channel, are used to simulate the conducting boundary provided by electrostatic focusing electrodes (see Fig. 1). The induced charge on these electrodes causes the image forces which are the subject of study. We assume here values of R = 24 mm d = 21.00 mm (see Fig. l), which is consistent with the absence of any dodecapole nonlinearity in the focusing field.1 No longitudinal acceleration is applied, and the calculation is non-relativistic.