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A hybrid fast-multipole technique for space-charge tracking with halos

The simulation of injection and accumulation of intense proton beams in synchrotrons and accumulator rings requires a flexible and robust treatment of space-charge effects. In particular, the simulation must be able to correctly incorporate the large-amplitude beam halo which is known to arise from a variety of mechanisms. This paper describes a technique for the efficient and accurate evaluation of transverse space-charge forces in a simulated beam that may include halo particles at arbitrarily large amplitudes. The technique uses the Fast Multipole Method (FMM), together with some elements of Particle-In-Cell (PIC) methods, to evaluate the space-charge field at the location of each macroparticle. Timing comparisons show that when a large-amplitude halo is present this hybrid technique is significantly faster than plain FMM and also offers performance advantages over PIC/FFT field calculations with equivalent spatial resolution. The hybrid FMM method has been implemented and tested in the multiparticle tracking and simulation code ACCSIM and some initial results are presented.