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.
Self-Consistent parallel multi bunch beam-beam simulation using a grid-multipole method
The simulation code COMBI has been developed to enable the study of coherent beam-beam effects in the full collision scenario of the LHC, with multiple bunches interacting at multiple crossing points over many turns. The parallel version of COMBI was first implemented using a soft-Gaussian collision model which entails minimal communication between worker processes. Recently we have extended the code to a fully self-consistent collision model using a Grid-Multipole method, which allows worker processes to exchange charge and field information in a compact form which minimizes communication overhead. In this paper we describe the Grid-Multipole technique and its adaptation to the parallel environment through preand post-processing of charge and grid data. Performance measurements in a Myrinet cluster environment will be given.
Stability of anisotropic beams with space charge
Based on self-consistent Vlasov-Poisson equations, we derive coherent frequencies and stability properties of anisotropic or ``nonequipartitioned'' beams with different focusing constants and emittances in the two transverse directions. The thus obtained dispersion relations of transverse multipole oscillations with quadrupolar, sextupolar, and octupolar symmetries are solved numerically. We find that for sufficiently large energy anisotropy some of the eigenmodes become unstable in the space-charge-dominated regime. Applying our results to high-current linear accelerators, we find that ``nonequipartitioned'' beams may exist in relatively large regions of parameter space under stable conditions. It is only in beams with strongly space-charge-depressed betatron tunes that harmful instabilities leading to emittance exchange should be expected.