A MULTI-BUNCH, THREE-DIMENSIONAL, STRONG-STRONG BEAM-BEAM SIMULATION CODE FOR PARALLEL COMPUTERS

For simulating the strong-strong beam-beam effect, us-ing Particle-In-Cell codes has become one of the methods of choice. While the two-dimensional problem is readily treatable using PC-class machines, the three-dimensional problem, i.e., a problem encompassing hourglass and phase-averaging effects, requires the use of parallel pro-cessors. In this paper, we introduce a strong-strong code NIMZOVICH1, which was specifically designed for par-allel processors and which is optimally used for many bunches and parasitic crossings. We describe the paral-lelization scheme and give some benchmarking results. PARALLELIZATION NIMZOVICH uses parallelization according to the SPMD (Single Program, Multiple Data) scheme. A cluster of processors is divided in two sections, called Rings. Each Ring is subdivided into several Bunches. Bunches within a Ring are completely independent. Bunches in opposing Rings are independent, except if they have a design or par-asitic interaction point in common, i.e., if one of their two geometric interaction points falls into a section of the ring (the Window) shared by both beams. Each Bunch is divided longitudinally into several Slices. For reasons of load balancing, the slicing scheme is cho-sen in such a way as to have the same number of particles within each slice, assuming an initial gaussian distribution of given length. Slice borders are, however, not dynami-cally adapted to changed longitudinal distributions. Given enough available processors, each Slice’s portion of particles can be further subdivided. Portions of a Bunch with the same subdivision index in each slice are called a Slab. They do not represent any geometric subdivision. Each processor on each Ring runs through the following sequence of steps for each Turn: • For each Bunch in the sequence of opposing Bunches: – For each Slice in the opposing Bunch: ∗ Deposit particles onto grid in the center of gravity of my slice ∗ Solve Poisson’s equation on that grid ∗ Calculate electric fiel