A Novel Massive Parallel Possion Solver for Beam Dynamics

Many problems in beam dynamics are concerned with calculation of the inter-particles forces for millions of particles. One particular hard example is described in this annual report, see [1]. In order to estimate the interparticle forces in the electrostatic approximation with intrinsic open boundary conditions we have naively to compute the electric field at every particle’s position by summing (in continuum) over the contributions from all other N − 1 particles: using qij = qi − qj and qij = | qi − qj |. This is exact up to numerics, as no spatial discretization is made, but at the price of the highest computational effort, namely O(N). In order to avoid a numerical breakdown at small interparticle distances, a softening parameter was included: