Fast Multipole Method (FMM)-Base Particle Accelerator Simulations in the Context of Tune Depression Studies

As part of the MACH-B (Multipole Accelerator Codes for Hadron Beams) project, Reservoir Labs has developed a\ Fast Multipole Method (FMM [1–7])-based tool for higher fidelity modeling of particle accelerators for high-energy physics within Fermilab’s Synergia [8, 9] simulation pack- age. We present results from our implementations with a focus on studying the difference between tune depression estimates obtained using PIC codes for computing the particle interactions versus those obtained using FMM-based algorithms integrated within Synergia. In simulating the self-interactions and macroparticle actions necessary for accurate simulations, we present a newly-developed kernel inside of a kernel-independent FMM, where near-field kernels are
modified to incorporate smoothing while still maintaining consistency at the boundary of the far-field regime. Each simulation relies on Synergia with one major difference: the way in which particles interactions are computed. Specifically, following our integration of the FMM into Synergia, changes between PIC-based computations and FMM-based computations are made by simply selecting the desired method for near-field (and self) particle interactions.