Langston, M.H. Lethin, R. Letourneau, P.D. Wei, J. JACoW Publishing Geneva, Switzerland 2226-0358 978-3-95450-221-9 10.18429/JACoW-ICALEPCS2021-MOPV048 English 271-276 simulation multipole space-charge hadron HOM Contribution to a conference proceedings 2022 2022-03 https://doi.org/10.18429/JACoW-ICALEPCS2021-MOPV048 https://jacow.org/icalepcs2021/papers/mopv048.pdf As part of the MACH-B (Multipole Accelerator Codes for Hadron Beams) project, we have developed a Fast Multipole Method (FMM**)-based tool for higher fidelity modeling of particle accelerators for high-energy physics within Fermilab’s Synergia* simulation package. 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 and 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 in which 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 were computed. Specifically, following our integration of the FMM into Synergia, changes between PIC-based computations and FMM-based computations are made by changing only the method for near-field (and self) particle interactions.