Fast Multipole Method Approaches in Particle Accelerator Simulations for the Computational and Intensity Frontiers: SnowMass 2021 Letter of Interest

In high intensity hadron beam accelerators, the space-charge effect from the interactions between charged particles can have significant impact on beam dynamics, including particle loss along the accelerator. At the beam pipe, these effects and losses can be especially pronounced. As the facilities for high energy physics grow in size and cost (in building, maintenance, and simulation energy usage), and as the constraints on beam loss increase, it is becoming more important for the Computational and Intensity Frontiers to be able to accurately predict the space-charge effect on beam loss with higher-fidelity computational approaches. Reservoir Labs is working on a project titled MACH-B (Multipole Accelerator Codes for Hadron Beams), in which we are developing a highly-scalable Fast Multipole Method (FMM)-based tool for higher fidelity modeling of particle accelerators for high energy physics within the next generation of the Synergia software [1, 24] system on heterogeneous architectures, which will rely further on the Kokkos [4] abstraction layer to provide source level portability of our code base between CPUs and GPUs. We will deploy new particle simulation capabilities and accurately model space charge through HPC software with the following components: • Fast Multipole Methods (FMMs): Originally designed for Coulomb interactions, FMM schemes achieve linear scaling [9, 12]. In the class of tree codes, FMMs separate nearand far-field interactions on a hierarchy of spatial scales using octree (3D) data structures. Because they achieve arbitrary precision at modest cost with straightforward error estimates, FMMs are best suited for large problems requiring high degrees of accuracy at scale such as those necessary in particle accelerator simulations. We are designing our FMM techniques to be kernel-independent [14, 15, 16, 17, 29, 30] to allow for maximum flexibility for multiple PDEs and has been shown to scale well to hundreds of thousands of processors. • Boundary Integral Solvers (BIS) and Boundary Conditions: For smooth/piecewise-smooth boundaries, such as those often seen near particle accelerator pipe walls, boundary integral equation approaches (1) require no need for complex mesh generation for calculating potentials, (2) allow far-field boundary conditions to be satisfied, and (3) result in higher degrees of accuracy [13]. At the beam pipe, a BIS can be specifically designed to couple with our domain-based FMM solver for an embedded boundary solver (EBS) [3, 18, 19, 26, 30]. In cases where periodic or mixed boundary conditions may be required, FMMs can be tailored to handle these [27, 28]. These boundary solvers are designed to work with unstructured geometries, can perform on-the-fly quadratures for singular and hypersingular kernels, and can be hierarchically parallelized.