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Space Charge Simulation in COSY Using Fast Multipole Method


A method is presented that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales with a high power of the order. Given an ensemble of N particles, the method allows the computation of the self-fields of all particles on each other with a computational expense that scales as O(N). Using remainder-enhanced DA methods, it is also possible to obtain rigorous estimates of the errors of the methods. Furthermore, the method allows the computation of all high-order multipoles of the space charge fields that are necessary for the computation of high-order transfer maps and all resulting aberrations. This method has been implemented in COSY Infinity, and the progress of applying it to simulating the 6D cooling channel for the Muon Collider is reported.

B. Loseth, M. Berz, K. Makino, H. Zhang, P. Snopok, in: Particle Accelerator Conference 2013, (2013) 195


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