Abstract
High fidelity charged particle beam dynamics, especially if collisional, require specialized numerical methods. The challenges include the ability to deal with very large particle numbers, long-range electromagnetic forces, and vast spatial and timescales. We developed a novel algorithm to address these challenges. The main characteristics of the algorithm are Strang splitting to separate near and far forces, the fast multipole method to lower the computational cost of the far region, and the Sim\`o integrator to capture all close encounters efficiently in the near region. The algorithm is fully adaptive both in space and time, while maintaining symplecticity to machine precision. Its performance is illustrated with two challenging examples from nonlinear multiparticle beam dynamics, including the first electron cooling simulations based on first principles.
Highlights
Charged particle beams are ensembles of close-by electrons or ions in directed motion
The vast majority of these codes are based upon variants of what generically may be called mean-field, collisionless codes. While this is sufficient for many applications, several recent beam physics applications emphasized the need for new, collisional algorithms and codes based on them
We briefly summarized two such applications here: ultracold electron beam generation based on arrays of sharp nanotips and electron cooling of ion beams
Summary
Charged particle beams are ensembles of close-by electrons or ions in directed motion. Based on a theorem of Simò [22] and aided by differential algebraic methods [23], we previously developed a collisional numerical integrator, the Simò integrator, with some provably optimal behavior [24] This integrator is variable order and adaptive with automatic selection of particle-by-particle optimal order and time step to minimize computational cost given an a priori user-selected tolerance for error. The resulting algorithm is an accurate and efficient collisional simulation of charged particle beams in external electromagnetic fields that is symplectic to machine precision and is provably the best in reaching an a priori set error level with minimized computational cost.
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