A treecode algorithm for simulating electron dynamics in a Penning-Malmberg trap

A treecode algorithm is presented for computing the electrostatic potential and electric field in a system of charged particles. The algorithm is grid-free and with N particles it reduces the operation count to O(N logN), as opposed to O(N 2 ) which is required for direct summation of pairwise interactions. The key idea is to replace the particle‐particle interactions by particle‐ cluster interactions which are evaluated using a Taylor approximation in Cartesian coordinates. The treecode is combined here with a boundary integral method to simulate electron dynamics in a Penning‐Malmberg trap.

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