A treecode algorithm for simulating electron dynamics in a Penning–Malmberg trap Original Research Article

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 image, as opposed to image 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.