Binary collisions of charged particles in a magnetic field

TL;DR

This paper develops a second-order perturbation theory to analyze binary collisions of charged particles in a magnetic field, valid across all field strengths, and compares results with classical Monte Carlo simulations.

Contribution

It introduces an improved binary collision treatment for charged particles in magnetic fields applicable to any field strength, including explicit energy transfer calculations for regularized potentials.

Findings

Perturbation theory matches Monte Carlo results for high velocities.

Energy transfer involves all harmonics of electron cyclotron motion.

The method is valid for both weak and strong magnetic fields.

Abstract

Binary collisions between charged particles in an external magnetic field are considered in second-order perturbation theory, starting from the unperturbed helical motion of the particles. The calculations are done with the help of an improved binary collisions treatment which is valid for any strength of the magnetic field, where the second-order energy and velocity transfers are represented in Fourier space for arbitrary interaction potentials. The energy transfer is explicitly calculated for a regularized and screened potential which is both of finite range and non-singular at the origin, and which involves as limiting cases the Debye (i.e., screened) and Coulomb potential. Two distinct cases are considered in detail. (i) The collision of two identical (e.g., electron-electron) particles; (ii) and the collision between a magnetized electron and an uniformly moving heavy ion. The energy transfer involves all harmonics of the electron cyclotron motion. The validity of the perturbation treatment is evaluated by comparing with classical trajectory Monte--Carlo calculations which also allows to investigate the strong collisions with large energy and velocity transfer at low velocities. For large initial velocities on the other hand, only small velocity transfers occur. There the non-perturbative numerical classical trajectory Monte--Carlo results agree excellently with the predictions of the perturbative treatment.