Model for Binary Collisions in Strongly Magnetized Plasmas

A reduced model is developed to describe the outcome of collisions between two charged particles in the presence of a strong magnetic field. The model applies to the asymptotic regime of strong magnetization, where the gyroradius is small compared to the interaction spatial scale (of the order of the Debye length in a weakly coupled plasma). The ion is assumed to be weakly magnetized in the case of a two-component interaction. The positron (or electron) magnetic moment is assumed to be conserved during the collision, satisfying the first adiabatic invariant. The model then solves for other aspects of the charged particle motion perturbatively in orders of the inverse magnetic field strength. For the two-component case, this includes the velocity vector of the ion, the change in velocity of the electron (or positron) parallel to the magnetic field, and the spatial shift of its gyrocenter. For the case of identical particles, this includes the relative speed of the two particles in the parallel direction, and the shift of the relative gyrocenters of the particles. An important aspect of the model is the identification of a generalized conserved momentum. The results enable the determination of the outcome of collisions with far lower computational resources than required for full orbit calculations, and can be utilized to rapidly evaluate transport rates for kinetic theories. The regimes considered are expected to be particularly relevant to antimatter experiments.