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A reduced model is developed to describe the outcome of collisions between two like-charged particles in the presence of a strong magnetic field. Two cases are considered: large mass ratio (e.g., positron–proton or electron–antiproton) and unity mass ratio (e.g., electron–electron or ion–ion). The model applies to the asymptotic regime of strong magnetization, where the gyroradius of the low-mass particle 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 two-component case. 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 positron–ion case, this includes the velocity vector of the ion, the change in velocity of the positron parallel to the magnetic field, and the spatial shift of the positron gyrocenter. For the identical particle case, 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 experiments that trap antimatter.