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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. 

Non-neutral plasma experiments are excellent benchmarks for validating transport models, including in strongly coupled conditions. Experiments with Penning–Malmberg traps operate under the Brillouin limit, which means that the plasma is also strongly magnetized in the sense that the gyrofrequency exceeds the plasma frequency. This is an unusual regime that is not described by traditional plasma kinetic theory, particularly when strong coupling and strong magnetization are both present. Here, we apply a recently developed generalized Boltzmann kinetic theory to compute the temperature anisotropy relaxation rate in this regime. Strong magnetization is found to severely suppress energy exchange during collisions, leading to a drastically reduced anisotropy relaxation rate. The results exhibit good agreement with previous work by Glinsky et al. when the plasma is weakly coupled and extend the calculation to the strongly coupled regime as well. Results are compared with published experimental measurements, demonstrating good agreement. Furthermore, the model is tested using molecular dynamics simulations over a broader range of parameters than the experiments reached. These simulations utilize a new Green–Kubo relation, enabling an equilibrium simulation method that is more accurate than previous non-equilibrium methods that have been applied to this problem. Finally, a discussion of detailed balance in strongly magnetized plasmas is provided. Specifically, it is shown that despite the absence of time-reversal symmetry, which is usually used to mathematically prove detailed balance, the results satisfy detailed balance to a high degree of numerical precision. 

In this tutorial, a derivation of magnetohydrodynamics (MHD) valid beyond the usual ideal gas approximation is presented. Non-equilibrium thermodynamics is used to obtain conservation equations and linear constitutive relations. When coupled with Maxwell's equations, this provides closed fluid equations in terms of material properties of the plasma, described by the equation of state and transport coefficients. These properties are connected to microscopic dynamics using the Irving–Kirkwood procedure and Green–Kubo relations. Symmetry arguments and the Onsager–Casimir relations allow one to vastly simplify the number of independent coefficients. Importantly, expressions for current density, heat flux, and stress (conventionally Ohm's law, Fourier's law, and Newton's law) take different forms in systems with a non-ideal equation of state. The traditional form of the MHD equations, which is usually obtained from a Chapman–Enskog solution of the Boltzmann equation, corresponds to the ideal gas limit of the general equations. 

Recent works have shown that strongly magnetized plasmas characterized by having a gyrofrequency greater than the plasma frequency exhibit novel transport properties. One example is that the friction force on a test charge shifts, obtaining components perpendicular to its velocity in addition to the typical stopping power component antiparallel to its velocity. Here, we apply a recent generalization of the Boltzmann equation for strongly magnetized plasmas to calculate the ion–electron temperature relaxation rate. Strong magnetization is generally found to increase the temperature relaxation rate perpendicular to the magnetic field and to cause the temperatures parallel and perpendicular to the magnetic field to not relax at equal rates. This, in turn, causes a temperature anisotropy to develop during the equilibration. Strong magnetization also breaks the symmetry of independence of the sign of the charges of the interacting particles on the collision rate, commonly known as the “Barkas effect.” It is found that the combination of oppositely charged interaction and strong magnetization causes the ion–electron parallel temperature relaxation rate to be significantly suppressed, scaling inversely proportional to the magnetic field strength.