Interaction between two charges in a uniform magnetic field

In joint work with Diogo Pinheiro, we reduced the dynamics of two charges in a uniform magnetic field to 3 degrees of freedom (DoF). If they have the same ratio of charge to mass we reduced to 2 DoF, by a symmetry we call locomotive coupling rod symmetry. For opposite signs of charge and charge to mass ratios not summing to zero, we proved every high enough energy level possesses chaotic coplanar motion, analogous to Poincaré’s second species orbits in celestial mechanics. The global motion can be considered as making transitions between ionic and free states. For same signs of charge, the state space is separated by the planar motions into pass-through and bounce-back motions. The work is the first step in an analysis of cross-field transport in quasi-symmetric magnetic fields.

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