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Interaction between two charges in a uniform magnetic field

Introductory Workshop: Hamiltonian systems, from topology to applications through analysis August 20, 2018 - August 24, 2018

August 24, 2018 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Robert MacKay (University of Warwick)
Location: MSRI: Simons Auditorium
  • Hamiltonian

  • Reduction

  • Chaos

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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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