Variational averaging of charged-particle motion in strong magnetic fields

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Résumé : Symmetries play an important role in the equations of plasma physics. Theses symmetries are manifest in various conservation laws, like volume preservation of the flow of a charged particle, or energy conservation, for instance. Numerical codes that mimic such symmetries often show increased stability and accuracy. We present a theory called “variational averaging” which provides an averaging procedure of the fast time scale (cyclotron frequency) on the level of the variational principle of the dynamics, thereby guaranteeing the preservation of symmetries. Our approach is related to the theory of "gyrokinetics", but does not require the use of Lie transforms or Lie derivatives. We discuss the scaling procedure that leads to the non-dimensional particle-field Lagrangian and then discuss the asymptotic limit of the variational principle as the magnetic field strength tends to infinity.