Symplectic gyrokinetic Vlasov-Maxwell theory

We consider a general form of electromagnetic gyrokinetic Vlasov-Maxwell theory in which the gyrocenter symplectic structure contains electric and magnetic perturbations that are necessary to cause the first-order gyrocenter polarization displacement to vanish. The gyrocenter Hamilton equations, which are expressed in terms of a gyrocenter Poisson bracket that contains electromagnetic perturbations and a gyrocenter Hamiltonian, satisfy the Liouville property exactly with a time-dependent gyrocenter Jacobian. The gyrokinetic Vlasov-Maxwell equations are derived from a variational principle, which also yields exact conservation laws through the Noether method. We show that the new symplectic gyrokinetic Vlasov-Maxwell equations retain all first-order polarization and magnetization effects without the need to consider second-order contributions in the gyrocenter Hamiltonian.

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