Hamiltonian in Guiding Center Theory: A Symplectic Structure Approach

The guiding center approximation represents a very powerful tool for analyzing and modeling a charged particle motion in strong magnetic fields. This approximation is based on the conservation of an adiabatic invariant, the magnetic moment. Hamiltonian equations for the guiding center motion are traditionally introduced using a non-canonical symplectic structure. Under such an approach one has to apply the non-canonical Hamiltonian perturbation theory in order to calculate the magnetic moment corrections. In this study we present an alternative approach with canonical Hamiltonian equations for the guiding center motion in time-dependent electromagnetic fields. We show that the derived Hamiltonian decouples three types of motion (gyrorotation, field-aligned motion, and cross-field drifts), and each type is described by a pair of conjugate variables. This form of Hamiltonian and symplectic structure allows easy introduction of adiabatic invariants and can be useful for the analysis of various plasma systems.