Stochasticity, superadiabaticity, and the theory of adiabatic invariants and guiding center motion

Abstract

The theory of adiabatic invariants is discussed within the modern framework of symplectic Hamiltonian dynamics. The distinctions between exact, adiabatic, and superadiabatic invariants are clarified. The intimate connection between adiabatic (as opposed to exact) invariance and resonant interactions between motions on disparate time scales is elucidated. For the important case of charged particle motion in a strong magnetic field, resonances between gyration, bounce motion, and an external sinusoidal perturbation are described explicitly by introducing a time-dependent symplectic formulation of the guiding center motion. Destruction of invariance is discussed for quite general situations of physical interest, including the case of a trapped particle in a tokamak.