Theory of charged particle heating by low-frequency Alfvén waves

The heating of charged particles by a linearly polarized and obliquely propagating shear Alfven wave (SAW) at frequencies a fraction of the charged particle cyclotron frequency is demonstrated both analytically and numerically. Applying Lie perturbation theory, with the wave amplitude as the perturbation parameter, the resonance conditions in the laboratory frame are systematically derived. At the lowest order, one recovers the well-known linear cyclotron resonance condition k∥v∥−ω−nΩ=0, where v∥ is the particle velocity parallel to the background magnetic field, k∥ is the parallel wave number, ω is the wave frequency, Ω is the gyrofrequency, and n is any integer. At higher orders, however, one discovers a novel nonlinear cyclotron resonance condition given by k∥v∥−ω−nΩ∕2=0. Analytical predictions on the locations of fixed points, widths of resonances, and resonance overlapping criteria for global stochasticity are also found to agree with those given by computed Poincare surfaces of section.