On wave–particle interaction in axisymmetric toroidal systems

A general formalism is developed to describe the interaction of charged particles with electromagnetic waves in terms of coupled finite difference mapping equations that incorporate tokamak topology. The approach is based on considering non-adiabatic changes in the constants of particle motion and it covers a range of wave–particle resonance frequencies, from the precessional to cyclotron frequencies of both passing and trapped ions. The concept of overlapping resonances is used to estimate the threshold for a single plane wave to cause stochastic particle motion. In the stochastic regime, the process is Markovian, and particle diffusion in three-dimensional phase space takes place. Estimations of diffusion coefficients are carried out in the two cases of waves interacting with passing and trapped ions by means of the cyclotron and bounce resonances, respectively, and previously known results are recovered in the proper limits. PACS numbers: 52.20.Dq, 52.25.Gj, 52.55.Fa (Some figures in this article are in colour only in the electronic version.)