Hamiltonian theory of the ion cyclotron minority heating dynamics in tokamak plasmas

Abstract

The question of heating a tokamak plasma by means of electromagnetic waves in the ion cyclotron range of frequencies (ICRF) is considered in the perspective of large rf powers and in the low collisionality regime. In such a case, the quasilinear theory (QLT) is validated by the Hamiltonian dynamics of the wave–particle interaction which exceeds the threshold of the intrinsic stochasticity. The Hamiltonian dynamics is represented by the evolution of a set of three canonical action angle variables well adapted to the tokamak magnetic configuration. This approach allows derivation of the rf diffusion coefficient with very few assumptions. The distribution function of the resonant ions is written as a Fokker–Planck equation but the emphasis is put on the QL diffusion instead of on the usual diffusion induced by collisions. The Fokker–Planck equation is then given a variational form from which a solution is derived in the form of a semianalytical trial function of three parameters: the percentage of resonant particles contained in the tail, an isotropic width ΔT, and an anisotropic width ΔP. This solution is successfully tested against real experimental observations. It is shown that in the case of the JET tokamak [Plasma Phys. Controlled Fusion 30, 1467 (1988)] the distribution function is influenced by adiabatic barriers which in turn limit the Hamiltonian stochasticity domain within energy values typically in the MeV range. Consequently and for a given ICRF power, the tail energy excursion is lower and its concentration higher than that from a bounce-averaged prediction. This may actually be an advantage for machines like JET [Plasma Phys. Controlled Fusion 30, 1467 (1988)] considering the energy range required to simulate the α-particle behavior in a relevant fusion reactor.