The high-frequency constitutive relation of axisymmetric toroidal plasmas

Abstract

The response of a hot axisymmetric toroidal plasma to oscillatory fields is derived by integrating the linearized Vlasov equation along the unperturbed orbits written in the drift approximation. The details of the equilibrium configuration are taken into account with the same degree of accuracy as in the gyrokinetic approach; instead of approximating the kinetic equation, however, we approximate its solution. The integral constitutive relation obtained is valid to all orders in the Larmor radius, and for arbitrary frequency, except for the omission of relativistic effects. Finite Larmor radius wave equations adequate for the numerical simulation of ion cyclotron heating and current drive in tokamaks can be obtained from the general results by expanding to second order in the Larmor radius, while neglecting the perpendicular particle drifts and the diamagnetic terms in the equilibrium distribution functions. In the low-frequency domain, in which these effects are important, our wave equations are essentially equivalent to those obtained from a gyrokinetic equation. Some additional approximations, not explicitly stated in the gyrokinetic derivation although usually physically justified, are, however, required to prove this equivalence.