Constant-k_∥ toroidal coordinates and their application to tokamak plasma high-frequency dielectric response theory: I. Anisotropic equilibria

A new straight-magnetic-field-line toroidal coordinate system is introduced by appropriate stretching of the poloidal and toroidal angles (Lamalle P U 2001 Europhys. Conf. Abstracts 25 A1145). In this system, the local wavenumber component of every poloidal-toroidal wave Fourier mode along the equilibrium magnetic field, k_∥, is rendered by construction constant on all magnetic surfaces. Semi-analytical expressions are derived for the radio-frequency (rf) response density of tokamak plasmas, providing a convenient description of wave-particle interactions at the fundamental ion cyclotron frequency in general geometry. The new coordinate system makes the analytical developments feasible and remarkably simple: for instance, the cyclotron resonance condition between a particle and a wave Fourier mode is a quadratic equation for the parallel guiding centre (gc) velocity, whereas it is cubic in Boozer coordinates and a transcendent equation in other systems. The theoretical results presented in this paper allow a realistic numerical simulation of rf wave propagation and absorption in the presence of strongly non-Maxwellian distribution functions, such as those created during intense ion cyclotron resonance minority heating scenarios. Extensions of the theory to incorporate finite Larmor radius effects and radial gc drifts are briefly discussed.