The conductivity tensor operator obtained by integrating the linearized Vlasovequation along the unperturbed orbits in the drift approximation isspecialized to frequencies well below the ion cyclotron frequency. Thediamagnetic contribution and the contribution of the particle drift motion areincluded, and finite Larmor radius effects are retained to all orders. Underappropriate assumptions of broad validity we obtain a set of coupledintegrodifferential wave equations for the amplitudes of the Fouriercomponents of the fields in the poloidal direction. These equations describedrift and shear Alfvén waves in axisymmetric toroidal geometry, and are in aform well suited for efficient numerical discretization. We have verified thatthey reproduce correctly several known results based on the gyrokinetic theoryunder the appropriate conditions. The essential equivalence between thetraditional Vlasov approach and the gyrokinetic formalism is therebyestablished. The range of validity of the approximations required to obtainthis result is explicitly stated, and the physical origin of the contributionsto the oscillating current and charge densities are clearly identified.
Constant-k|| toroidal coordinates and their application to tokamak plasma high-frequency dielectric response theory: I. Anisotropic equilibria