Maxwell's equations are solved in a toroidal axisymmetric plasma. The numerical method implemented in the PENN code is based on a formulation in terms of the electromagnetic potentials and a discretization with standard bilinear or bicubic Hermite finite elements. Two models for the dielectric tensor operator yield different physical problems, which can be used comparatively to study small amplitude plasma perturbations down to the Alfven range of frequencies. The first treats the plasma as resistive fluids and gives results that are in good agreement with toroidal fluid codes. The second is a kinetic model taking into account the finite size of the Larmor radii; it is here successfully tested against a similar model in cylindrical geometry. New results are obtained for kinetic effects in toroidal geometry, showing that it might be difficult to use an Alfven wave heating scheme to heat a plasma up to temperatures that are relevant for a tokamak reactor.