[en] The wave equation for strongly toroidal small aspect ratio (spherical) tokamaks with non-circular cross-section is properly formulated and solved for global waves, in the Alfven frequency range. The current-carrying toroidal plasma is surrounded by a helical sheet-current antenna, which is enclosed within a perfectly conducting wall. The problem is formulated in terms of the vector and scalar potentials (A,Φ), thus avoiding the numerical solution occurring in the case of (E,B) formulation. Adequate boundary conditions are applied at the vacuum - metallic wall interface and the magnetic axis. A recently derived dielectric tensor-operator, able to describe the anisotropic plasma response in spherical tokamaks, is used for this purpose; except for its linear character, no physical or geometrical limitations are imposed on it. The equilibrium profiles (magnetic field, pressure and current) are obtained from a numerical solution of the Grad-Shafranov equation. Specifically, the wave equation is solved by the aid of a numerical code we developed for the present problem, based on the well documented 2(1/2)D finite element solver proposed by E.G. Sewell. With the definitions V_i(θ,ρ) = U_i(-θ,ρ) (V_iU_i = A_j, Φ; j = ρ,φ,θ), our code solves simultaneously 16 second order partial differential equations (eight equations for each of real and imaginary set of functions V_i, U_i). A systematic analysis of the solutions obtained for various values and combinations of wavenumbers and frequencies in the Alfven range is presented