Simple, yet exact, analytic solutions for the shear and compressional Alfvén wave are obtained for helical magnetohydrodynamic (MHD) waves in cylindrical geometry with both resistivity and viscosity included. The current driven by all possible combinations of these waves is examined in the quasilinear regime (i.e., where the magnetic field produced by the driven current is not self-consistently included in the equilibrium where the wave equations are derived). It is found in all cases that it is not possible to drive significant bulk axial current with small amplitude wave fields. Thus, any useful low-frequency current drive scheme will have to be based on phenomena more complicated than those discussed here.
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