We explore fundamentals of low-frequency current drive produced by a packet of arbitrarily polarized nonlinear shear Alfven waves in an infinite, uniform magnetized plasma. Analysis of the magnetohydrodynamic equations with resistivity and viscosity yields coupled nonlinear equations for the Alfven wave amplitude and an induced magnetic field. Particular solutions relate the plasma current to the helicity of the Alfven wave and the difference between the viscosity and magnetic diffusivity.