A numerical model of current drive is developed in an infinitely long plasma cylinder, by means of two counter-rotating magnetic fields (RMFs) where the frequency of the (+) RMF is allowed to vary. The accessibility of steady state solutions where both RMFs penetrate into the plasma much farther than the classical skin depth, the electron fluid rotating synchronously with the (−) RMF and the ion fluid rotating synchronously with the (+) RMF, is examined. It is demonstrated that the steady state solutions are accessible from a broader class of initial conditions by allowing the frequency of the (+) RMF to decrease linearly. The rate of change in the frequency of the (+) RMF is required to be greater than the ion relaxation rate due to collisions with the electron fluid.