Full wave calculations based on the use of eikonal trial functions that are locally solutions of the homogeneous problem are carried out for solving the lower hybrid (LH) current drive problem in tokamaks, when geometrical optics assumptions are no longer valid in the description of the wave dynamics. The LH power deposition profile as well as the non-inductive driven current are determined self-consistently with a two dimensional (2-D)relativistic Fokker-Planck solver. The first consistent simulations are performed for the high aspect ratio tokamak TRIAM-1M, when the toroidal n|| upshift is bounded and insufficient to bridge the large spectral gap and cause wave damping.