The two‐dimensional Fokker–Planck equation with strong quasilinear diffusion on the tail of the electron distribution function is solved analytically and numerically. The quasilinear diffusion is taken to be parallel to the confining magnetic field of the plasma, as is appropriate for lower‐hybrid current drive. The radio frequency fields that produce this quasilinear diffusion are assumed to be imposed by external sources. It is found that an appreciable broadening of the resonant plateau in the direction perpendicular to the toroidal magnetic field leads to more particles carrying the current. As a result both the current (J) and the power dissipated (Pd) are substantially enhanced, compared with the predictions of one‐dimensional theory. The figure of meritJ/Pdis three times larger than the one found from the one‐dimensional theory.