Performing high-power long-duration discharges on Tore Supra has allowed us to investigate new physics at evanescent loop voltage in the situation where the current diffusion has fully taken place. Discharges with dominant noninductive current have been realized for many years, in a variety of configurations and plasma scenarios. They have allowed in-depth investigation on a number of physical phenomena governing the plasma behavior whenever the ohmic field is absent or negligible. The main results obtained in this area of research are summarized in this paper. They include, e.g., significant advances in the fast electron physics; the discovery of a new improved confinement regime (lower hybrid enhanced performance regime); the discovery of a new tokamak plasma regime with nonlinear temperature oscillations (O-regime); specific magnetohydrodynamic regimes associated with reversed safety factor profiles; investigation of the anomalous particle transport, obtained in vanishing loop voltage discharges; and the first experimental demonstration of synergy effects between electron cyclotron and lower hybrid current drive in a steady-state plasma.