Nonlinear aspects of the neoclassical theory of plasma rotation and equilibrium bifurcations

It is shown that large velocities and electric fields occurring in a thin layer are consistent with the revised neoclassical theory of the plasma edge. The latter includes finite Larmor radius effects and nonlinear drive of the poloidal rotation, as well as a momentum source term and momentum losses by charge exchange collisions. The description of the space and time evolution of the parallel flow velocity and the radial electric field is given by a nonlinear first order partial differential equation away from the singular layer, but by a nonlinear second order differential equation near to it. The occurrence of large local velocities and velocity shears may be identified with the trigger of the transport barriers and bifurcations from the low (L) to the high (H) energy confinement mode observed in tokamaks and stellarators. Most of the results which are presented are independent from the particular choice of boundary condition imposed on the last closed magnetic surface. A particular type of boundary condition is thoroughly discussed which leads: (i) to negative local values of the large radial electric field; (ii) to either aperiodic or periodic solutions according to the values of the various parameters here kept fixed (i.e, those describing the temperature, the density and the Z(eff) profiles, as well as the charge exchange neutrals and the momentum injection rate). The results suggest that, under these conditions, steepening of the temperature profile after the transition from L to H confinement may ultimately lead to ELMy behaviour (type III ELMs) with ELM frequencies of the order of 10-20 s(-1).