Bifurcation of solutions to MHD equilibrium equations for toroidal plasmas

The appearance of transport barriers in plasmas is usually taken to be the result of bifurcations in the transport equations, in which the possible control parameters are the radial electric field in association with shear flow, which may contribute to the reduction or suppression of turbulent fluctuations. On the other hand, such barriers show up globally as modifications in the profile of the safety factor, which is related to the equilibrium solutions. Solano has suggested to study transport barriers under the point of view of the criticality of the Grad- Shafranov equation, and finding the bifurcations in its solutions. Ball et al., on the other hand, have studied the problem using economical or minimal models, based on reduced Magnetohydrodynamic (MHD) equations with phenomenological terms, which allow an optimization approach, by controlling such parameters as those related to the power source, damping and shear flow driving rate. Then they study the bifurcations for such model. The purpose of this work is to explore Solano's idea, but using a modified Grad-Shafranov equation which can properly take into account equilibria with shear flow. Bifurcations of he solutions are studied for different properties of the shear flow. (author)