Local Negative Shear and the Formation of Transport Barriers

We present a set of 3D nonlinear equations describing drift-resistive ballooning modes in a torus including the self-consistent modification of the local magnetic shear due to the finite $\beta$ shift of the flux surfaces. Simulations using these equations reveal that a bifurcation of the transport occurs when the local magnetic shear on the outside midplane reverses sign. A fully self-consistent bifurcation diagram is calculated which reveals significant hysteresis, i.e., the transport barrier is maintained at lower values of $\beta$ than is required for the formation of the barrier, as expected from the experimental observations.