Thermal confinement bifurcation and the L- to H-mode transition in tokamaks

A bifurcation in the thermal confinement of tokamaks, which resembles the L- to H-mode transition, is shown to follow from properties of edge turbulence recently derived by Biglari et al. [Phys. Fluids B 2, 1 (1990)], and the standard neoclassical theory of poloidal rotation. The temperature profiles develop a pedestal at the plasma edge, and the poloidal rotation near the edge is considerably increased, when the heating power exceeds a critical value. The energy confinement time is a discontinuous function of increasing heating power, but is continuous for decreasing power (power hysteresis). Critical values of density and magnetic field are found, which must be exceeded in order for the bifurcation to occur. The scaling of the power threshold with density, magnetic field, and ion mass is similar to what is found experimentally.