Particle and energy confinement bifurcation in tokamaks

A bifurcation in the particle and energy confinement properties of a tokamak plasma, with properties similar to the experimentally observed L-mode to H-mode transition, is shown to follow from a simple model for the transport. The basic assumptions are that the edge turbulence is suppressed by sheared E×B flow, and the radial ion pressure gradient is approximately balanced by the radial electric field. The particle and thermal diffusivities are assumed to be given by simple nonlinear functions of the radial electric field shear, which is related to the density and pressure gradients. The steady-state density and pressure profiles are found to have large gradient regions near the plasma edge when the product of edge energy flux and particle flux exceeds a threshold value, which corresponds to the H-mode threshold. The particle and energy confinement times are significantly larger when this threshold is exceeded. The confinement times exhibit hysteresis, corresponding to a dependence of quasiequilibrium states on the time history. The width of the edge layer where the gradients are large is determined mainly by the particle source profile, which is assumed to be concentrated near the plasma edge. This edge layer width increases slowly with increasing edge heat flux or heating power, as observed experimentally.