Self-sustained turbulence and L-mode confinement in toroidal plasmas. I

A theory of L-mode confinement in toroidal plasmas is developed. The effect of the anomalous transport, which is caused by microscopic fluctuations, on the pressure-gradient-driven modes is analysed. The E*B nonlinearity is renormalized as a form of the transport coefficient such as the thermal diffusivity, the ion viscosity and the current diffusivity. Destabilization by current diffusivity and stabilization by thermal transport and ion viscosity are analysed. By use of the mean-field approximations, the nonlinear dispersion relation is solved. Growth rate and stability conditions are expressed in terms of the renormalized transport coefficients. The transport coefficients in the steady state are obtained by the marginal stability condition for the microscopic ballooning mode in tokamaks. A formula for the anomalous transport is obtained. The role of the pressure gradient in enhancing the anomalous transport is identified. An important role is found for the collisionless skin depth. Effects of geometrical parameters such as the rotational transform and magnetic shear are also quantified. Comparison with experimental observations shows a good agreement in a various aspects of the L-mode confinement, including the dependences on the ion mass, plasma current, internal inductance and reversed shear. The large transport coefficient at the edge is also explained. The typical wavenumber and level of fluctuations for self-sustained turbulence are also obtained.