Convective equilibrium and mixing-length theory for stellarator reactors

In high beta stellarator and Tokamak reactors, the plasma pressure gradient in some regions of the plasma may exceed the critical pressure gradient set by ballooning instabilities. In these regions, convective cells break out to enhance the transport. As a result, the pressure gradient can rise only slightly above the critical gradient and the plasma is in another state of equilibrium-'convective equilibrium'-in these regions. Although the convective transport cannot be calculated precisely, it is shown that the density and temperature profiles in the convective region can still be estimated. A simple mixing-length theory, similar to that used for convection in stellar interiors, is introduced to provide a qualitative description of the convective cells and to show that the convective transport is highly efficient. A numerical example for obtaining the density and temperature profiles in a stellarator reactor is given.