L-H transition in tokamaks and stellarators

It is shown that the bifurcation dynamics in the H-mode theory based on the ion orbit loss and nonlinear viscosity is not sensitive to the radial pressure and temperature gradients after bifurcation. This allows the poloidal flow velocity to be opposite to that of the poloidal E*B velocity in the H-mode phase if the pressure gradient is steep. Here, E(B) is the electric (magnetic) field. The theory is also extended to stellarator configurations to demonstrate that the tokamak H-mode theory can be tested in a controlled manner in those devices. A set of poloidal and toroidal momentum evolution equations is derived in which the radial current density outside the last closed flux surface is expressed in terms of the radial integral of the poloidal current density into the divertor plates. This facilitates the calculation of the radial electric field profile across the separatrix.