Transport-Driven Toroidal Rotation with Generally Varying Diffusivity

Future devices like ITER will have limited capacity to drive toroidal rotation, increasing the risk of instabilities like resistive wall modes. Fortunately, many experiments have found that tokamak plasmas rotate “intrinsically”, that is, without applied torque. The modulated-transport model shows that such rotation may be caused by the interaction of ion drift-orbit excursions with the strong spatial variation of the turbulent momentum diffusivity. The model captures intriguing qualitative behavior, such as the strong dependence of edge intrinsic toroidal rotation on the major-radial position of the X-point. However, quantitative modeling applications need more detailed experimental features. For example, the original model required the turbulent momentum diffusivity to decay exponentially in the radial direction, while experiments have more complicated variation. In this work, we generalize the modulated-transport model to allow the turbulent momentum diffusivity to depend on space in a completely arbitrary way. The normalized diffusivity is assumed to be weak, a condition that is typically met for experimental applications, because the normalization is large. The new calculation may serve as a basis for future extensions, including shaped geometry and trapped particles.