Rigorous Calculation of 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 [1]. We recently generalized the modulated-transport model to allow the turbulent momentum diffusivity to depend on space in a completely arbitrary way, using a boundary-layer asymptotic analysis. In the present work, we rigorously derive the result using an alternate variable-transform method that employs new kernels for semi-differential operations. The new derivation permits a rigorous error bound on the asymptotic results, and gives explicit approximations for the solution in the layer, as are needed for applications that depend on details of scrape- off-layer flows. [1] T. Stoltzfus-Dueck. “Transport-driven toroidal rotation in the tokamak edge”. Phys. Rev. Lett. 108 (2012), 065002.