Gyro-kinetic study of toroidal momentum transport

This paper will report on a gyro-kinetic study of toroidal momentum transport. Both linear as well as non-linear results will be presented, and both the diagonal (proportional to the velocity gradient) as well as the pinch velocity contribution (proportional to the toroidal velocity) of the radial momentum flux are investigated. All simulations use the flux tube geometry, and are performed with the gyro-kinetic code GKW. The study aims at both clarifying the physics processes involved in toroidal momentum transport as well as accurately predicting the rotation profiles. The diagonal part of the momentum transport is expressed in a Prandtl number, i.e., the ratio of the momentum diffusivity and the ion heat conductivity coefficients. The Prandtl number (Pr) is found to be in the range 0.6-1.2 over a wide range of plasma parameters in both linear as well as non-linear simulations. The parallel velocity shear drive is found to be small. The paper then reports on the momentum pinch velocity due to curvature effects on micro-instabilities in a toroidal plasma. This pinch can be elegantly derived in the co-moving system, and is then connected with the 'Coriolis drift'. A simple fluid model is used to highlight the physics mechanism. The derived pinch velocity will be split into a part due to the gradients, and the part due to the turbulent equipartition. Turbulent equipartition alone will be shown to be unable to generate peaked rotation profiles in low collisionality H-mode plasmas. The accuracy of the analytic models is found to be limited through the calculations using the full gyro-kinetic model. The normalized pinch is smaller by roughly 40% compared with the analytic model, and its dependence on the density gradient is weaker. Non-linear simulations reproduce the pinch found in linear theory. The results indicate that the pinch is somewhat weaker than the linear theory suggests, and follows roughly the same scaling. The results of this study predict a moderately peaked rotation profile for ITER assuming zero momentum input. (author)