Toroidal Momentum Transport

Full text: Plasma rotation plays a key role in the regulation of turbulence and has a beneficial effect on energy confinement in fusion devices. It can also stabilize resistive wall modes. In reactor plasmas the external torque is relatively small, and for a long time toroidal plasma rotation has been assumed negligible under these conditions. This picture was radically changed by the experimental observation of a large rotation in the absence of an external torque (known as intrinsic rotation). Subsequently, mechanisms of toroidal momentum transport have attracted much attention in the community, leading to a very rapid development in theory and modelling. This paper will give an overview of ALL the developments in this relatively new area and puts them in a global perspective. The emphasis is on theory development and modelling, but experimental validation will also be reviewed. Toroidal momentum transport results from a breaking of symmetry in the direction along the magnetic field. This can be shown at a fundamental level from the symmetry in the gyrokinetic equation, allowing also for the identification of all processes that can generate momentum transport. In the gyrokinetic ordering (expansion in the Larmor radius normalized to the major radius), five processes emerge at lowest order: the finite radial gradient of the rotation, the E x B shearing, the Coriolis force due to the plasma rotation, a finite particle flux in the presence of a toroidal rotation, and the up-down asymmetry in the magnetic equilibrium. At the next order additional effects, such as the parallel velocity non-linearity, appear, only some of which have been identified. The higher order fluxes are small in a reactor plasma, and this paper will concentrate on the leading order effects. The process of momentum transport is complex, and nonlinear simulations play an important role in unravelling the physics, and are necessary for quantifiable predictions. The paper reports on the extensive analytic / numeric study of the five leading order effects and their interaction. Various experiments that have been undertaken to validate the physics model will be reviewed. This discussion also reveals how the various mechanisms interact to generate the rotation profile. Finally, the paper will discuss the expectations for a reactor based on our present knowledge. (author)