Intrinsic rotation in axisymmetric devices

Toroidal rotation is critical for fusion in tokamaks, since it stabilizes instabilities that can otherwise cause disruptions or degrade confinement. Unlike present-day devices, ITER might not have enough neutral-beam torque to easily avoid these instabilities. We must therefore understand how the plasma rotates 'intrinsically,' that is, without applied torque. Experimentally, torque-free plasmas indeed rotate, with profiles that are often non-flat and even non-monotonic. The rotation depends on many plasma parameters including collisionality and plasma current, and exhibits sudden bifurcations ('rotation reversals') at critical parameter values.Since toroidal angular momentum is conserved in axisymmetric systems, and since experimentally inferred momentum transport is much too large to be neoclassical, theoretical work has focused on rotation drive by nondiffusive turbulent momentum fluxes. In the edge, intrinsic rotation relaxes to a steady state in which the total momentum outflux from the plasma vanishes. Ion drift orbits, scrape-off-layer flows, separatrix geometry, and turbulence intensity gradient all play a role. In the core, nondiffusive and viscous momentum fluxes balance to set the rotation gradient at each flux surface. Although many mechanisms have been proposed for the nondiffusive fluxes, most are treated in one of two distinct but related gyrokinetic formulations. In a radially local fluxtube, appropriate for , the lowest-order gyrokinetic formulations exhibit a symmetry that prohibits nondiffusive momentum flux for nonrotating plasmas in an up-down symmetric magnetic geometry with no shear. Many symmetry-breaking mechanisms have been identified, but none have yet been conclusively demonstrated to drive a strong enough flux to explain commonly observed experimental rotation profiles. Radially global gyrokinetic simulations naturally include many symmetry-breaking mechanisms, and have shown cases with experimentally relevant levels of nondiffusive flux. These promising early results motivate further work to analyze, verify, and validate.This article provides a pedagogical introduction to intrinsic rotation in axisymmetric devices. Intended for both newcomers to the topic and experienced practitioners, the article reviews a broad range of topics including experimental and theoretical results for both edge and core rotation, while maintaining a focus on the underlying concepts.