Experimental observations of driven and intrinsic rotation in tokamak plasmas

Abstract

Experimental observations of driven and intrinsic rotation in tokamak plasmas are reviewed. For momentum sources, there is direct drive from neutral beam injection, lower hybrid and ion cyclotron range of frequencies waves (including mode conversion flow drive), as well as indirect j B × forces from fast ion and electron orbit shifts, and toroidal magnetic field ripple loss. Counteracting rotation drive are sinks, such as from neutral drag and toroidal viscosity. Many of these observations are in agreement with the predictions of neo-classical theory while others are not, and some cases of intrinsic rotation remain puzzling. In contrast to particle and heat fluxes which depend on the relevant diffusivity and convection, there is an additional term in the momentum flux, the residual stress, which can act as the momentum source for intrinsic rotation. This term is independent of the velocity or its gradient, and its divergence constitutes an intrinsic torque. The residual stress, which ultimately responds to the underlying turbulence, depends on the confinement regime and is a complicated function of collisionality, plasma shape, and profiles of density, temperature, pressure and current density. This leads to the rich intrinsic rotation phenomenology. Future areas of study include integration of these many effects, advancement of quantitative explanations for intrinsic rotation and development of strategies for velocity profile control.

Tracing the Pathway from Drift-Wave Turbulence with Broken Symmetry to the Production of Sheared Axial Mean Flow

“…The modelization of intrinsic macroscopic flow in plasmas also involves symmetry breaking in the turbulence. Intrinsic flow is of great importance in magnetic confinement fusion due to its promise of stabilizing MHD instabilities [7] and reducing turbulent transport [8,9], particularly in burning plasma devices like ITER, where momentum input is limited. Measurements from Alcator C-Mod [10] indicate that intrinsic toroidal flow in H-mode is driven by edge ∇T.…”

“…While many observations manifest the correlation between macroscopic intrinsic flow and edge profile gradients [9,14], investigations of the microscopic mechanism have been limited. Probe measurements from the edge of TJ-II [15] and TEXTOR [16] suggest that the non-diffusive residual stress, Π Res r z , scales linearly with edge gradients.…”

Direct toroidal torque driven by ICRF heating and its dependence on the plasma rotation

“…For typical plasmas of medium-size experiments like ASDEX-Upgrade (AUG), we show that this is a small effect, since the toroidal momentum carried by waves is much smaller that that carried by neutrals of the neutral beam injection (NBI) system [11,12]. This is not in contradiction with the common experimental finding that ICRF heating can substantially influence plasma rotation [8,13]. In fact, ICRF heating modifies the plasma pressure profiles, influences turbulence and MHD activity.…”

“…The impact of ICRF heating on plasma toroidal momentum is an ample and complex topic. For an exhaustive overview of the present understanding we refer to [7,8] and the references therein. Here, our interest is focused mainly on the recent work by Xu and co-workers where they pointed out that in rotating plasmas there is a net torque exerted by RF waves, even when operating in ICRF-heating mode [9].…”

A tokamak pertinent analytic equilibrium with plasma flow of arbitrary direction

“…However, it is well known that macroscopic plasma flows, being either externally driven or intrinsic, are present in tokamaks (e.g. see [3]). Plasma rotation affects the stability properties of the equilibria and moreover sheared flows contribute in the reduction of turbulent transport thereby playing a role in the transition to the advanced confinement regimes (L-H transitions).…”