# The toroidal momentum pinch velocity due to the Coriolis drift effect on small scale instabilities in a toroidal plasma

### A.G. Peeters, C. Angioni, D. Strintzi

### Phys. Rev. Lett. **98**, 265003 (2007)

Copyright (2007) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.Download the PDF or go to the journal link

Abstract

In this Letter, the influence of the “Coriolis drift” on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.

Description

This paper describes a novel pinch velocity for the anomalous toroidal momentum transport in a tokamak. (anomalous here means due to small scale turbulence). The effect is generated through the Coriolis drift in the co-moving system, which leads to a coupling of the parallel velocity fluctuations with the density and temperature perturbations. The latter are generated by small scale turbulence driven by the radial temperature and density gradients. The gradients of temperature and density, over the coupling with the momentum balance, therefore, also generate a radial flux of toroidal momentum. Such a flux is of interest since plasma rotation is known to have a positive influence on confinement and stability properties of the plasma. In a reactor the torque on the plasma is, however, expected to be small, and only an anomalous pinch term can generate a finite rotation.

The figure shows the normalized momentum flux (R/2LT )Γφ /Qi as a function of the normalized toroidal velocity (u) for three values of the normalized poloidal wave vector kθ ρi 0.5 (o), 0.2 (squares), and 0.8 (diamonds). The top right graph shows the growth rate as a function of the normalized toroidal velocity and the down left graph the contour lines of normalized momentum flux (R/2LT )Γφ /Qi as a function of toroidal velocity and the radial gradient of the toroidal velocity (u'). The latter results are obtained for kθ ρi = 0.5. In the graph the thick line denotes zero momentum ﬂux, i.e. the stationary point for zero torque

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