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Transport bifurcation induced by sheared toroidal flow in tokamak plasmas^{a)}

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10.1063/1.3642611

### Abstract

First-principles numerical simulations are used to describe a transportbifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear, because in the former case the component of the sheared toroidal flow that is perpendicular to the magnetic field has the strongest suppressing effect on the turbulence. In the zero-magnetic-shear regime, there are no growing linear eigenmodes at any finite value of flow shear. However, subcritical turbulence can be sustained, owing to the existence of modes, driven by the ion temperature gradient and the parallel velocity gradient, which grow transiently. Nonetheless, in a parameter space containing a wide range of temperature gradients and velocity shears, there is a sizeable window where all turbulence is suppressed. Combined with the relatively low transport of momentum by collisional (neoclassical) mechanisms, this produces the conditions for a bifurcation from low to high temperature and velocity gradients. A parametric model is constructed which accurately describes the combined effect of the temperature gradient and the flow gradient over a wide range of their values. Using this parametric model, it is shown that in the reduced-transport state, heat is transported almost neoclassically, while momentum transport is dominated by subcritical parallel-velocity-gradient-driven turbulence. It is further shown that for any given input of torque, there is an optimum input of heat which maximises the temperature gradient. The parametric model describes both the behaviour of the subcritical turbulence (which cannot be modelled by the quasi-linear methods used in current transport codes) and the complicated effect of the flow shear on the transport stiffness. It may prove useful for transportmodelling of tokamaks with sheared flows.

© 2011 American Institute of Physics

Received 31 May 2011
Accepted 27 August 2011
Published online 12 October 2011

Acknowledgments: We are grateful for helpful discussions with I. Abel, P. de Vries, W. Dorland, and G. W. Hammett. This work was supported by EPSRC (EGH, FIP), STFC (AAS), EURATOM/CCFE Association (MAB,CMR,SCC), and the Leverhulme Network for Magnetised Plasma Turbulence. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Computing time was provided by HPC-FF and by EPSRC grant EP/H002081/1. Much of this work was carried out at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, during the programme “Gyrokinetics for Laboratory and Astrophysical Plasmas.”

Article outline:

I. INTRODUCTION

II. EQUATIONS AND NUMERICS

A. Gyrokinetics with velocity shear

B. Numerical setup

III. TURBULENT FLUXES

A. Heat flux

B. Momentum flux

C. Turbulent Prandtl number

IV. SUBCRITICAL TURBULENCE

V. TRANSPORTBIFURCATION

A. Possibility of bifurcation

B. Inverting the problem

C. Interpolation

D. Neoclassical transport

E. Bifurcation

VI. PARAMETERISED MODEL

A. Modelling Q_{t}

1. Dependence of Q_{t} on κ

2. Parameterisation of Q_{t}

B. Modelling Π_{t}

C. The modelled bifurcation

VII. THE REDUCED TRANSPORT STATE

A. Heat flux at constant Π/Q

B. Temperature gradient jump

C. Neoclassical heat flux, turbulent momentum flux

D. Bifurcation by lowering Q/Q_{gB}

E. Optimum Q

F. Transition region

VIII. CONCLUSIONS

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2011-10-12

2014-04-17

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