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A competition for the spontaneous rotation of the plasma

Control of rotation is a major challenge in order to obtain a stable and well-confined plasma in future tokamak fusion reactor. While energetic neutral particle injectors allow partial control of flows in medium-sized tokamaks, the large volume of plasma in ITER will make this control more difficult. However, the flows play a key role in the stability of the plasma and the quality of the confinement.

A fascinating observation is that a tokamak plasma rotates, even in the absence of an external source of momentum. This phenomenon is called "intrinsic rotation". There are two mechanisms leading to intrinsic rotation : the force exerted by turbulence and magnetic braking effects.

The turbulence acts on the rotation via an exchange of momentum between waves and particles, which locally bring a net angular momentum to the plasma. The resulting velocity is called "self-generated velocity". The 3D effects of the magnetic field have the consequence of constraining the trajectories of the particles. These constraints are responsible for collisional magnetic braking which imposes the flow velocity of the plasma. This velocity, called “relaxed velocity”, is finite and depends on the temperature gradient. Each of these effects taken separately is well documented.

However, the competition between these two mechanisms has never been studied before. For this study, the 3D perturbation of the magnetic field considered is the "ripple", i.e. the modulation of this field due to the finite number of coils. The larger the amplitude of this perturbation, the more the plasma velocity will tend to reach its relaxed prediction. Conversely, if this amplitude is low or the turbulent intensity is high, it is towards the self-generated prediction that the plasma flows.

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Evolution temporelle de la vitesse toroidale (haut) et poloidale (bas) du plasma obtenu grâce à des simulations gyrocinétiques avec différentes amplitudes ripple. L’amplitude ripple critique obtenue pour cette turbulence est estimée à environ δc∼0.55%. On voit alors que le cas à faible ripple δ0=0.1% ne s’écarte presque pas du cas sans ripple, alors que celui à fort ripple δ0=1% est nettement contrôlé par les effets néoclassiques.

 

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Rotation toroidale avec (droite) et sans (gauche) ripple magnétique due au nombre fini de bobines générant le champ magnétique. Ces résultats de simulations obtenus avec GYSELA montrent que le ripple change fortement la rotation du plasma.

The idea is that there is a critical ripple amplitude at which the velocity is closer to its relaxed prediction than to the self-generated one. From an analytical theoretical model, a simple expression of this threshold has been obtained. Its validity has been proven by means of gyrokinetic simulations with the GYSELA code, which take into account both mechanisms in a self-consistent manner, performed with ripple amplitudes below and above this threshold. As expected, the effect of turbulence is subdominant in the high ripple amplitude case, and vice versa for the low amplitude case. Using the critical ripple expression, first estimates on ITER seem to show that the ripple effect will not be negligible near the plasma edge.

Associated publication : R. Varennes et al, Phys. Rev. Lett. 128, 255002

Contact at LPP : Laure Vermare


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