Intrinsic Plasma Rotation Determined by Neoclassical Toroidal Plasma Viscosity in Tokamaks

Intrinsic steady state plasma rotation is important for plasma confinement in ITER, since the momentum input is expected to be small. It is well known that the intrinsicplasma rotation in stellarator is determined by non-ambipolar diffusion due to helical ripple [1]. The non-ambipolar diffusion due to small 3D magnetic perturbation described by theNeoclassical Toroidal plasma Viscosity (NTV) theory [2] may be important in determiningthe intrinsic plasma rotation in tokamaks, because intrinsic error field cannot be avoided,and furthermore, resonant magnetic perturbation is frequently used to control Edge LocalizedMode and Resistive Wall Mode. The NTV theory in different collisionality regimes has beenwell developed in the last few years, and it has been summarized in [3]. The numerical resultsshowed a good agreement with the analytic solutions in different asymptotic limits [4]. Theflux of the trapped electron was found to be important in low collisionatlity case [5].The intrinsic toroidal plasma rotation determined by the NTV effect in tokamaks is in-vestigated in this paper. It is found by searching the root of the ambipolarity constraintΓi(Ωφ) − Γe(Ωφ) = 0, where Ωφ is the toroidal rotation and Γi and Γe are the ion and elec-tron particle fluxes, respectively. The ion and electron fluxes are evaluated from the numericalmodeling developed in [4].It is found that the result strongly depends on the plasma collisionality. For high collision-ality case, the ion flux is dominant and the intrinsic steady state flow is in counter-currentdirection. It corresponds to the ’ion root’ named in stellarators. For low collisionality case,there are three roots. Two of them are stable roots. One corresponds to the ’ion root’ in the counter-current. The second stable one corresponds to the ’electron root’ in co-current direction, near which the electron flux is dominant. The third one is an unstable root. The NTV torque drives the plasma rotation towards one of the stable roots. This means that the intrinsic toroidal rotation in low collisionality case can also be possible in co-current direction.Both of these two roots scale like|ω∗T | ≡ | qdρTρB0| ∝ | ρdρTR0Ip|, where q is the safety factor,T is temperature, ρ ≡√ΨT/(πB0) reduces to minor radius in cylindrical coordinate, Ψt isthe toroidal magnetic flux, B0 is the magnetic field strength on the magnetic axis, and Ip isthe plasma current. The prediction of intrinsic rotation due to NTV on ITER will also bediscussed.