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Abstract:

Introducing up–down asymmetry into the tokamak magnetic equilibria appears to be a feasible method to drive fast intrinsic toroidal rotation in future large devices. In this paper we investigate how the intrinsic momentum transport generated by up–down asymmetric shaping scales with the mode number of the shaping effects. Making use the gyrokinetic tilting symmetry (Ball et al 2016 Plasma Phys. Control. Fusion 58 045023), we study the effect of envelopes created by the beating of different high-order shaping effects. This reveals that the presence of an envelope can change the scaling of the momentum flux from exponentially small in the limit of large shaping mode number to just polynomially small. This enhancement of the momentum transport requires the envelope to be both up–down asymmetric and have a spatial scale on the order of the minor radius.

Abstract:

>We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, α ⟪ 1. Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, pi. The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered l = ρi/δ, where δ ⟪ 1 is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong electric field E in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with α = δ = 0. By using these new coordinates as variables in the limit α ~ δ ⟪ 1, we obtain a generalized ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.

Abstract:

Recent experiments at JET studied the effect of density on the rotation of Ohmic divertor plasmas. As the density increased, two core rotation reversals were observed, showing two regimes of peaked co-current rotation. The experiment was done with hydrogen and deuterium plasmas, critical densities for reversal appear to be independent on isotope type.

Abstract:

The flow shear associated with the differential toroidal rotation of tokamak plasmas breaks an underlying symmetry of the turbulent fluctuations imposed by the up-down symmetry of the magnetic equilibrium. Using experimental Beam-Emission-Spectroscopy (BES) measurements and gyrokinetic simulations, this symmetry breaking in ion-scale turbulence in MAST is shown to manifest itself as a tilt of the spatial correlation function and a finite skew in the distribution of the fluctuating density field. The tilt is a statistical expression of the "shearing" of the turbulent structures by the mean flow. The skewness of the distribution is related to the emergence of long-lived density structures in sheared, near-marginal plasma turbulence. The extent to which these effects are pronounced is argued (with the aid of the simulations) to depend on the distance from the nonlinear stability threshold. Away from the threshold, the symmetry is effectively restored.