Transport of Parallel Momentum Induced by Current-Symmetry Breaking in Toroidal Plasmas

The symmetry of a physical system strongly impacts on its properties. In toroidal plasmas, the symmetry along a magnetic field line usually constrains the radial flux of parallel momentum to zero in the absence of background flows. By breaking the up-down symmetry of the toroidal currents, this constraint can be relaxed. The parallel asymmetry in the magnetic configuration then leads to an incomplete cancellation of the turbulent momentum flux across a flux surface. The magnitude of the subsequent toroidal rotation increases with the up-down asymmetry and its sign depends on the direction of the toroidal magnetic field and plasma current. Such a mechanism offers new insights in the interpretation and control of the intrinsic toroidal rotation in present day experiments.

Figure 1

Parallel structure of the electrostatic potential $\varphi$ and of the parallel velocity moment $w$ of the perturbed distribution function for an up-down symmetric (thin blue) and an up-down asymmetric (thick red) flux surface. The real and imaginary part are plotted in full and dashed lines, respectively. The parallel coordinate $s$ is zero at the LFS midplane (on the right of the flux surface) and increases anticlockwise.

Figure 2

Variation of the perpendicular component of the curvature and $\nabla B$ drifts ${\mathcal{D}}^{\zeta }$ (left plot) and of the metric tensor element $g^{\zeta \zeta }$ (right plot) as a function of the parallel coordinate $s$ for the two cases shown in Fig. 1 (same line coding).

Figure 3

Left: variation of $C_{\varphi }/{\chi }_{\varphi }$ as a function of the LFS wave vector $k_{\theta }{\rho }_i$ (growth rate variation in the insert) for $k_r{\rho }_i=0$ (full line) and $k_r{\rho }_i=0.02$ (dashed line). Right: dependence of $C_{\varphi }/{\chi }_{\varphi }$ on $R/L_{\mathrm{Te}}$. The filled and open symbols represent a perturbation propagating in the ion and electron diamagnetic drift direction, respectively.

Figure 4

Right (color plot): radial variation of $C_{\varphi }/{\chi }_{\varphi }$. The dashed lines indicate the flux surfaces labeled by $r/r_{\max }=0.1$ to 0.9, with steps of 0.1. Top left: safety factor profile corresponding to the equilibrium shown on the right. Bottom left: impact of the direction of the magnetic field $B$ and plasma current $I_p$ on $C_{\varphi }/{\chi }_{\varphi }$. Positive values indicate a radial outward flux of momentum in the direction of $B$.