Recent work demonstrated that breaking the up-down symmetry of tokamak flux surfaces removes a constraint that limits intrinsic momentum transport, and hence toroidal rotation, to be small. We show, through MHD analysis, that ellipticity is most effective at introducing up-down asymmetry throughout the plasma. We detail an extension to GS2, a local $\delta f$ gyrokinetic code that self-consistently calculates momentum transport, to permit up-down asymmetric configurations. Tokamaks with tilted elliptical poloidal cross-sections were simulated to determine nonlinear momentum transport. The results, which are consistent with experiment in magnitude, suggest that a toroidal velocity gradient, $(\partial u_{ \zeta i} / \partial \rho) / v_{ th i}$, of 5% of the temperature gradient, $(\partial T_{ i} / \partial \rho) / T_{ i}$, is sustainable. Here $v_{ th i}$ is the ion thermal speed, $u_{ \zeta i}$ is the ion toroidal mean flow, $\rho$ is the minor radial coordinate normalized to the tokamak minor radius, and $T_{ i}$ is the ion temperature. Since other intrinsic momentum transport mechanisms scale poorly to larger machines, these results indicate that up-down asymmetry is the most feasible method to generate the current experimentally-measured rotation levels in reactor-sized devices.
Categories: physics.plasm-ph