Intrinsic momentum transport in up-down asymmetric tokamaks

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, $(\mathrm{\partial }{u}_{\zeta i}\mathrm{/}\mathrm{\partial }\rho )\mathrm{/}{v}_{thi}$, of 5% of the temperature gradient, $(\mathrm{\partial }{T}_i\mathrm{/}\mathrm{\partial }\rho )\mathrm{/}{T}_i$, is sustainable. Here $v_{thi}$ 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.