Strong-flow gyrokinetic simulations with a unified treatment of all length scales.

Tokamak turbulence exhibits interaction on all length scales, but standard gyrokinetic treatments consider global scale flows and gyroscale flows separately, and assume a separation between these length scales. However, the use of a small-vorticity ordering (Dimits, 2010) allows for the presence of large, time-varying flows on large length scales, whilst providing a unified treatment including shorter length scales near and below the gyroradius. We present the numerical implementation of these gyrokinetic equations, benchmarking of the resulting code, and differences in representation compared to the weak-flow theory.

Our Euler-Lagrange and Poisson equations contain an implicit dependence that appears as a partial time derivative of the E × B flow. This is analogous to the v_||-formulation of gyrokinetics. However, as these implicit terms are small, we use an iterative scheme to resolve this. Additionally, we have developed a stand-alone Poisson solver based on that from the ORB5 code, and use this to simulate certain flow and density gradient driven instabilities in cylindrical geometry.

We also explain the differences in representation of trajectories and distribution functions between the weak- and strong-flow theories.