Intrinsic rotation driven by the radial variation of phase velocity and turbulence intensity in tokamaks

Tokamak plasmas can spontaneously develop differential toroidal rotation without external torque. This 'intrinsic rotation', which may be necessary for the success of future fusion devices, has proven difficult to model. This is partly due to the fact that for up-down symmetric plasmas with no equilibrium flow shear, symmetries of the lowest-order gyrokinetic equation prohibit the transport of toroidal angular momentum, and so intrinsic rotation depends on next-order terms in the gyrokinetic expansion that are typically not included in simulations. Terms dealing with system-scale radial variation are particularly problematic, as they necessitate a global approach. We present a study on intrinsic rotation due to radial variation of the equilibrium gradients and intensity of turbulent fluctuations using the recently developed global version of the gyrokinetic code stella, whose approach allows for precise control over the next-order corrections to the equilibrium kinetic and magnetic profiles. It is found that intrinsic rotation is insensitive to the radial profile variation of turbulent intensity; rather, profile variation of the phase velocity plays the dominant role in setting the transport of toroidal angular momentum. This mode of transport is shown to be analogous to that driven by equilibrium flow shear, biasing the radial wavenumber at the outboard midplane which, by acting with the radial magnetic drift, provides the required symmetry breaking for the net generation of intrinsic rotation.