Turbulence-driven zonal flows in helical systems with radial electric fields

Collisionless long-time responses of the zonal-flow potential to the initial condition and turbulence source in helical systems having radial electric fields are derived theoretically. All classes of particles in passing, toroidally trapped, and helical-ripple-trapped states are considered. The transitions between the toroidally trapped and helical-ripple-trapped states are taken into account while solving the gyrokinetic equation analytically by taking its average along the particle orbits. When the radial displacements of helical-ripple-trapped particles are reduced either by neoclassical optimization of the helical geometry lowering the radial drift or by strengthening the radial electric field E-r to boost the poloidal rotation, enhanced zonal-flow responses are obtained. Under the identical conditions on the magnitude of E-r and the magnetic geometry, using ions with a heavier mass gives rise to a higher zonal-flow response, and therefore the turbulent transport is expected to show a more favorable ion-mass dependence than the conventional gyro-Bohm scaling.