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 Er to boost the poloidal rotation, enhanced zonal-flow responses are obtained. Under the identical conditions on the magnitude of Er 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.