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