Zonal flows in toroidal systems

An analytic study of the shielding and time evolution of zonal flows in tokamaks and stellarators is presented, using the action-angle formalism. This framework permits one to solve the kinetic equation without expansion of that equation in small parameters of radial excursions and time scales, resulting in more general expressions for the dielectric shielding, and with a scaling extended from that in earlier work. From these expressions, it is found that for each mechanism of collisional transport, there is a corresponding shielding mechanism, of closely related form and scaling. The effect of these generalized expressions on the evolution and size of zonal flows, and their implications for stellarator design are considered.