Short wavelength effects on the collisionless neoclassical polarization and residual zonal flow level

Sheared zonal flow helps to reduce the turbulent transport caused by the ion temperature gradient mode. Rosenbluth and Hinton (R-H) calculated the residual zonal flow level for radial wavelengths that are much larger than the ion poloidal gyroradius. Their calculation is extended to treat arbitrary radial wavelengths. For the radial wavelengths that approach the ion poloidal gyroradius, but are much larger than the ion gyroradius, an analytical formula is obtained. For radial wavelengths that are comparable or shorter than the poloidal ion gyroradius and the ion gyroradius a numerical solution is provided. These small radial wavelength results are then extended into the electron temperature gradient regime, where the residual zonal flow level is large but ineffective in regulating the turbulence, indicating that the conventional R-H explanation that zonal flow regulates turbulence is incomplete.