PSFC/JA-06-23 Collisional zonal flow damping for ITG modes

Zonal ‡ow helps reduce and control the level of ion temperature gradient (ITG) turbulence in a tokamak. The collisional damping of zonal ‡ow has been estimated by Hinton and Rosenbluth (H-R). Their calculation shows that the damping of zonal ‡ow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, H-R calculated the neoclassical polarization in the low and high collisionality limits. A new approach, based on an eigenfunction expansion of the collision operator, is employed to evaluate the neoclassical polarization and the zonal ‡ow residual for arbitrary collisionality. An analytical expression for the temporal behavior of the zonal ‡ow is also given showing that the damping rate tends to be somewhat slower than previously thought. These results are expected to be useful extensions of the original H-R collisional work that can provide an e¤ective benchmark for numerical codes for all regimes of collisionality.