@techreport{oai:nifs-repository.repo.nii.ac.jp:00010255,
 author = {"Sugama,  H. and Watanabe,  T.-H. and Horton,  W."},
 month = {Dec},
 note = {"A novel kinetic-fluid model is presented, which describes collisionless time evolution of zonal flows in tokamaks. In the new zonal-flow closure relations, the parallel heat fluxes are written by the sum of short- and long-time-evolution parts. The former part is given in the dissipative form of the parallel heat diffusion and relates to collisionless damping processes. The latter is derived from the long-time-averaged gyrocenter distribution and plays a major role in describing low-frequency or stationary zonal flows, for which the parallel heat fluxes are expressed in terms of the parallel flow as well as the nonlinear-source and initial-condition terms. It is shown analytically and numerically that, when applied to the zonal flow driven by either ion or electron temperature gradient turbulence, the kinetic-fluid equations including the new closure relations can reproduce the same long-time zonal-flow responses to the initial condition and to the turbulence source as those obtained from the gyrokinetic model."},
 title = {Collisionless Kinetic-fluid Model of Zonal Flows in Toroidal Plasmas},
 year = {2006}
}