Collisionless kinetic-fluid closure and its application to the three-mode ion temperature gradient driven system

A novel closure model is presented to give a set of fluid equations which describe a collisionless kinetic system. In order to take account of the time reversal symmetry of the collisionless kinetic equation, the new closure model relates the parallel heat flux to the temperature and the parallel flow in terms of the real-valued coefficients in the unstable wave number space. Effects of the closure model on turbulence saturation and anomalous transport are investigated based on kinetic and fluid entropy balances. When the closure model is applied to the three-mode ion temperature gradient (ITG) driven system, the fluid system of equations reproduces the exact nonlinear kinetic solution found by Watanabe, Sugama, and Sato [Phys. Plasmas 7, 984 (2000)]. Oscillatory behaviors and initial amplitude dependence of other numerical kinetic solutions of the three-mode ITG problem can also be accurately described by the fluid system.