Nonlinear fluid closure: Three-mode slab ion temperature gradient problem with diffusion

The three-mode slab ion temperature gradient problem was considered. Starting from the drift kinetic equation with nonlinear term and diffusion, the hierarchy of fluid equations up to fourth moment was developed. As a closure, the nonlinear fluid closure by N. Mattor and S. Parker [Phys. Rev. Lett. 79, 3419 (1997)] was applied. Numerical solutions of the system of fluid equations have been obtained and analyzed. The time evolution of electrostatic potential shows that nonlinear fluid closure is able to capture particle trapping, which is important for fusion plasmas. Great attention was paid to studies of the role of diffusion. Diffusion here represents effects of background turbulence and can be described by a Fokker–Planck operator [A. Zagorodny and J. Weiland, Phys. Plasmas 6, 2359 (1999)]. The three wave system can be considered as a system of test waves in a turbulent background. This system can be used to study situations of varying partial coherence.