Excitation of zonal flows and fluid closure

J. Weiland1), S. Dastgeer2), R. Moestam1), I. Holod1), S. Gupta 3)

1) Chalmers University of Technology, EURATOM-VR Association, Gothenburg, S-41296, Sweden.
2) University of California, Riverside, CA 92521, USA
3) University of Wisconsin, Madison, WI 53706, USA

The excitation of zonal flows by ion temperature gradient driven modes is studied by numerical and analytical methods using a reactive advanced fluid model. It is shown analytically that the dominant nonlinearity is the convection in the energy equation. The excitation of zonal flows is particularly strong just above linear marginal stability leading to a nonlinear upshift in the critical gradient for steady transport. Turbulence simulations confirm the overall expectations and a nonlinear upshift in agreement with Dimits nonlinear particle simulations(1) is obtained(2). The strong excitation of zonal flows just above marginal linear stability is due to the fluid resonance in the energy equation. This is exactly where the fluid closure is made so the excitation of zonal flows depends sensitively on this closure. This has been analyzed in more detail by adding a gyro-fluid resonance to the reactive fluid model(3) and using a resonant ordering in Taniutis Reductive perturbation method. A detuning of the resonance was found. This is in agreement with the smaller nonlinear upshift obtained by the IFS-PPPL model in the Cyclone work(1). Further support for the importance of the resonance for the nonlinear upshift comes from the fact that this is the regime which was most sensitive to the convergence with respect to number of particles in the kinetic Cyclone simulations(1). For convergence, a sufficient number of particles in the resonant regions of phase space is required. Thus the conclusion is that the nonlinear upshift, due to zonal flows, is particularly sensitive to the kinetic resonance. This makes the nonlinear upshift dynamics particularly sensitive to the fluid closure and it is rather remarkable that fluid models at all are able to deal with this dynamics. The general effects of closure and diffusion on a simple three-wave system has also recently been studied(4). Parallels between the systems can be drawn.

References

1. A Dimits, G. Bateman, M.A. Beer et.al. Comparisons and Physics Basis of Tokamak Transport Models and Turbulence Simulations, Phys. Plasmas 7, 969 (2000).
2. Sheik Dastgeer, Sangeeta Mahajan and Jan Weiland, Zonal flows and transport in ion temperature gradient turbulence, Phys. Plasmas 9, 4911 (2002).
3. Robert. Moestam, Dastgeer Sheik and Jan Weiland, Self consistent theory of zonal flows in ion temperature gradient turbulence. Paper 1E46, 2003 International Sherwood Fusion Theory Meeting, April 12-23, Corpus Cristi, Texas.
4. I. Holod, J. Weiland and A. Zagorodny, Nonlinear fluid closure: Three-mode slab ion temperature gradient problem with diffusion, Physics of Plasmas 9, 1217 (2002).