Three-dimensional Turbulence Simulation of Edge Transport and Impact of Plasma Rotation Satoru SUGITA 1;2 , Peter BEYER 2;3 , Guillaume FUHR 2;3 , Sadruddin BENKADDA 2;3 , Xavier GARBET 4 , Masatoshi YAGI 2;5;6 , Sanae-I. ITOH 1;2;6 , and Kimitaka ITOH 2;6;7 1 Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka 816-8580, Japan 2 France–Japan Magnetic Fusion Laboratory, LIA 336 CNRS, Aix-Marseille Universite ´-CNRS, F-13397 Marseille, France 3 International Institute for Fusion Science, LIA 336 CNRS, Aix-Marseille Universite ´-CNRS, F-13397 Marseille, France 4 CEA, IRFM, F-13108 Saint Paul Lez Durance, France 5 Japan Atomic Energy Agency, Rokkasho, Aomori 039-3212, Japan 6 Itoh Research Center for Plasma Turbulence, Kyushu University, Kasuga, Fukuoka 816-8580, Japan 7 National Institute for Fusion Science, Toki, Gifu 509-5292, Japan (Received May 30, 2011; accepted January 10, 2012; published online March 1, 2012) Global simulations of edge plasma turbulence are studied. The gradient-flux relation is fitted to a model with two parameters: stiffness and intercept. The slope of the grad-p vs flux curve is clearly lower in the case of spontaneous rotation than in the case of artificially suppressed rotation. The causes of this difference are studied by imposing a specified velocity shear. The slopes are similar between cases of controlled rotation with different amplitudes. That is, the stiffness does not change significantly, while the intercept changes. Therefore, the change in the slope observed in the case of spontaneous rotation has to be attributed to the fact that the velocity shear amplitude itself is increasing with the pressure source. The increase in the velocity shear is conjectured to cause a change in the intercept in the case of spontaneous rotation, but not a change in the stiffness. KEYWORDS: edge turbulence, resistive ballooning mode, profile stiffness, poloidal rotation 1. Introduction One remarkable progresses in the area of physics of magnetized plasmas is that the physics picture for multiple- scale turbulence has been established. 1,2) That is, turbulence and turbulent transport are governed not only by local microscopic fluctuations, but also by meso-scale and macro- scale perturbations. New views of turbulence have been developed 1) theoretically 3,4) and experimentally. 5,6) Theories have shown that fluctuations with long radial correlations can affect transient transport. 1) Recent experiments at JET have shown that driving a large-scale rotation of plasma improves confinement. In particular, the so-called stiffness level of the ion temperature profile is found to decrease with plasma rotation. 7) [The ‘‘stiffness’’ s is introduced by the relation Q / s rT ðrT rT crit Þ, where Q indicates the energy flux, rT the ion temperature gradient, and rT crit the threshold of the temperature gradient.] The stiffness level characterizes the fact that, above a critical value of the ion temperature inverse gradient length (R=L T i ¼ RjrT i j=T i , where R indicates the tokamak major radius), the ion heat flux increases strongly with R=L T i . This behavior is attributed to turbulent transport. 8–10) Observations have been made in the core, 7) but the ingredients for investigating this problem are included in all turbulence and rotation simulations. As a step in understanding the problem of ‘‘stiffness’’ in the transport relation, a fluid edge turbulence code is applied here. The role of E B flow shear stabilization 11,12) has been investigated in nonlinear gyro-kinetic and fluid simulations with background flow 13–17) for the core turbulence. In this work, we report on 3D turbulent simulations for edge plasma using a flux-driven configuration (i.e., with self-consistent profile evolution under the prescribed heat source at an edge), revealing the behavior of the mean pressure gradient as a function of the heat flux at the radial center. Different scenarios with respect to plasma rotation (spontaneous rotation, artificially suppressed rotation or controlled rota- tion) are studied. 18) 2. Model 2.1 Model equation The two-field reduced-resistive ballooning mode (re- duced-RBM) equations are solved to reproduce the plasma edge turbulence in the tokamak geometry. 19–24) The follow- ing equations are employed for the normalized electrostatic potential and the pressure p: @ @t r 2 ? þ½; r 2 ? ¼ r 2 k Gp þ r 4 ? þ ^ control r 2 ? ð imp 0;0 Þ; ð1Þ @p @t þ½; p¼ c G þ k r 2 k p þ ? r 2 ? p þ SðrÞ: ð2Þ The notations and symbols are explained as follows. r k ¼ @=@z þð=qÞ@=@y with ¼ðL s r 0 Þ=ðR 0 bal Þ is the gradient parallel to the field line, and r 2 ? ¼ @ 2 =@x 2 þ @ 2 =@y 2 is the gradient perpendicular to the to the field line, where qðrÞ is the safety factor, L s is the magnetic shear length, r 0 is the minor radius of the reference surface, R 0 is the major radius at the reference surface, and bal is the scale length of the resistive ballooning mode, which is described as follows. ½ f;g¼ð@f =@xÞð@g=@yÞð@f =@yÞð@g=@xÞ is the Poisson bracket. The curvature operator G ¼ sin ð@=@xÞþ cos ð@=@yÞ is introduced. indicates the collisional ion viscosity, and k and ? are parallel and perpendicular collisional heat diffusivities. imp ðrÞ indicates the artificially imposed E B velocity shear to the 0;0 component, where the subscript 0; 0 indicates the ðm; nÞ¼ð0; 0Þ Fourier E-mail: satoru@riam.kyushu-u.ac.jp Journal of the Physical Society of Japan 81 (2012) 034502 034502-1 FULL PAPERS #2012 The Physical Society of Japan DOI: 10.1143/JPSJ.81.034502