Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

Abstract

The relation between magnetic geometry and the level of ion-temperature-gradient (ITG) driven turbulence in stellarators is explored through gyrokinetic theory and direct linear and nonlinear simulations. It is found that the ITG radial heat flux is sensitive to details of the magnetic configuration that can be understood in terms of the linear behavior of zonal flows. The results throw light on the question of how the optimization of neoclassical confinement is related to the reduction of turbulence.Understanding the turbulence present in tokamaks and stellarators is one of the most important challenges in plasma physics. A particularly interesting question in this context is how the magnetic geometry affects the nature and amplitude of the turbulence. In plasmas where the ion-temperature-gradient (ITG) instability is significant, so-called zonal flows (ZFs) have a favorable effect on the confinement [1]. However, the complexity introduced by nonaxisymmetry had rendered, only until very recently, the study of ZFs in stellarator configurations intractable. The dynamical character of the ZF response in a stellarator was first predicted analytically in Refs. [2,3] and was later confirmed by linear gyrokinetic simulations [4,5]. In a tokamak, the linear response to an imposed ZF perturbation consists of geodesic acoustic mode (GAM) oscillations followed by a steady state so-called Rosenbluth-Hinton (RH) residual level [6]. In stellarators, there is an intermediate stage of slow (compared with the GAM) damped ZF oscillations, and the RH residual level can be much lower than in tokamaks [3,5]. The details of this behavior depend on the magnetic configuration in question.Recent work [7] sought to reduce turbulence in stellarators by directly targeting the ITG instability. Complementing that study, here we investigate the role of ZF dynamics in regulating turbulent transport. As will become apparent, the situation is different from that in tokamaks, since the residual level is not always reached before turbulence saturates (see Figs. 4,6), and in these cases, the RH level alone cannot account for differences in the heat flux (as sometimes claimed in the tokamak literature, see e.g., Ref.[8]). Furthermore, we identify the geodesic curvature as an important ingredient affecting the ZF oscillations, viz., minimizing the geodesic curvature proves to have a significant favorable effect on the confinement. Finally, we revisit the relationship between neoclassical (nc) optimization and turbulence reduction. Although these two concepts turn out to be correlated (see also Refs. [4,9]), here we show that turbulence must be treated in addition to nc optimization. It should be remembered that turbulent transport is important in optimized stellarators, especially at low temperatures [10].As a preparatory step, to gain confidence in the numerical treatment, we present (the first published) linear and nonlinear benchmarks in stellarator geometry. Most of the presented simulations are performed with the GENE code (see, e.g., Refs. [11...

Zonal flows in stellarators in an ambient radial electric field

“…[8] and [13]). The zonal flow oscillations have been observed numerically both in global particle-in-cell (PIC) simulations using the EUTERPE code [13,14] and in flux-tube Eulerian simulations using the GENE code [13,15]. They appear to be more pronounced in optimised configuration such as the Wendelstein 7-X (W7-X) [16] whereas their damping is rather strong in a more "classical" heliotron (such as the LHD device).…”

Gyrokinetic turbulent transport simulation of a high ion temperature plasma in large helical device experiment

“…Plasmas 19, 042504 (2012) geometry on zonal flows and turbulence in helical systems. [24][25][26][27] Figure 5(a) shows the power spectra of the turbulent potential fluctuations in the k y space normalized by gyro-Bohm unit T i q ti =eR 0 , which are obtained by integrating the squared potential fluctuations over the k x space P k x hje/ k x ;k y R 0 =T i q ti j 2 i=Dk y , and taking the time averages in the saturated phases for three simulation runs at each radial position. In the plots, we also show the simulation result obtained by using the vacuum (or zero beta) magnetic field configuration at q ¼ 0:65, where the same simulation parameters of the experiment #88343 at q ¼ 0:65 are used except for the field configuration and the values of minimum wavenumbers ðDk x q ti ; Dk y q ti Þ ¼ ð0:126; 0:036Þ.…”

Experimental Evidence of Turbulent Transport Regulation by Zonal Flows

“…Due to the twodimensional nature of plasma turbulence in the plane perpendicular to the magnetic field of toroidally confined plasmas, the energetics obey an inverse cascade [2]. Consequently, the ZFs are supposed to gain energy from small-scale drift-wave turbulence by a self-organizing process which was described theoretically [3], observed in nonlinear turbulence simulations [4,5,6], and investigated experimentally in detail [7,8,9,10,11]. It was shown that the flux surface average of the radial derivative of the Reynolds stress ṽ rṽθ is the driving term for ZFs, and that the energy is transferred non-locally in k-space, i.e.…”