Oscillations of zonal flows in stellarators

Helander, P.; Mishchenko, A.; Kleiber, R.; Xanthopoulos, P.

doi:10.1088/0741-3335/53/5/054006

Cited by 37 publications

(118 citation statements)

References 15 publications

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“…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].…”

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confidence: 78%

“…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.…”

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confidence: 99%

“…As we shall see, the situation is more complicated. To understand why, we first provide a brief analytical treatment that explains the existence of ZF oscillations in a generic stellarator configuration [5]. The linear gyrokinetic equation for the ZF component of the electrostatic potential with perpendicular wavevector k ⊥ = k r ∇r reads…”

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Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

et al. 2011

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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...

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Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

et al. 2011

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“…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.…”

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

et al. 2012

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Ion temperature gradient turbulent transport in the large helical device (LHD) is investigated by means of gyrokinetic simulations in comparison with the experimental density fluctuation measurements of ion-scale turbulence. The local gyrokinetic Vlasov simulations are carried out incorporating full geometrical effects of the LHD configuration, and reproduce the turbulent transport levels comparable to the experimental results. Reasonable agreements are also found in the poloidal wavenumber spectra of the density fluctuations obtained from the simulation and the experiment. Numerical analysis of the spectra of the turbulent potential fluctuations on the two-dimensional wavenumber space perpendicular to the magnetic field clarifies the spectral transfer into a high radial wavenumber region which correlates with the regulation of the turbulent transport due to the zonal flows. The resultant transport levels at different flux surfaces are expressed in terms of a simple linear relation between the transport coefficient and the ratio of the squared turbulent potential fluctuation to the averaged zonal flow amplitude. V C 2012 American Institute of Physics. [http://dx

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“…The question: to what extent different magnetic configurations can host zonal flow structures? has gathered some attention [4,5,6]. For non-symmetric systems, Sugama and Watanabe [4] found the suggestive result that neoclassical optimization could lead to reduced ZF damping and a turbulent transport optimization as a 'welcome side-effect'.…”

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confidence: 99%

Dynamics of zonal-flow-like structures in the edge of the TJ-II stellarator

Alonso

Velasco

Arévalo

et al. 2012

Plasma Phys. Control. Fusion

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Abstract. The dynamics of fluctuating electric field structures in the edge of the TJ-II stellarator, that display zonal flow-like traits, is studied. These structures have been shown to be global and affect particle transport dynamically [1]. In this article we discuss possible drive (Reynolds stress) and damping (Neoclassical viscosity, geodesic transfer) mechanisms for the associated E × B velocity. We show that: (a) while the observed turbulence-driven forces can provide the necessary perpendicular acceleration, a causal relation could not be firmly established, possibly because of the locality of the Reynolds stress measurements, (b) the calculated neoclassical viscosity and damping times are comparable to the observed zonal flow relaxation times, and (c) although an accompanying density modulation is observed to be associated to the zonal flow, it is not consistent with the excitation of pressure side-bands, like those present in geodesic acoustic oscillations, caused by the compression of the E × B flow field.

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Oscillations of zonal flows in stellarators

Cited by 37 publications

References 15 publications

Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

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

Dynamics of zonal-flow-like structures in the edge of the TJ-II stellarator

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