A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations

The linear response of a collisionless stellarator plasma to an applied radial electric field is calculated, both analytically and numerically. Unlike in a tokamak, the electric field and associated zonal flow develop oscillations before settling down to a stationary state, the so-called Rosenbluth-Hinton flow residual. These oscillations are caused by locally trapped particles with radially drifting bounce orbits. These particles also cause a kind of Landau damping of the oscillations that depends on the magnetic configuration. The relative importance of geodesic acoustic modes and zonal-flow oscillations therefore varies among different stellarators.

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“…The trapped particles provide the dominant contribution to the integral (12) in the definition of Λ 1 ,…”

Section: Late-time Behaviormentioning

confidence: 99%

“…GENE is an Eulerian code solving the gyrokinetic system of equations in either tokamak [11] or stellarator [12] geometry. It has recently been extended to cover the full minor radius in tokamak geometry, but the stellarator version operates in a flux tube with periodic boundary conditions.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Oscillations of zonal flows in stellarators

Helander¹,

Mishchenko²,

Kleiber³

et al. 2011

Plasma Phys. Control. Fusion

108

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“…Most of the presented simulations are performed with the GENE code (see, e.g., Refs. [11,12]), which solves the nonlinear, gyrokinetic system of equations in flux-tube geometry of an arbitrary toroidal configuration with closed flux surfaces. For the benchmarking, we compare GENE with the GKV code (see, e.g., Ref.…”

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confidence: 99%

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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“…For instance, if we consider a large-aspect-ratio axisymmetric toroidal plasma with circular cross section, in suitably normalized units, we have [24,25] …”

Section: Model Equationmentioning

confidence: 99%

Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

et al. 2016

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The effects of a non-axisymmetric (3D) equilibrium magnetic field on the linear ion-temperaturegradient (ITG) driven mode are investigated. We consider the strongly driven, toroidal branch of the instability in a global (on the magnetic surface) setting. Previous studies have focused on particular features of non-axisymmetric systems, such as strong local shear or magnetic ripple, that introduce inhomogeneity in the coordinate along the magnetic field. In contrast, here we include non-axisymmetry explicitly via the dependence of the magnetic drift on the field line label α, i.e. across the magnetic field, but within the magnetic flux surface. We consider the limit where this variation occurs on a scale much larger than that of the ITG mode, and also the case where these scales are similar. Close to axisymmetry, we find that an averaging effect of the magnetic drift on the flux surface causes global (on the surface) stabilization, as compared to the most unstable local mode. In the absence of scale separation, we find destabilization is also possible, but only if a particular resonance occurs between the magnetic drift and the mode, and finite Larmor radius effects are neglected. We discuss the relative importance of surface global effects and known radially global effects.

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A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations

Cited by 73 publications

References 17 publications

Oscillations of zonal flows in stellarators

Oscillations of zonal flows in stellarators

Zonal Flow Dynamics and Control of Turbulent Transport in Stellarators

Geometric stabilization of the electrostatic ion-temperature-gradient driven instability. I. Nearly axisymmetric systems

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