Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator

Faber, B. J.; Pueschel, M. J.; Proll, J. H. E.; Xanthopoulos, P.; Terry, P. W.; Hegna, C. C.; Weir, G.; Likin, K. M.; Talmadge, J. N.

doi:10.1063/1.4926510

Cited by 36 publications

(82 citation statements)

References 54 publications

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“…A substantial benefit of this approach to low-magnetic-shear configurations is that the radial box size of the simulation is no longer determined by (A 7), which states L x ∝ (ŝk min y ) −1 . For HSX, using k min y = 0.1 yields L x ≈ 220ρ s , a value comparable with macroscopic equilibrium scale lengths (Faber et al 2015). Despite such large simulation domains, this is not physically problematic provided the turbulent correlation lengths are both smaller than experimental correlation lengths and the background length scales, such as L n,T .…”

Section: Zero-magnetic-shear Approximationmentioning

confidence: 96%

“…Calculations of linear eigenmodes are performed using the GENE code (Jenko et al 2000). GENE has previously been applied to examine drift waves and turbulence in a variety of stellarator configurations Merz 2008;Proll et al 2013;Faber et al 2015;Xanthopoulos et al 2016). The GIST package (Xanthopoulos et al 2009) is used to generate the necessary components for flux-tube simulations of the magnetic geometry along a field line from reconstructed equilibria.…”

Section: Linear Mode Calculationsmentioning

confidence: 99%

“…While there are distinct advantages to this approach, such as the elimination of destructive magnetohydrodynamic instabilities and the ability to manipulate the magnetic geometry to target specific physics issues, using three-dimensional (3-D) magnetic fields increases complexity in both theory and experiment (Gates et al 2018). Paralleling the rise of interest in stellarators, computing capabilities have reached a level enabling comprehensive simulations of computationally challenging problems in a stellarator geometry, such as modelling turbulence with gyrokinetic codes Baumgaertel et al 2011;Proll, Xanthopoulos & Helander 2013;Faber et al 2015;Xanthopoulos et al 2016). In this work, gyrokinetic simulations are employed to describe the microturbulence properties of stellarators in the limit of small averaged magnetic shear.…”

Section: Introductionmentioning

confidence: 99%

“…In the absence of large global magnetic shear, mode localization is determined by the interplay of local shear and curvature, which is non-trivial for stellarators. This can manifest with modes that extend far along field lines or balloon in locations other than the outboard midplane (Merz 2008;Faber et al 2015), adding significant complexity to the simulation and analysis of stellarator turbulence. Furthermore, the computational domain dimensions for flux tube simulations are inversely proportional to global magnetic shear, which can make flux-tube simulations for low-magnetic-shear stellarators comparatively expensive in the conventional formulation (Beer, Cowley & Hammett 1995).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, a gyrokinetic study of the low-magnetic-shear stellarator HSX demonstrates that properly resolving parallel correlation lengths with extended simulation domains is crucial for accurate theoretical predictions. Turbulence is studied in the 'bean' flux tube of the quasi-helically symmetric (QHS) configuration of HSX, used previously in Faber et al (2015) and shown for different geometry elements in figure 1. The rotational transform ι -for HSX is constrained such that ι axis ≈ 1.05 and ι edge ≈ 1.1 and at the half-radius in the toroidal flux coordinate Ψ /Ψ edge = 0.5, where ψ edge is the toroidal flux at the last closed flux surface.…”

Section: Introductionmentioning

confidence: 99%

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Stellarator microinstabilities and turbulence at low magnetic shear

et al. 2018

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Gyrokinetic simulations of drift waves in low-magnetic-shear stellarators reveal that simulation domains comprised of multiple turns can be required to properly resolve critical mode structures important in saturation dynamics. Marginally stable eigenmodes important in saturation of ion temperature gradient modes and trapped electron modes in the Helically Symmetric Experiment (HSX) stellarator are observed to have two scales, with the envelope scale determined by the properties of the local magnetic shear and an inner scale determined by the interplay between the local shear and magnetic field-line curvature. Properly resolving these modes removes spurious growth rates that arise for extended modes in zero-magnetic-shear approximations, enabling use of a zero-magnetic-shear technique with smaller simulation domains and attendant cost savings. Analysis of subdominant modes in trapped electron mode (TEM)-driven turbulence reveals that the extended marginally stable modes play an important role in the nonlinear dynamics, and suggests that the properties induced by low magnetic shear may be exploited to provide another route for turbulence saturation.

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Section: Zero-magnetic-shear Approximationmentioning

confidence: 96%

Section: Linear Mode Calculationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stellarator microinstabilities and turbulence at low magnetic shear

et al. 2018

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Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

et al. 2018

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The threshold for the resonant destabilisation of ion-temperature-gradient (ITG) driven instabilities that render the modes ubiquitous in both tokamaks and stellarators is investigated. We discover remarkably similar results for both confinement concepts if care is taken in the analysis of the effect of the global shearŝ. We revisit, analytically and by means of gyrokinetic simulations, accepted tokamak results and discover inadequacies of some aspects of their theoretical interpretation. In particular, for standard tokamak configurations, we find that global shear effects on the critical gradient cannot be attributed to the wave-particle resonance destabilising mechanism of Hahm & Tang (Phys. Plasmas, vol. 1, 1989, pp. 1185-1192, but are consistent with a stabilising contribution predicted by Biglari et al. (Phys. Plasmas, vol. 1, 1989, pp. 109-118). Extensive analytical and numerical investigations show that virtually no previous tokamak theoretical predictions capture the temperature dependence of the mode frequency at marginality, thus leading to incorrect instability thresholds. In the asymptotic limitŝι 1, where ι is the rotational transform, and such a threshold should be solely determined by the resonant toroidal branch of the ITG mode, we discover a family of unstable solutions below the previously known threshold of instability. This is true for a tokamak case described by a localŝ − α local equilibrium, and for the stellarator Wendelstein 7-X, where these unstable solutions are present even for configurations with a small trapped-particle population. We conjecture they are of the Floquet type and derive their properties from the Fourier analysis of toroidal drift modes of Connor & Taylor (Phys. Fluids, vol. 30, 1987, pp. 3180-3185), and to Hill's theory of the motion of the lunar perigee (Acta Math., vol. 8, 1886, pp. 1-36). The temperature dependence of the newly determined threshold is given for both confinement concepts. In the first case, the new temperature-gradient threshold is found to be rather insensitive to the temperature ratio T i /T e , at least for T i /T e 1, and to be a growing function of the density gradient scale for T i /T e 1. For Wendelstein 7-X, the new critical temperature gradient is a growing function of the temperature ratio. The importance of these findings for the assessment of turbulence in stellarators and low-shear tokamak configurations is discussed.

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Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

2018

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Kinetic ballooning modes in magnetically confined toroidal plasmas are investigated putting emphasis on specific stellarator features. In particular, we propose a Mercier criterion which is purposely designed to allow for direct comparison with local flux-tube gyrokinetics simulations. We investigate the influence on the marginal frequency of the mode of a magnetic curvature which is inhomogeneous on the magnetic flux surface due to the fieldline-label dependence. This is a typical (surface) global effect present in non-axisymmetry. Finally, we propose an artificial equilibrium model that explicitly retains the fieldline-label dependence in the magnetic drift, and analyse the stability of the system by introducing a representation of the perturbations similar to the flux-bundle model of Sugama et al. (Plasma Fusion Res., vol. 7, 2012, 2403094). The coupling of flux bundles is shown to have a stabilising effect on the most unstable local flux-tube mode.

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Gyrokinetic studies of trapped electron mode turbulence in the Helically Symmetric eXperiment stellarator

Cited by 36 publications

References 54 publications

Stellarator microinstabilities and turbulence at low magnetic shear

Stellarator microinstabilities and turbulence at low magnetic shear

Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas

Strongly driven surface-global kinetic ballooning modes in general toroidal geometry

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