Three-dimensional inhomogeneity of electron-temperature-gradient turbulence in the edge of tokamak plasmas

Parisi, Jason; Parra, Felix; Roach, C. M.; Hardman, Michael; Schekochihin, A. A.; Abel, Ian; Aiba, N.; Ball, Justin; Barnes, Michael; Chapman-Oplopoiou, B.; Dickinson, David; Dorland, W.; Giroud, C.; Hatch, D. R.; Hillesheim, J. C.; Ruiz, J. Ruiz; Saarelma, S.; St-Onge, Denis A.; Contributors, Jet

doi:10.1088/1741-4326/ac786b

Cited by 14 publications

(16 citation statements)

References 120 publications

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“…2022, 2023; Parisi et al. 2022). Whether our results are robust to the effects of significant magnetic shear and other forms of equilibrium shaping that can amplify the importance of FLR – and thus undermine the possible separation between FLR effects and a putative outer scale – is a subject for future work.…”

Section: Summary and Discussionmentioning

confidence: 98%

“…Apart from some interesting exceptions (Parisi et al. 2020, 2022), the general effect of these Bessel functions is to provide a cutoff for instabilities at large perpendicular wavenumbers, restricting the region of instability on the ultraviolet side and providing a sink of energy (dissipation) beyond the wavenumbers where the sETG growth rate peaks. The constant-flux arguments of § 5 assumed that there was sufficient separation between the outer scale and these dissipation regions in order to allow an inertial range to develop at the intermediate scales.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…edge plasmas (Parisi et al. 2020, 2022) or in stellarators (Roberg-Clark, Plunk & Xanthopoulos 2022), where magnetic fields have parallel structure on scales shorter than the connection length.…”

Section: Inertial-range Dynamicsmentioning

confidence: 99%

“…2022; Parisi et al. 2022; Field et al. 2023), the saturation of such turbulence remains significantly less well-understood than its ITG cousin.…”

Section: Introductionmentioning

confidence: 99%

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Scale invariance and critical balance in electrostatic drift-kinetic turbulence

2023

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The equations of electrostatic drift kinetics are observed to possess a symmetry associated with their intrinsic scale invariance. Under the assumptions of spatial periodicity, stationarity, and locality, this symmetry implies a particular scaling of the turbulent heat flux with the system's parallel size, from which its scaling with the equilibrium temperature gradient can be deduced under some additional assumptions. This macroscopic transport prediction is then confirmed numerically for a reduced model of electron-temperature-gradient-driven turbulence in slab geometry. The system realises this scaling through a turbulent cascade from large to small perpendicular spatial scales. The route of this cascade through wavenumber space (i.e. the relationship between parallel and perpendicular scales in the inertial range) is shown to be determined by a balance between nonlinear-decorrelation and parallel-dissipation timescales. This type of ‘critically balanced’ cascade, which maintains a constant energy flux despite the presence of parallel dissipation throughout the inertial range (as well as order-unity dissipative losses at the outer scale) is expected to be a generic feature of plasma turbulence. The outer scale of the turbulence, on which the turbulent heat flux depends, is determined by the breaking of drift-kinetic scale invariance due to the existence of large-scale parallel inhomogeneity (the parallel system size).

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Section: Summary and Discussionmentioning

confidence: 98%

Section: Summary and Discussionmentioning

confidence: 99%

Section: Inertial-range Dynamicsmentioning

confidence: 99%

“…2022; Parisi et al. 2022; Field et al. 2023), the saturation of such turbulence remains significantly less well-understood than its ITG cousin.…”

Section: Introductionmentioning

confidence: 99%

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Scale invariance and critical balance in electrostatic drift-kinetic turbulence

2023

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“…2002; Parisi et al. 2020, 2022, and references therein). Thankfully, however, it can be relaxed if one is willing to pay the price of complicated analytical expressions.…”

Section: From Drift Kinetics To Gyrokineticsmentioning

confidence: 99%

An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field

Ivanov

Adkins

2023

J. Plasma Phys.

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Starting from the equations of collisionless linear gyrokinetics for magnetised plasmas with an imposed inhomogeneous magnetic field, we present the first known analytical, closed-form solution for the resulting velocity-space integrals in the presence of resonances due to both parallel streaming and constant magnetic drifts. These integrals are written in terms of the well-known plasma dispersion function (Faddeeva & Terent'ev, Tables of Values of the Function $w(z)=\exp (-z^2)(1+2i/\sqrt {\pi }\int _0^z \exp (t^2) \,\mathrm {d} t)$ for Complex Argument, 1954. Gostekhizdat. English translation: Pergamon Press, 1961; Fried & Conte, The Plasma Dispersion Function, 1961. Academic Press), rendering the subsequent expressions simpler to treat analytically and more efficient to compute numerically. We demonstrate that our results converge to the well-known ones in the straight-magnetic-field and two-dimensional limits, and show good agreement with the numerical solver by Gürcan (J. Comput. Phys., vol. 269, 2014, p. 156). By way of example, we calculate the exact dispersion relation for a simple electrostatic, ion-temperature-gradient-driven instability, and compare it with approximate kinetic and fluid models.

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Complex structure of turbulence across the ASDEX Upgrade pedestal

Leppin,

Görler,

Cavedon

et al. 2023

J. Plasma Phys.

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The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to the pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma $\beta$ values. The turbulent transport is found to exhibit a multi-channel, multi-scale character throughout the pedestal with the dominant contribution transitioning from ion-scale trapped electron modes/micro-tearing modes at the pedestal top to electron-scale electron temperature gradient modes in the steep gradient region. Consequently, the turbulent electron heat flux changes from ion to electron scales and the ion heat flux reduces to almost neoclassic values in the pedestal centre. $E\times B$ shear is found to strongly reduce heat flux levels in all channels (electron, ion, electrostatic, electromagnetic) and the interplay of magnetic shear and pressure gradient is found to locally stabilise ion-scale instabilities.

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Three-dimensional inhomogeneity of electron-temperature-gradient turbulence in the edge of tokamak plasmas

Cited by 14 publications

References 120 publications

Scale invariance and critical balance in electrostatic drift-kinetic turbulence

Scale invariance and critical balance in electrostatic drift-kinetic turbulence

An analytical form of the dispersion function for local linear gyrokinetics in a curved magnetic field

Complex structure of turbulence across the ASDEX Upgrade pedestal

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