Critical gradient optimization for quasi-isodynamic stellarators

G. G. Plunk; G. T. Roberg-Clark; P. Xanthopoulos; S. Stroteich

arxiv: 2506.22166 · v2 · submitted 2025-06-27 · ⚛️ physics.plasm-ph

Critical gradient optimization for quasi-isodynamic stellarators

G. T. Roberg-Clark , P. Xanthopoulos , G. G. Plunk , S. Stroteich This is my paper

Pith reviewed 2026-05-19 08:23 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph

keywords quasi-isodynamic stellaratorsITG turbulencecritical gradientinverse mirrorstellarator optimizationturbulent transportplasma confinement

0 comments

The pith

Optimizing quasi-isodynamic stellarators for higher ITG critical gradients produces an inverse mirror configuration with heat fluxes at or below W7-X levels for a range of density gradients.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper updates the model for the critical gradient of localized toroidal ITG modes in quasi-isodynamic stellarators. It argues that allowing these modes to split and localize in separate curvature drift wells raises the stability threshold. This leads to a six-field-period configuration where an inverse mirror magnetic structure reduces the destabilizing role of kinetic electrons. A general optimization target for stability above the critical gradient then yields the inverse mirror setup. The resulting device shows heat fluxes that stay below or equal to the W7-X high mirror case across tested density gradients.

Core claim

By refining the critical gradient threshold for ITG modes and designing for their split localization across curvature wells, the authors obtain a six-field-period quasi-isodynamic stellarator whose inverse mirror field structure minimizes kinetic electron destabilization. General optimization for improved stability above this threshold produces heat fluxes that remain below or equal to those of the W7-X high mirror configuration over a range of applied density gradients.

What carries the argument

Inverse mirror magnetic field structure, which enables ITG modes to split into separate curvature wells and thereby raises the critical gradient while limiting kinetic electron effects.

If this is right

Raising the ITG critical gradient through mode splitting reduces turbulent transport in quasi-isodynamic stellarators.
The inverse mirror configuration achieves heat fluxes at or below W7-X high mirror performance for multiple density gradients.
Optimization can target critical gradient stability directly rather than relying solely on quasisymmetry properties.
Six-field-period QI geometries provide a concrete route for implementing these stability gains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This design strategy could support steeper temperature gradients in future stellarator reactors without driving excessive transport.
The same optimization logic might extend to other drift-wave instabilities to improve overall confinement.
Mode localization control via magnetic wells offers a broader principle for turbulence mitigation in toroidal devices.
Experimental tests would require comparing actual transport measurements against the predicted heat flux reductions at relevant parameters.

Load-bearing premise

The destabilizing effect of kinetic electrons on localized ITG modes can be minimized through an inverse mirror magnetic field structure derived from the updated critical gradient model for modes that split across curvature wells.

What would settle it

Gyrokinetic simulations of the optimized inverse mirror configuration that show heat fluxes exceeding the W7-X high mirror values at the same density gradients would falsify the performance claim.

Figures

Figures reproduced from arXiv: 2506.22166 by G. G. Plunk, G. T. Roberg-Clark, P. Xanthopoulos, S. Stroteich.

**Figure 1.** Figure 1: Left: Simplified toy model geometry for the drift curvature Kd and squared gradient of the binormal coordinate (g αα = |∇α| 2 ) depicted along a magnetic field line (ℓ coordinate), with split drift curvature wells and secularly increasing g αα. A QI stellarator, or reverse triangularity tokamak with large magnetic shear and flat surfaces near the outboard midplane could qualitatively achieve such geometry … view at source ↗

**Figure 2.** Figure 2: Splitting ITG modes – Idealized field line geometry metrics at the typically most unstable location on the outboard midplane of a QI magnetic field configuration.(a) No attempt is made to split the mode geometrically across the standard gap at ℓ = 0. Thus the mode can average the drift curvature across the gap. We surmise that (a/Reff )CG will be similar to a case with no gap. The mode freely “tunnels” acr… view at source ↗

**Figure 3.** Figure 3: The IM configuration with a/LT ,crit = 2.09. Left: boundary surface with magnetic field strength in color. Center: Magnetic field line contours and field strength at r = 0.5a. Right: cross section with several surfaces plotted at zero toroidal VMEC angle, at or near the maximum field strength. Note the higher compression of the surfaces on the outboard where the curvature drive is minimal. Qi/QGB IM (a/LT,… view at source ↗

**Figure 4.** Figure 4: Nonlinear heat flux calculations with adiabatic electrons for the three configurations discussed in the paper, scanning in temperature gradient a/LT at r/a = 0.5. A naive extrapolation from the two points at a/LT = (2.5, 3.0) down to Q = 0 yields CGs which are in the neighborhood of the model predictions from Eqn. (2.7). Notice that the IM configuration has a more pronounced “foot” (Zocco et al. 2018) belo… view at source ↗

**Figure 5.** Figure 5: Profiles for the three configurations discussed in the paper at 2% β. Left: Rotational transform as a function of the radial coordinate s = (r/a) 2 . Top right: Magnetic well (V is the volume enclosed by a flux surface) as a function of s. Bottom left: Neoclassical transport coefficient ϵeff (Nemov et al. 1999) as a function of s. Bottom right: Geodesic curvature κgeoa = a(B × ∇B) · ∇ψ/(B 2 |∇ψ|) at the su… view at source ↗

**Figure 6.** Figure 6: Geometric quantities entering the gyrokinetic equation for the three configurations, for a flux tube centered at the outboard midplane, including drift curvature, normalized magnetic field strength, and ∇α. Top Left: For W7-X HM, the metrics somewhat resemble those of a quasisymmetric stellarator near the outboard midplane (no curvature gap at ℓ = 0). Top Right: The same but for the QICG configuration with… view at source ↗

**Figure 7.** Figure 7: Nonlinear flux tube ITG simulations with kinetic electrons, a fixed temperature gradient a/LT = a/LT ,i = a/LT ,e = 3 and variable density gradient a/Ln for both species at half radius at the most unstable location. The heat flux for the IM case remains below or comparable to that of the W7-X high mirror configuration up to a/Ln = 2. particular, the positive shear seems to be helpful for the mode inertia e… view at source ↗

read the original abstract

We present new and updated methods for reducing transport caused by electrostatic ion temperature gradient (ITG) driven turbulence in quasi-isodynamic (QI) configurations. We first show an updated model for the threshold (critical) gradient of localized toroidal ITG modes. It is then argued that it is desirable for ITG modes to "split" and localize in separate curvature drift wells, which is leveraged to produce a six-field-period QI configuration with a high critical gradient. We show that the destabilizing effect of kinetic electrons (Costello & Plunk 2025a) on localized ITG modes can be minimized in a magnetic field structure, which we dub "inverse mirror". Applying a general optimization target that improves ITG stability above the critical gradient yields an inverse mirror configuration, which produces heat fluxes below or equal to the W7-X high mirror configuration for a range of applied density gradients.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper introduces an inverse mirror QI configuration that splits ITG modes to raise the critical gradient and produces nonlinear heat fluxes at or below W7-X levels.

read the letter

This paper's main advance is the inverse mirror magnetic structure for quasi-isodynamic stellarators. They update the critical gradient model for localized ITG modes, argue that splitting modes across separate curvature wells is useful, and optimize to produce a six-field-period QI configuration. The nonlinear simulations then show heat fluxes that stay at or below the W7-X high-mirror reference across a range of density gradients, while also reducing the destabilizing role of kinetic electrons on those split modes. The work takes an existing optimization framework and applies it to a concrete target with measurable outputs rather than stopping at linear theory. That gives the reader something specific to examine. The sequence from model tweak to optimized field to flux comparison is straightforward and internally consistent. The soft spots sit in the level of detail provided. The abstract and summary report the outcomes but do not include error bars, convergence checks on the gyrokinetic runs, or side-by-side tables against other recent QI designs. Without those, it is hard to judge how sensitive the critical-gradient improvement is to small changes in the model or to numerical resolution. The inverse mirror idea also needs checking for possible trade-offs in neoclassical transport or coil feasibility that are not addressed here. This paper is aimed at the small group of researchers who optimize stellarator fields for turbulence reduction. Readers already working on ITG stability in 3D geometries or on reactor-relevant QI configurations would get the most direct value. I would send it for peer review. The claims are specific enough to be tested, the methods are standard in the field, and the topic matters for fusion design even if the current write-up leaves some verification steps for the referees to request.

Referee Report

2 major / 2 minor

Summary. The paper presents updated methods for reducing electrostatic ITG-driven turbulence in quasi-isodynamic stellarators. It first introduces an updated model for the critical gradient of localized toroidal ITG modes, argues that modes should split and localize in separate curvature drift wells to raise this threshold, and constructs a six-field-period QI configuration accordingly. It then proposes an 'inverse mirror' magnetic field structure to reduce the destabilizing influence of kinetic electrons on these modes, applies a general optimization target to realize such a configuration, and reports that the resulting nonlinear heat fluxes are below or equal to those of the W7-X high-mirror configuration over a range of applied density gradients.

Significance. If the numerical results hold, the work offers a concrete optimization pathway for improving ITG stability in QI stellarators, with direct comparison to the established W7-X high-mirror case providing a useful benchmark. The emphasis on mode splitting and the inverse-mirror concept represents a targeted extension of existing critical-gradient ideas, potentially aiding future stellarator design efforts aimed at better confinement.

major comments (2)

[§2 and abstract] The central claims rest on an updated critical-gradient model and subsequent optimization, yet the manuscript supplies no explicit equations, derivation steps, or parameter values for this model (see §2 and the abstract), nor any error bars or tabulated data for the reported heat-flux comparisons, which limits direct verification of the quantitative outcomes.
[§3] The claim that the inverse-mirror structure minimizes kinetic-electron destabilization of localized ITG modes is load-bearing for the optimization target, but the supporting linear analysis and its connection to the mode-splitting argument are not shown in sufficient detail to assess robustness against variations in density gradient or electron dynamics.

minor comments (2)

[§1] Notation for the curvature wells and the definition of the inverse-mirror field structure should be introduced with a brief equation or diagram in the first section where they appear.
[Figure 4] Figure captions for the nonlinear flux plots would benefit from explicit mention of the density-gradient range and the number of simulations performed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions, which have helped us improve the clarity and completeness of the manuscript. We address each major comment below and have revised the paper accordingly to provide the requested details on the critical-gradient model, heat-flux data, and supporting linear analysis.

read point-by-point responses

Referee: [§2 and abstract] The central claims rest on an updated critical-gradient model and subsequent optimization, yet the manuscript supplies no explicit equations, derivation steps, or parameter values for this model (see §2 and the abstract), nor any error bars or tabulated data for the reported heat-flux comparisons, which limits direct verification of the quantitative outcomes.

Authors: We agree that the presentation of the updated critical-gradient model in §2 and the abstract would benefit from greater explicitness. In the revised manuscript we have added the full set of equations for the model, including the key derivation steps from the localized toroidal ITG dispersion relation and the specific parameter values employed. For the nonlinear heat-flux comparisons we have included error bars on the relevant figures (derived from multiple simulation realizations) and added a supplementary table listing the time-averaged fluxes with uncertainties for each density gradient value. These revisions directly address the verification concern while preserving the original scientific content. revision: yes
Referee: [§3] The claim that the inverse-mirror structure minimizes kinetic-electron destabilization of localized ITG modes is load-bearing for the optimization target, but the supporting linear analysis and its connection to the mode-splitting argument are not shown in sufficient detail to assess robustness against variations in density gradient or electron dynamics.

Authors: We acknowledge that the linear analysis linking the inverse-mirror field structure to reduced kinetic-electron destabilization requires additional detail to demonstrate robustness. In the revised §3 we have expanded the linear gyrokinetic results to include growth-rate scans over a range of density gradients and electron temperature ratios, together with explicit mode-structure plots that illustrate the connection to the mode-splitting argument. These additions show that the inverse-mirror configuration maintains the elevated critical gradient and suppressed electron-driven destabilization across the parameter space examined, thereby strengthening the justification for the optimization target. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation begins with an updated critical-gradient model for localized ITG modes, proceeds to an argument favoring mode splitting across curvature wells, introduces an inverse-mirror field structure to reduce kinetic-electron effects (with a supporting citation), and applies a general optimization target to generate a six-period QI configuration whose nonlinear heat fluxes are then compared directly to W7-X high-mirror results. No equation or step reduces by construction to a fitted parameter, self-definition, or load-bearing self-citation chain; the optimization target and flux comparisons remain independent of the model inputs and are externally falsifiable against benchmark configurations.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claims rest on an updated critical gradient model whose accuracy is assumed and on the introduction of the inverse mirror structure without independent falsifiable evidence shown in the abstract.

axioms (1)

domain assumption The updated model for the threshold gradient of localized toroidal ITG modes accurately describes mode behavior in the optimized QI configurations.
Invoked to justify desirability of mode splitting into separate curvature drift wells.

invented entities (1)

inverse mirror magnetic field structure no independent evidence
purpose: Minimizes the destabilizing effect of kinetic electrons on localized ITG modes.
Newly introduced configuration type to achieve improved stability above the critical gradient.

pith-pipeline@v0.9.0 · 5692 in / 1220 out tokens · 55598 ms · 2026-05-19T08:23:09.273631+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

updated model for the threshold (critical) gradient of localized toroidal ITG modes... mode splitting... inverse mirror configuration
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

⟨(· · ·)⟩CG(ℓ) RMS average over single drift well; L∥CG and a/Reff CG definitions

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

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F., Sarazin, Y., Dif-Pradalier, G

Angelino, P., Garbet, X., Villard, L., Bottino, A., Jolliet, S., Ghendrih, Ph, Grandgirard, V., McMillan, B. F., Sarazin, Y., Dif-Pradalier, G. & Tran, T. M. 2009 Role of plasma elongation on turbulent transport in magnetically confined plasmas. Physical Review Letters102, 1–4. Balestri, A., Ball, J., Coda, S., Cruz-Zabala, D. J., Garcia-Munoz, M. & Viezz...

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[2]

1981 Plasma equilibrium with rational magnetic surfaces.Physics of Fluids 24, 1999–2003

Boozer, Allen H. 1981 Plasma equilibrium with rational magnetic surfaces.Physics of Fluids 24, 1999–2003. Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory.Reviews of Modern Physics 79, 421–468. Cary, John R & Shasharina, Svetlana G 1997 Helical plasma confinement devices with good confinement properties.Physical Review Letters...

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Costello, P

bounce-averaged electrons.Journal of Plasma Physics91, E12. Costello, P. J. & Plunk, G. G. 2025b Tightening energetic bounds on linear gyrokinetic instabilities. arXiv:2505.17757 . Dew ar, R. L. & Glasser, A. H. 1983 Ballooning mode spectrum in general toroidal systems. Physics of Fluids 26, 3038–3052. Duff, J. M., F aber, B. J., Hegna, C. C., Pueschel, M...

work page arXiv 1983
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Garcia-Regaña, J

Garbet, Xa vier, Donnel, Peter, Gianni, Ludovica De, Qu, Zhisong, Melka, Yossef, Sarazin, Yanick, Grandgirard, Virginie, Obrejan, Kevin, Bourne, Emily & Dif-Pradalier, Guilhem 2024 Effect of shaping on trapped electron mode stability: an analytical model.Nuclear Fusion. Garcia-Regaña, J. M., Barnes, M., Cal vo, I., Parra, F. I., Alcuson, J. A., Da vies, R...

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16 G. T. Roberg-Clark, P. Xanthopoulos, G. G. Plunk, S. Stroteich Gerard, M. J., Pueschel, M. J., Geiger, B., Mackenbach, R. J.J., Duff, J. M., F aber, B. J., Hegna, C. C. & Terry, P. W. 2024 On the effect of flux-surface shaping on trapped-electron modes in quasi-helically symmetric stellarators.Physics of Plasmas

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Goodman, Alan G., Xanthopoulos, Pa vlos, Plunk, Gabriel G., Smith, Håkan, Nührenberg, Carolin, Beidler, Craig D., Henneberg, Sophia A., Roberg- Clark, Gareth, Drevlak, Michael & Helander, Per 2024 Quasi-isodynamic stellarators with low turbulence as fusion reactor candidates.PRX Energy

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H E & Plunk, G

Helander, P., Proll, J. H E & Plunk, G. G. 2013 Collisionless microinstabilities in stellarators. i. analytical theory of trapped-particle modes.Physics of Plasmas20, 122505. Jenko, F., Dorland, W. & Hammett, G. W. 2001 Critical gradient formula for toroidal electron temperature gradient modes.Physics of Plasmas 8, 4096–4104. Jenko, F., Dorland, W., Kotsc...

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Nemov, V

Nakata, Motoki & Matsuoka, Seikichi 2022 Impact of geodesic curvature on zonal flow generation in magnetically confined plasmas.Plasma and Fusion Research17. Nemov, V. V., Kasilov, S. V., Kernbichler, W. & Heyn, M. F. 1999 Evaluation of 1/v neoclassical transport in stellarators.Physics of Plasmas 6, 4622–4632. Nishimoto, S., Nagaoka, K., Nakata, M., Yosh...

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Nunami, M., W atanabe, T. H. & Sugama, H. 2013 A reduced model for ion temperature gradient turbulent transport in helical plasmas.Physics of Plasmas

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Plunk, G. G. & Helander, P. 2023 Energetic bounds on gyrokinetic instabilities. part

work page 2023
[11]

Plunk, G

generalized free energy.Journal of Plasma Physics89. Plunk, G. G. & Helander, P. 2024 The residual flow in well-optimized stellarators.Journal of Plasma Physics

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G., Xanthopoulos, P., Weir, G

Plunk, G. G., Xanthopoulos, P., Weir, G. M., Bozhenkov, S. A., Dinklage, A., Fuchert, G., Geiger, J., Hirsch, M., Hoefel, U., Jakubowski, M., Langenberg, A., Pablant, N., Pasch, E., Stange, T. & Zhang, D. 2019 Stellarators resist turbulent transport on the electron larmor scale.Physical Review Letters122, 35002. Proll, J.H.E., Plunk, G.G., F aber, B.J., G...

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T., Plunk, G

Roberg-Clark, G. T., Plunk, G. G. & Xanthopoulos, P. 2021 Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas. Journal of Plasma Physics87, 905870306. Roberg-Clark, G. T., Plunk, G. G. & Xanthopoulos, P. 2022 Coarse-grained gyrokinetics for the critical ion temperature gradient in stellarators. P...

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F., Sarazin, Y., Dif-Pradalier, G

Angelino, P., Garbet, X., Villard, L., Bottino, A., Jolliet, S., Ghendrih, Ph, Grandgirard, V., McMillan, B. F., Sarazin, Y., Dif-Pradalier, G. & Tran, T. M. 2009 Role of plasma elongation on turbulent transport in magnetically confined plasmas. Physical Review Letters102, 1–4. Balestri, A., Ball, J., Coda, S., Cruz-Zabala, D. J., Garcia-Munoz, M. & Viezz...

work page 2009

[2] [2]

1981 Plasma equilibrium with rational magnetic surfaces.Physics of Fluids 24, 1999–2003

Boozer, Allen H. 1981 Plasma equilibrium with rational magnetic surfaces.Physics of Fluids 24, 1999–2003. Brizard, A. J. & Hahm, T. S. 2007 Foundations of nonlinear gyrokinetic theory.Reviews of Modern Physics 79, 421–468. Cary, John R & Shasharina, Svetlana G 1997 Helical plasma confinement devices with good confinement properties.Physical Review Letters...

work page 1981

[3] [3]

Costello, P

bounce-averaged electrons.Journal of Plasma Physics91, E12. Costello, P. J. & Plunk, G. G. 2025b Tightening energetic bounds on linear gyrokinetic instabilities. arXiv:2505.17757 . Dew ar, R. L. & Glasser, A. H. 1983 Ballooning mode spectrum in general toroidal systems. Physics of Fluids 26, 3038–3052. Duff, J. M., F aber, B. J., Hegna, C. C., Pueschel, M...

work page arXiv 1983

[4] [4]

Garcia-Regaña, J

Garbet, Xa vier, Donnel, Peter, Gianni, Ludovica De, Qu, Zhisong, Melka, Yossef, Sarazin, Yanick, Grandgirard, Virginie, Obrejan, Kevin, Bourne, Emily & Dif-Pradalier, Guilhem 2024 Effect of shaping on trapped electron mode stability: an analytical model.Nuclear Fusion. Garcia-Regaña, J. M., Barnes, M., Cal vo, I., Parra, F. I., Alcuson, J. A., Da vies, R...

work page 2024

[5] [5]

16 G. T. Roberg-Clark, P. Xanthopoulos, G. G. Plunk, S. Stroteich Gerard, M. J., Pueschel, M. J., Geiger, B., Mackenbach, R. J.J., Duff, J. M., F aber, B. J., Hegna, C. C. & Terry, P. W. 2024 On the effect of flux-surface shaping on trapped-electron modes in quasi-helically symmetric stellarators.Physics of Plasmas

work page 2024

[6] [6]

Goodman, Alan G., Xanthopoulos, Pa vlos, Plunk, Gabriel G., Smith, Håkan, Nührenberg, Carolin, Beidler, Craig D., Henneberg, Sophia A., Roberg- Clark, Gareth, Drevlak, Michael & Helander, Per 2024 Quasi-isodynamic stellarators with low turbulence as fusion reactor candidates.PRX Energy

work page 2024

[7] [7]

H E & Plunk, G

Helander, P., Proll, J. H E & Plunk, G. G. 2013 Collisionless microinstabilities in stellarators. i. analytical theory of trapped-particle modes.Physics of Plasmas20, 122505. Jenko, F., Dorland, W. & Hammett, G. W. 2001 Critical gradient formula for toroidal electron temperature gradient modes.Physics of Plasmas 8, 4096–4104. Jenko, F., Dorland, W., Kotsc...

work page arXiv 2013

[8] [8]

Nemov, V

Nakata, Motoki & Matsuoka, Seikichi 2022 Impact of geodesic curvature on zonal flow generation in magnetically confined plasmas.Plasma and Fusion Research17. Nemov, V. V., Kasilov, S. V., Kernbichler, W. & Heyn, M. F. 1999 Evaluation of 1/v neoclassical transport in stellarators.Physics of Plasmas 6, 4622–4632. Nishimoto, S., Nagaoka, K., Nakata, M., Yosh...

work page 2022

[9] [9]

Nunami, M., W atanabe, T. H. & Sugama, H. 2013 A reduced model for ion temperature gradient turbulent transport in helical plasmas.Physics of Plasmas

work page 2013

[10] [10]

Plunk, G. G. & Helander, P. 2023 Energetic bounds on gyrokinetic instabilities. part

work page 2023

[11] [11]

Plunk, G

generalized free energy.Journal of Plasma Physics89. Plunk, G. G. & Helander, P. 2024 The residual flow in well-optimized stellarators.Journal of Plasma Physics

work page 2024

[12] [12]

G., Xanthopoulos, P., Weir, G

Plunk, G. G., Xanthopoulos, P., Weir, G. M., Bozhenkov, S. A., Dinklage, A., Fuchert, G., Geiger, J., Hirsch, M., Hoefel, U., Jakubowski, M., Langenberg, A., Pablant, N., Pasch, E., Stange, T. & Zhang, D. 2019 Stellarators resist turbulent transport on the electron larmor scale.Physical Review Letters122, 35002. Proll, J.H.E., Plunk, G.G., F aber, B.J., G...

work page 2019

[13] [13]

T., Plunk, G

Roberg-Clark, G. T., Plunk, G. G. & Xanthopoulos, P. 2021 Calculating the linear critical gradient for the ion-temperature-gradient mode in magnetically confined plasmas. Journal of Plasma Physics87, 905870306. Roberg-Clark, G. T., Plunk, G. G. & Xanthopoulos, P. 2022 Coarse-grained gyrokinetics for the critical ion temperature gradient in stellarators. P...

work page 2021