Pith. sign in

REVIEW 3 major objections 4 minor 80 references

Residual stress in tokamak core momentum transport follows a V-shaped curve across the ITG-to-TEM transition, collapsing onto a linear dependence on electron kinetic profile gradients, with weaker E×B shearing pushing it counter-current.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Residual stress (intrinsic torque) in DIII-D is co-current in deep ITG and deep TEM turbulence but near-zero/counter-current in the mixed-mode transition, correlating with electron gradient scale lengths.

T0 review reviewed 2026-08-01 challenge →

load-bearing objection Solid experimental extension of momentum-transport analysis to DIII-D deep-TEM, low-torque regimes with a genuinely interesting residual-stress trend, but the headline V-shape rests on normalization and functional-form assumptions the authors flag but never quantify. the 3 major comments →

arxiv 2607.15484 v1 pith:AENVPL7R submitted 2026-07-16 physics.plasm-ph

Dependence of Momentum Transport on the Dominant Turbulence Regime in the DIII-D Tokamak

C. F. B. Zimmermann , C. Chrystal , E. Perez , T. Tala , C. Angioni , S. Haskey , F. Khabanov , R. M. McDermott
show 3 more authors
G. McKee A. Salmi L. Schmitz
This is my paper
classification physics.plasm-ph PACS 52.55.Fa52.25.Fi
keywords toroidal momentum transportresidual stressintrinsic torqueITG-TEM transitiontrapped electron modesplasma rotationPrandtl numbergyrokinetic validation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The reading

The paper tries to establish how the turbulent transport of toroidal momentum in the core of a tokamak changes when the dominant instability shifts from ion-temperature-gradient (ITG) turbulence, driven by ion temperature gradients, to trapped-electron-mode (TEM) turbulence, driven by electron dynamics. By modulating neutral beam torque and Fourier-analyzing the rotation response, the authors separate momentum transport into diffusion, convection, and a non-Fickian residual stress that acts as an intrinsic torque. They find that residual stress is the regime-sensitive piece: co-current in deep ITG and deep TEM conditions, near-zero or counter-current in the intermediate mixed-mode regime, forming a V-shape when ordered by electron-to-ion temperature ratio. The V-shape collapses onto an approximately linear trend against electron kinetic profile gradients, indicating that profile-shearing symmetry breaking, with background E×B shear as a modifier, sets the sign and magnitude of the intrinsic torque. If correct, future low-torque reactor rotation predictions need residual stress driven by profile gradients and shear, not just a turbulence-regime label.

Core claim

On its own terms, the central discovery is that the normalized residual stress—the off-diagonal part of the turbulent momentum flux that can spin the plasma up from rest—does not follow the ITG/TEM regime label directly. It is co-current in the deep ITG and deep TEM limits, near-zero or counter-current in the mixed-mode middle, and this V-shaped dependence collapses onto an approximately linear dependence on the logarithmic electron temperature gradient R/LTe. The paper interprets this as evidence that residual stress is generated by profile-shearing effects—the tilting of turbulent eddies by kinetic-profile gradients—with the background E×B shearing rate acting as a second ordering paramete

What carries the argument

The load-bearing object is the residual stress flux ΠRS, normalized by the momentum diffusivity as RΠRS/χφ: the intrinsic-torque contribution to radial toroidal momentum transport that is independent of both the rotation gradient (diffusion) and the rotation itself (convection). The experiment separates these three contributions from the rotation response to a torque modulation using Fourier analysis: diffusion dominates the phase profile, convection shapes the amplitude, and the residual stress is the remaining non-Fickian flux. The interpretation is organized by profile-shearing symmetry breaking: turbulent eddies are tilted by second derivatives of the kinetic profiles, with the logarithm

Load-bearing premise

The load-bearing premise is that the measured rotation response can be separated into transport contributions using the assumed functional forms—momentum diffusivity scaling linearly with ion heat diffusivity, and convective velocity and residual stress having cubic-polynomial radial shapes—so if those shapes are wrong, the inferred V-shaped residual-stress trend could be an artifact of the fit.

What would settle it

Run nonlinear global gyrokinetic simulations that compute residual stress directly from the measured kinetic profiles for deep ITG, mixed, and deep TEM discharges: if the predicted normalized residual stress does not form the V-shape against R/LTe and does not shift counter-current when E×B shear is reduced, the profile-shearing interpretation fails. A cheaper check is to refit the same rotation data with freely shaped transport-coefficient profiles and see whether the V-shape persists.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Predictive models for low-torque reactor plasmas must include residual stress as an intrinsic torque source; in mixed ITG-TEM regimes it can vanish or reverse, so omitting it will mispredict core rotation.
  • Residual stress should be ordered by electron kinetic profile gradients and by background E×B shear, not simply by which turbulence mode dominates.
  • Linear gyrokinetic calculations appear adequate for the diffusive and convective momentum transport coefficients even in TEM-dominated regimes, supporting their use in transport modeling.
  • The Prandtl-number normalization by ion heat diffusivity becomes questionable in strongly electron-driven turbulence, so future studies need a more robust reference for momentum diffusivity across regime transitions.
  • Deep ITG and deep TEM conditions both favor co-current intrinsic torque and peaked rotation profiles, while the mixed transition region is the least favorable for building rotation in low-torque devices.

Where Pith is reading between the lines

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

  • If the profile-shearing interpretation is right, core rotation in future devices could be steered by shaping electron temperature and density gradients—for example by auxiliary-heating deposition—rather than by external torque alone; a dedicated ECH-position scan at fixed torque would test this.
  • The residual stress shift with E×B shear suggests that seemingly small differences in background rotation from beam geometry can flip the sign of core intrinsic torque, which may explain scatter in earlier momentum transport experiments and should be included in inter-machine comparisons.
  • The deep-TEM co-current branch implies that strongly electron-heated, low-rotation plasmas do not automatically lose intrinsic rotation drive as long as the TEM is fully developed; whether this branch survives at lower collisionality is a testable extension.
  • A direct nonlinear gyrokinetic computation of residual stress from these experimental profiles is the natural next check: it would either confirm the V-shape from gradients alone or reveal additional mechanisms beyond profile shearing.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper applies a momentum transport analysis framework previously developed for ASDEX Upgrade to seven DIII-D discharges with modulated neutral beam injection, covering a transition from ITG-dominated to deeply TEM-dominated turbulence. Using Fourier analysis of the rotation response, the authors infer diffusive, convective, and residual-stress contributions, reporting Prandtl numbers near unity, pinch numbers ordered by density gradient, and a non-monotonic, V-shaped normalized residual-stress trend when ordered by Te/Ti. The V-shape is further reported to collapse onto a linear dependence on R/LTe, with weaker E x B shearing shifting residual stress toward counter-current values. Linear CGYRO and TGLF calculations characterize the ITG-TEM transition, and linear CGYRO predictions for Prandtl and pinch numbers agree with experiment for representative ITG and TEM discharges.

Significance. If the residual-stress trend is robust, the result is significant: it suggests that intrinsic torque is not simply a function of turbulence regime, but is ordered by kinetic profile gradients (profile shearing) and modified by background E x B shear, with implications for rotation prediction in low-torque reactor scenarios. The paper also delivers a methodological transfer of the AUG framework to DIII-D, including a co-/counter-NBI torque modulation at constant power, and provides a useful gyrokinetic validation of Prandtl and pinch numbers in a TEM-dominated plasma. However, the central residual-stress claim is inferred under specific parameterized functional forms, and the paper does not quantify the associated systematic uncertainty.

major comments (3)
  1. [Section 2, Eq. (1) and parameterization after Eq. (1)] The residual stress is parameterized as proportional to the momentum diffusivity, which is itself set to a(rho) times the ion heat diffusivity chi_i. The plotted quantity R*Pi_RS/chi_phi is therefore essentially the fitted polynomial coefficient c(rho_phi) (up to the imposed scaling), not a direct measurement of the residual stress divided by an independently measured diffusivity. If the true Pi_RS does not scale with chi_i, or if chi_i is poorly defined in TEM-dominated conditions (as the paper itself states in Section 6 for discharge #200416), the inferred coefficient, and hence the V-shaped trend in Figs. 6(c), 6(f), 7(b), and 8, can be systematically biased. No sensitivity scan, alternative normalization (e.g., with chi_e), or synthetic-inversion test is provided to quantify this. Since this trend is the headline claim, this is a load-bearing gap.
  2. [Section 5, Figs. 6 and 7] The V-shaped dependence and the subsequent collapse onto R/LTe are based on only seven discharges with substantial error bars. The 'collapse' in Fig. 7(b) has two clear outliers (#200414 and #200419) that are explained post hoc by E x B shearing rather than included in a joint regression. With multiple candidate ordering parameters (Te/Ti, R/Lne, R/LTe, E x B shear) and no statistical measure of trend significance or model comparison, the present support for a linear collapse over a monotonic trend is weak. A combined regression with confidence intervals, or at least a quantitative test of whether the V-shape is preferred, is needed before this result can be regarded as established.
  3. [Section 6] The linear CGYRO validation is performed only for the Prandtl and pinch numbers, not for the residual stress. The paper explicitly notes that nonlinear calculations for residual stress are beyond scope. This is a reasonable limitation, but combined with the model-dependence of the residual-stress inference, it means the central claim lacks independent verification. The manuscript should either supply a sensitivity analysis demonstrating robustness of the residual-stress trend to the assumed functional forms, or explicitly reframe the residual-stress result as a model-dependent hypothesis rather than a measured quantity.
minor comments (4)
  1. [Figures 6 and 7] The y-axis label 'R*Pi_RS/chi_phi (0.01 kg/m/s)' is confusing: it is unclear whether the plotted values are multiplied by 0.01 or whether the unit is 0.01 kg/m/s. Please clarify the factor and use consistent units.
  2. [Table 1 and Appendix A] Table 1 uses abbreviations such as 'co-ctr.', 'med.', 'low', and 'max.' without a legend; please define these. Additionally, Fig. 10 includes discharges #200412, #200413, and #200420 that are not listed in Table 1; this should be noted or the figure restricted to the analyzed set.
  3. [Section 5, paragraph 3] The sentence 'attempts to establish such a correlation via statistical analysis were unsuccessful' is not supported by any details. Please either remove it or provide the analysis (e.g., correlation coefficients, p-values) in an appendix.
  4. [Section 6, Fig. 9(c)] The open circle marker for chi_phi/chi_e at the innermost radial point is not explained in the caption. Since the text discusses this point, please add an explicit reference in the caption or figure.

Circularity Check

0 steps flagged

No significant circularity found: the central residual-stress trend is an experimental inference from a stated transport model, not a fitted parameter renamed as a prediction, and the independent CGYRO comparison covers the main predicted transport coefficients.

full rationale

The paper's central claim is an experimentally inferred trend in the normalized residual stress across an ITG-to-TEM transition. The transport coefficients are indeed fitted to the measured rotation response, but the paper does not present the fitted values as predictions; they are reported as inferred quantities. The V-shaped dependence and its collapse against R/LTe are correlations between the fitted residual-stress coefficient and externally measured plasma gradients, not quantities forced by the model parameterization. The normalization by chi_phi cancels the assumed chi_i scaling if the residual stress is parameterized as proportional to chi_phi, as stated in Section 2 ('linked to the momentum diffusivity to scale with the turbulence amplitude'), so the trend is not simply the shape of the assumed ion-heat-diffusivity scaling. The paper explicitly acknowledges the limitation that 'the common assumption that momentum diffusivity scales primarily with ion heat diffusivity may become insufficient when the turbulence is increasingly electron-driven' (Section 7) and that in the deep TEM case the diffusivities are 'a not very well defined quantity' (Section 6); these are robustness caveats, not circular reductions. The CGYRO comparison for Prandtl and pinch numbers is an independent check of the two other transport coefficients, and the paper does not claim a gyrokinetic prediction of residual stress. Self-citations to the AUG analysis framework are methodological references to an established tool, and no load-bearing argument reduces to a self-citation or imported uniqueness theorem. Therefore no specific circular step can be identified under the required standard.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The central experimental results are inferred through a transport model whose free parameters (Prandtl profile, convection polynomial, residual stress polynomial) are fitted to the rotation response. No new physical entities are introduced; the gyrokinetic comparison provides an external check for diffusive and convective coefficients but not for residual stress.

free parameters (4)
  • Prandtl number profile coefficients a(ρ) = not tabulated (see Fig. 2g)
    Momentum diffusivity parameterized as χφ = a(ρ)·χi with a(ρ) linear; coefficients fitted to rotation modulation data.
  • Convective velocity polynomial coefficients b(ρ) = not tabulated
    Vc represented as cubic polynomial scaled with turbulence amplitude; coefficients fitted.
  • Residual stress polynomial coefficients c(ρ) = not tabulated
    ΠRS represented as cubic polynomial; coefficients fitted.
  • Rotation boundary condition at pedestal top = experimental vφ at boundary
    Prescribed from CER measurements; sensitivity small.
axioms (6)
  • domain assumption Momentum flux decomposes as Fickian diffusion + convection + residual stress (Eq. 1)
    Standard transport modeling assumption; the decomposition is the basis for interpreting the fit.
  • ad hoc to paper Momentum diffusivity scales with ion heat diffusivity with linear-in-radius Prandtl number
    Modeling choice used to reduce degrees of freedom; acknowledged in Discussion as possibly insufficient for TEM-dominated regimes.
  • ad hoc to paper Convective velocity and residual stress have cubic polynomial radial shapes
    Smoothness/regularization choice; not derived from physics.
  • domain assumption Carbon impurity rotation represents main-ion rotation
    Standard assumption; Appendix A provides supporting comparison of modulation amplitude/phase.
  • domain assumption Poloidal rotation and density modulation are negligible
    Density modulations <1%; poloidal rotation small; stated in Section 3.
  • domain assumption Linear CGYRO quasilinear estimates give total momentum fluxes
    Used for Pr and pinch comparison; standard but approximate; nonlinear effects neglected.

reviewed 2026-08-01 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Dependence of Momentum Transport on the Dominant Turbulence Regime in the DIII-D Tokamak." pith.science (2026). https://pith.science/paper/AENVPL7R

@misc{pith2026260715484,
  author       = {Pith},
  title        = {Pith review of: Dependence of Momentum Transport on the Dominant Turbulence Regime in the DIII-D Tokamak},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AENVPL7R}},
  note         = {Machine review of arXiv:2607.15484}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Accurate prediction of toroidal plasma rotation is essential for optimizing confinement and stability in future fusion devices. This work investigates turbulent core momentum transport in the DIII-D tokamak across a transition from ion-temperature-gradient (ITG)- to trapped-electron-mode (TEM)-dominated turbulence. A momentum transport framework previously developed for ASDEX Upgrade is applied to modulated neutral beam injection experiments, separating diffusive, convective, and residual-stress contributions via Fourier analysis of the rotation response. The dataset spans low-rotation conditions, dominant electron heating, and background ExB shearing rates below turbulence growth rates, accessing more reactor-relevant conditions. Gyrokinetic CGYRO and gyrofluid TGLF calculations confirm the scan covers an ITG-to-TEM transition. The analysis yields Prandtl numbers near unity. The pinch number shows no explicit dependence on the transition, instead ordering roughly with the logarithmic density gradient. The normalized residual stress, in contrast, exhibits a non-monotonic, V-shaped dependence across the transition: co-current in deep ITG and deep TEM regimes, near-zero or counter-current in the intermediate mixed-mode regime. This trend collapses onto an approximately linear dependence against electron kinetic profile gradients, suggesting residual stress generation by profile-shearing effects. Weaker background ExB shearing further shifts residual stress toward counter-current values. Linear CGYRO simulations for representative ITG and TEM discharges yield Prandtl and pinch numbers in good agreement with experiment, supporting gyrokinetic momentum-transport predictions in TEM-dominated regimes. These results indicate residual stress plays an important role in core rotation prediction for low-torque plasmas and should be included in predictive models of future reactor scenarios.

Figures

Figures reproduced from arXiv: 2607.15484 by A. Salmi, C. Angioni, C. Chrystal, C. F. B. Zimmermann, E. Perez, F. Khabanov, G. McKee, L. Schmitz, R. M. McDermott, S. Haskey, T. Tala.

Figure 1
Figure 1. Figure 1: Main time traces of the reference discharge #200408, the analysis time window is between [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results of the momentum transport analysis for the selected reference discharge # 200408. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Key parameters of the studied dataset. Panel (a) shows main engineering parameters of applied [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Linear CGYRO growth rates (Panel a) and real frequencies (Panel b) from local flux-tube [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: TGLF calculations for the ITG case #200403 (left) and the TEM case #200416 (right). Colors [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Dependence of inferred transport parameters on the temperature ratio [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of gradient scale lengths versus pinch and residual stress numbers at [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Normalized residual stress as a function of [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of CGYRO calculations (markers) against experimental analysis results (blue line [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the rotation modulation (a) amplitude and (b) phase for main-ion and impurity [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

80 extracted references

  1. [1]

    Angioni et al

    C. Angioni et al. 2012.Physics of Plasmas. 19. 122311

    2012

  2. [2]

    F. J. Casson et al. 2013.Nuclear Fusion. 53. 063026

    2013

  3. [3]

    Angioni et al

    C. Angioni et al. 2014.Nuclear Fusion. 54. 083028

    2014

  4. [4]

    F. J. Casson et al. 2015.Plasma Physics and Controlled Fusion. 57. 014031

    2015

  5. [5]

    Angioni et al

    C. Angioni et al. 2015.Physics of Plasmas. 22. 055902

    2015

  6. [6]

    Biglari et al

    H. Biglari et al. 1990.Physics of Fluids B: Plasma Physics. 2. 1–4

    1990

  7. [7]

    T. S. Hahm. 1994.Physics of Plasmas. 1. 2940–2944

    1994

  8. [8]

    R. E. Waltz et al. 1995.Physics of Plasmas. 2. 2408–2416

    1995

  9. [9]

    T. S. Hahm and K. H. Burrell. 1995.Physics of Plasmas. 2. 1648–1651

    1995

  10. [10]

    K. H. Burrell. 1997.Physics of Plasmas. 4. 1499–1518

    1997

  11. [11]

    P. W. Terry. 2000.Reviews of Modern Physics. 72. 109–165

    2000

  12. [12]

    E. J. Strait et al. 1995.Physical Review Letters. 74. 2483–2486

    1995

  13. [13]

    A. M. Garofalo et al. 2002.Physical Review Letters. 89. 235001

    2002

  14. [14]

    Reimerdes et al

    H. Reimerdes et al. 2007.Physical Review Letters. 98. 055001

    2007

  15. [15]

    P. A. Politzer et al. 2008.Nuclear Fusion. 48. 075001

    2008

  16. [16]

    R. J. Buttery et al. 2008.Proceedings of 22nd IAEA Fusion Energy Conference

    2008

  17. [17]

    P. C. de Vries et al. 2011.Nuclear Fusion. 51. 053018

    2011

  18. [18]

    Bardoczi et al

    L. Bardoczi et al. 2024.Nucl. Fusion. 64. 126005

    2024

  19. [19]

    P. H. Diamond et al. 2009.Nuclear Fusion. 49. 045002

    2009

  20. [20]

    Camenen et al

    Y. Camenen et al. 2009.Physical Review Letters. 102. 125001

    2009

  21. [21]

    Camenen et al

    Y. Camenen et al. 2011.Nuclear Fusion. 51. 073039

    2011

  22. [22]

    Stoltzfus-Dueck

    T. Stoltzfus-Dueck. 2012.Physical Review Letters. 108. 065002

    2012

  23. [23]

    Sun et al

    H. Sun et al. 2024.Nuclear Fusion. 64. 036026

    2024

  24. [24]

    Ida et al

    K. Ida et al. 1995.Phys. Rev. Lett.74. 1990–1993

    1995

  25. [25]

    J. E. Rice et al. 1998.Nuclear Fusion. 38. 75

    1998

  26. [26]

    W. D. Lee et al. 2003.Physical Review Letters. 91. 205003

    2003

  27. [27]

    Yoshida et al

    M. Yoshida et al. 2008.Physical Review Letters. 100. 105002

    2008

  28. [28]

    Yoshida et al

    M. Yoshida et al. 2009.Physical Review Letters. 103. 065003

    2009

  29. [29]

    W. M. Solomon et al. 2009.Nuclear Fusion. 49. 085005

    2009

  30. [30]

    W. M. Solomon et al. 2011.Nuclear Fusion. 51. 073010

    2011

  31. [31]

    Angioni et al

    C. Angioni et al. 2011.Physical Review Letters. 107. 215003

    2011

  32. [32]

    R. M. McDermott et al. 2011.Plasma Physics and Controlled Fusion. 53. 035007

    2011

  33. [33]

    R. M. McDermott et al. 2011.Plasma Physics and Controlled Fusion. 53. 124013

    2011

  34. [34]

    C. F. B. Zimmermann et al. 2026.Plasma Physics and Controlled Fusion. 68. 055020

    2026

  35. [35]

    Kluy et al

    N. Kluy et al. 2009.Physics of Plasmas. 16. 122302

    2009

  36. [36]

    G. M. Staebler et al. 2013.Physical Review Letters. 110. 055003

    2013

  37. [37]

    B. A. Grierson et al. 2017.Physical Review Letters. 118. 015002

    2017

  38. [38]

    W. A. Hornsby et al. 2018.Nuclear Fusion. 58. 056008. 17

    2018

  39. [39]

    C. F. B. Zimmermann et al. 2024.Physics of Plasmas. 31. 042306

    2024

  40. [40]

    C. F. B. Zimmermann et al. 2022.Plasma Physics and Controlled Fusion. 64. 055020

    2022

  41. [41]

    C. F. B. Zimmermann et al. 2023.Nuclear Fusion. 63. 124003

    2023

  42. [42]

    C. F. B. Zimmermann et al. 2023.Nuclear Fusion. 63. 126006

    2023

  43. [43]

    B. A. Grierson et al. 2012.Review of Scientific Instruments. 83. 10D529

    2012

  44. [44]

    Chrystal et al

    C. Chrystal et al. 2016.Review of Scientific Instruments. 87. 11E512

    2016

  45. [45]

    E. Fable. 2015.Plasma Physics and Controlled Fusion. 57. 045007

    2015

  46. [46]

    Pereverzev and P

    G. Pereverzev and P. N. Yushmanov. 2002.Max Planck Institute for Plasma Physics, Garching, Germany

    2002

  47. [47]

    Fable et al

    E. Fable et al. 2013.Plasma Physics and Controlled Fusion. 55. 124028

    2013

  48. [48]

    2026.Plasma Physics and Controlled Fusion

    G Tardini et al. 2026.Plasma Physics and Controlled Fusion. 68. 065024

    2026

  49. [49]

    A. G. Peeters et al. 2007.Physical Review Letters. 98. 265003

    2007

  50. [50]

    A. G. Peeters and C. Angioni. 2005.Physics of Plasmas. 12. 072515

    2005

  51. [51]

    R. E. Waltz et al. 2007.Physics of Plasmas. 14. 056116

    2007

  52. [52]

    Weiland et al

    J. Weiland et al. 2009.Nuclear Fusion. 49. 065033

    2009

  53. [53]

    A. G. Peeters et al. 2006.Plasma Physics and Controlled Fusion. 48. B413

    2006

  54. [54]

    Strintzi et al

    D. Strintzi et al. 2008.Physics of Plasmas. 15. 044502

    2008

  55. [55]

    A. G. Peeters et al. 2011.Nuclear Fusion. 51. 094027

    2011

  56. [56]

    Storn and K

    R. Storn and K. Price. 1997.Journal of Global Optimization. 11. 341–359

    1997

  57. [57]

    Pankin et al

    A. Pankin et al. 2004.Computer Physics Communications. 159. 157–184

    2004

  58. [58]

    Breslau et al

    J. Breslau et al. 2018.Princeton Plasma Physics Laboratory (PPPL), Princeton, New Jersey, United States

    2018

  59. [59]

    An empirical approach to tokamak transport

    R. J. Hawryluk. “An empirical approach to tokamak transport”. In:Physics of plasmas close to thermonuclear conditions. Elsevier, 1981, pp. 19–46

    1981

  60. [60]

    R. W. Harvey and A. P. Smirnov.The GENRAY Ray Tracing Code. CompX Report CompX-2000-

    2000

  61. [61]

    E. A. Belli and J Candy. 2017.Plasma Physics and Controlled Fusion. 59. 045005

    2017

  62. [62]

    G. M. Staebler et al. 2007.Physics of Plasmas. 14. 055909

    2007

  63. [63]

    G. R. McKee et al. 2010.Review of Scientific Instruments. 81. 10D741

    2010

  64. [64]

    W. A. Peebles et al. 2010.Review of Scientific Instruments. 81. 10D902

    2010

  65. [65]

    Tala et al

    T. Tala et al. 2009.Physical Review Letters. 102. 075001

    2009

  66. [66]

    Fable et al

    E. Fable et al. 2009.Plasma Physics and Controlled Fusion. 52. 015007

    2009

  67. [67]

    Angioni et al

    C. Angioni et al. Feb. 2011.Nucl. Fusion. 51. 023006

    2011

  68. [68]

    Fable et al

    E. Fable et al. 2019.Nuclear Fusion. 59. 076042

    2019

  69. [69]

    W. X. Wang et al. 2009.Physical Review Letters. 102. 035005

    2009

  70. [70]

    W. X. Wang et al. 2010.Physics of Plasmas. 17. 072511

    2010

  71. [71]

    R. R. Dominguez and G. M. Staebler. 1993.Physics of Fluids B: Plasma Physics. 5. 3876–3886

    1993

  72. [72]

    Garbet et al

    X. Garbet et al. 2002.Physics of Plasmas. 9. 3893–3905

    2002

  73. [73]

    ¨O. D. G¨ urcan et al. 2007.Physics of Plasmas. 14. 042306

    2007

  74. [74]

    F. J. Casson et al. 2009.Physics of Plasmas. 16. 092303

    2009

  75. [75]

    Validation of Momentum Transport Theory in the Core Plasma of the ASDEX Upgrade Tokamak

    C. F. B Zimmermann. “Validation of Momentum Transport Theory in the Core Plasma of the ASDEX Upgrade Tokamak”. PhD thesis. Technische Universit¨ at M¨ unchen, 2024.url:https : //mediatum.ub.tum.de/1728062

    arXiv 2024

  76. [76]

    Kotschenreuther et al

    M. Kotschenreuther et al. 1995.Physics of Plasmas. 2. 2381–2389

    1995

  77. [77]

    B. A. Grierson et al. 2012.Physics of Plasmas. 19. 056107

    2012

  78. [78]

    B. A. Grierson et al. 2013.Nuclear Fusion. 53. 063010. 18

    2013

  79. [79]

    Chrystal et al

    C. Chrystal et al. 2017.Physics of Plasmas. 24. 042501

    2017

  80. [80]

    Meneghini et al

    O. Meneghini et al. 2015.Nuclear Fusion. 55. 083008. 19

    2015

This paper was first reviewed by deepseek-v4-flash on August 1, 2026.