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arxiv: 2603.04709 · v2 · submitted 2026-03-05 · ⚛️ physics.plasm-ph

Hollow toroidal rotation profiles in strongly electron heated H-mode plasmas in the ASDEX Upgrade tokamak

C. F. B. Zimmermann , R. M. McDermott , C. Angioni , B. P. Duval , R. Dux , E. Fable , A. Salmi , T. Tala
show 3 more authors
G. Tardini T. P\"utterich the ASDEX Upgrade Team
This is my paper

Pith reviewed 2026-05-15 16:03 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords toroidal momentum transporthollow rotation profilesECRH heatingH-mode plasmasintrinsic torqueconvective momentum pinchpedestal densityASDEX Upgrade
0
0 comments X p. Extension

The pith

Hollow toroidal rotation profiles form when counter-current intrinsic torque balances inward convective momentum transport in electron-heated H-mode plasmas.

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

This paper examines how strong electron cyclotron resonance heating collapses the toroidal rotation profile into a hollow shape in ASDEX Upgrade type-I ELMy H-mode plasmas, even with unchanged neutral beam torque. The authors apply the standard momentum transport analysis to NBI modulation data and find that the hollow profile arises because a strong counter-current intrinsic torque is offset by inward convection. The pedestal-top rotation level, set mainly by local density, controls how pronounced the hollow shape becomes. Linear gyrokinetic calculations tie the torque sign change to a shift from ITG to ITG-TEM mixed turbulence. The result matters because future tokamaks will run with far less external torque, so intrinsic sources and convection will decide whether rotation stays favorable for confinement.

Core claim

The central claim is that hollow rotation profiles emerge from a balance between counter-current intrinsic torque and inward convective momentum transport. This balance is strongly influenced by the pedestal-top rotation level, which is dominantly set by variations in the pedestal-top density. The diffusive Prandtl number and Coriolis pinch stay comparable with and without strong ECRH, while the intrinsic torque reverses to counter-current only in the high-ECRH phase. Gyrokinetic simulations confirm the turbulence regime change that produces the observed torque sign and particle pinch.

What carries the argument

Self-consistent inference of diffusive, convective, and residual-stress momentum transport coefficients from NBI modulation experiments, which remain robust when strong ECRH is added.

If this is right

  • Intrinsic torque and inward convection can maintain usable rotation profiles in future low-torque tokamak operation.
  • Pedestal-top density provides a practical control knob for the overall rotation profile shape.
  • The momentum transport framework remains usable for predictive modeling when electron heating dominates.
  • Edge-localized torque generation mechanisms become critical once external torque is reduced.

Where Pith is reading between the lines

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

  • Similar density-dependent torque balances may set rotation in other machines or heating mixes once external torque is low.
  • Targeted edge density control experiments could test whether rotation can be shaped on demand without changing core heating.
  • If the ITG-TEM transition is general, reduced-torque scenarios in ITER-scale devices may routinely develop hollow profiles unless edge torque sources are engineered.

Load-bearing premise

The established momentum transport analysis framework can be applied self-consistently to infer the coefficients even when strong ECRH is added, without unaccounted changes in the underlying transport physics.

What would settle it

A direct observation that the inferred counter-current intrinsic torque fails to reproduce the measured rotation collapse when the same transport coefficients are used in the modeling, or that the gyrokinetic turbulence regime does not shift to ITG-TEM under the experimental ECRH conditions.

Figures

Figures reproduced from arXiv: 2603.04709 by A. Salmi, B. P. Duval, C. Angioni, C. F. B. Zimmermann, E. Fable, G. Tardini, R. Dux, R. M. McDermott, the ASDEX Upgrade Team, T. P\"utterich, T. Tala.

Figure 1
Figure 1. Figure 1: Most important time traces of #29216. The studied discharge phases are indi [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Kinetic profiles for #29216 for the discharge phase with dominant NBI heating [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Ion heat diffusivity (a) from ASTRA calculations. Ion heat fluxes (b), electron [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The error bars shown for the gradient quantities are obtained from Gaussian process [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of dimensionless parameters in the plasma core of #29216 for the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Modeling of the discharge phase with dominant NBI heating (#29216, 2 [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Modeling of the discharge phase with NBI+ECRH (#29216, 5 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Comparison of the inferred transport coefficients for #29216 for the discharge [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Turbulence growth rate γ and real mode frequency ωr scanned as a function of kyρi using experimental input at mid-radius for both discharge phases of #29216 for the discharge phase with dominant NBI heating (2.0 − 4.5 s, l.h.s.) and for the phase with NBI+ECRH (5.5 − 7.0 s, r.h.s). in the LHD device [90]. In LHD, TEM-dominated scenarios, associated with relatively flat density profiles, exhibit co-current … view at source ↗
Figure 9
Figure 9. Figure 9: Cost function values of the modeling optimization for the NBI+ECRH phase [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the momentum fluxes for both discharge phases for #29216 for [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Kinetic profiles for the high-ne (#42339, 5.09–7.09 s, dotted orange) and low-ne (#42340, 6.09–7.89 s, solid blue) reproductions of the NBI+ECRH phase of #29216 (black dashed). The high-ne case closely resembles #29216 and reproduces the hollow rotation profile, while the low-ne case exhibits a more peaked rotation profile. The shaded bands indicate the standard deviation across the analyzed time windows … view at source ↗
Figure 12
Figure 12. Figure 12: Selected dimensionless quantities for the high- [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Ion heat diffusivity (a) from ASTRA calculations. Ion heat fluxes (b), equipar [PITH_FULL_IMAGE:figures/full_fig_p019_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Application of the transport coefficients from the NBI+ECRH phase of #29216 [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
read the original abstract

This work investigates toroidal momentum transport in type-I ELMy H-mode plasmas in the ASDEX Upgrade tokamak, focusing on the formation of hollow rotation profiles under strong electron cyclotron resonance heating (ECRH). Applying the established momentum transport analysis framework to a neutral beam injection (NBI) modulation experiment, momentum transport coefficients were inferred self-consistently. This was done for phases with dominant NBI heating and with additional strong ECRH, during which the rotation profile severely collapsed without significant changes in the externally applied torque. The experimental rotation profiles were accurately reproduced, confirming the robustness of the inferred diffusive, convective, and residual-stress contributions. While the Prandtl number and inward Coriolis pinch remained comparable between phases, the NBI+ECRH phase exhibited a strong counter-current intrinsic torque. Linear gyrokinetic simulations indicate a transition from ion-temperature-gradient (ITG) turbulence to an ITG-trapped-electron-mode (TEM) mixed regime under strong ECRH, consistent with the observed counter-current intrinsic torque and particle pinch behavior. Additional high-ECRH discharges with modified density demonstrated that hollow rotation profiles emerge from a balance between counter-current intrinsic torque and inward convective momentum transport, strongly influenced by the pedestal-top rotation level, which is dominantly set by variations in the pedestal-top density. These findings highlight the importance of intrinsic torque and inward convection for maintaining favorable rotation profiles in future low-torque tokamak scenarios and motivate further exploration of edge torque generation mechanisms.

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.

Referee Report

3 major / 2 minor

Summary. The paper claims that hollow toroidal rotation profiles in strongly ECRH-heated ASDEX Upgrade H-mode plasmas arise from a balance between strong counter-current intrinsic torque and inward convective momentum transport. Coefficients (diffusive, convective, residual-stress) are inferred self-consistently from NBI-modulation experiments in both NBI-only and NBI+ECRH phases; the measured profiles are reproduced, Prandtl number and Coriolis pinch remain comparable, and linear gyrokinetic simulations show an ITG-to-mixed-ITG/TEM transition consistent with the observed torque sign. Additional high-ECRH discharges demonstrate that the hollow shape is controlled by the pedestal-top rotation level, which is set primarily by variations in pedestal-top density.

Significance. If the central attribution holds, the work supplies concrete evidence that intrinsic torque and inward convection can dominate rotation-profile evolution once external torque is low, with direct implications for rotation control in ITER and DEMO. The experimental inference plus linear-GK cross-check is a strength; the density dependence offers a testable, falsifiable prediction for edge torque mechanisms.

major comments (3)
  1. [§4] §4 (NBI-modulation analysis): the reproduction of the rotation profiles using coefficients inferred from the same dataset is partly tautological; quantitative validation metrics (e.g., reduced χ², residual norms, or cross-validation on held-out time slices) and uncertainty ranges on the fitted Prandtl number, pinch velocity, and residual stress are not reported, weakening the claim that the three-coefficient model remains valid across the ITG-to-ITG/TEM transition.
  2. [§5] §5 (linear gyrokinetic simulations): the transition to a mixed ITG/TEM regime is shown to be consistent with counter-current torque, yet the manuscript does not demonstrate that the momentum flux spectrum in the mixed state is still captured by a radially constant diffusive-convective-residual-stress model; a direct comparison of the simulated momentum flux (including possible radial variation of the pinch or residual-stress spectrum) against the inferred coefficients is needed to close the loop.
  3. [§6] §6 (density-variation discharges): the assertion that pedestal-top rotation is 'dominantly set by variations in the pedestal-top density' requires explicit quantification (e.g., correlation coefficient or partial-derivative sensitivity) and exclusion of confounding changes in edge Er or neutral-beam deposition; without these, the causal link to the hollow-profile formation remains correlative rather than demonstrated.
minor comments (2)
  1. [Figure 3] Figure 3: axis labels and units for the inferred residual stress should be stated explicitly; the color scale for the linear growth rates in the accompanying GK plots is not defined.
  2. Notation: the symbol for the Coriolis pinch velocity is introduced without a clear definition in the text; a short table of symbols would improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address each major comment point by point below, providing clarifications and indicating the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: §4 (NBI-modulation analysis): the reproduction of the rotation profiles using coefficients inferred from the same dataset is partly tautological; quantitative validation metrics (e.g., reduced χ², residual norms, or cross-validation on held-out time slices) and uncertainty ranges on the fitted Prandtl number, pinch velocity, and residual stress are not reported, weakening the claim that the three-coefficient model remains valid across the ITG-to-ITG/TEM transition.

    Authors: We agree that quantitative validation metrics would strengthen the analysis. The reproduction of the profiles is a standard consistency check in momentum transport studies, but we acknowledge it is not fully independent. In the revised manuscript, we will report reduced χ² values for the coefficient fits in both NBI-only and NBI+ECRH phases, provide uncertainty ranges on the Prandtl number, Coriolis pinch velocity, and residual stress obtained from the fitting procedure, and include a cross-validation test on held-out time slices where feasible. These additions will better demonstrate the robustness of the three-coefficient model across the turbulence transition. revision: yes

  2. Referee: §5 (linear gyrokinetic simulations): the transition to a mixed ITG/TEM regime is shown to be consistent with counter-current torque, yet the manuscript does not demonstrate that the momentum flux spectrum in the mixed state is still captured by a radially constant diffusive-convective-residual-stress model; a direct comparison of the simulated momentum flux (including possible radial variation of the pinch or residual-stress spectrum) against the inferred coefficients is needed to close the loop.

    Authors: We appreciate the suggestion to strengthen the connection between simulation and experiment. The linear gyrokinetic simulations were used to identify the ITG-to-mixed ITG/TEM transition and its consistency with the observed torque sign. A direct quantitative comparison of the momentum flux spectrum would require nonlinear simulations or additional post-processing assumptions not included in the present work. In the revised manuscript, we will add a discussion clarifying this limitation, noting that the sign agreement supports the interpretation, and emphasizing that the radially constant model is an experimental approximation validated by profile reproduction. A full direct comparison lies beyond the current scope. revision: partial

  3. Referee: §6 (density-variation discharges): the assertion that pedestal-top rotation is 'dominantly set by variations in the pedestal-top density' requires explicit quantification (e.g., correlation coefficient or partial-derivative sensitivity) and exclusion of confounding changes in edge Er or neutral-beam deposition; without these, the causal link to the hollow-profile formation remains correlative rather than demonstrated.

    Authors: We agree that explicit quantification is required to establish causality. In the revised manuscript, we will add a correlation analysis (Pearson coefficient) between pedestal-top density and rotation level across the high-ECRH discharges, together with a sensitivity study (partial derivatives via regression). We will also explicitly discuss and exclude confounding effects by showing that edge Er and NBI deposition profiles exhibit no significant correlated variations with the observed rotation changes in these discharges. This will convert the current correlative evidence into a more quantitative demonstration. revision: yes

Circularity Check

1 steps flagged

Reproduction of rotation profiles is tautological after fitting coefficients to the same NBI-modulation data

specific steps
  1. fitted input called prediction [Abstract (momentum transport analysis paragraph)]
    "Applying the established momentum transport analysis framework to a neutral beam injection (NBI) modulation experiment, momentum transport coefficients were inferred self-consistently. ... The experimental rotation profiles were accurately reproduced, confirming the robustness of the inferred diffusive, convective, and residual-stress contributions."

    Coefficients are extracted from the NBI-modulation data to match the observed rotation evolution; the subsequent statement that the model reproduces the same profiles is then guaranteed by the fitting procedure rather than constituting an independent prediction.

full rationale

The paper infers diffusive, convective and residual-stress coefficients self-consistently from NBI-modulation experiments and then states that the experimental rotation profiles were accurately reproduced with those coefficients. This reproduction step reduces by construction to the fitting procedure itself. Linear gyrokinetic simulations supply an independent check on the ITG-to-ITG/TEM transition, and the additional density-variation discharges provide separate evidence for the role of pedestal-top density. The central claim therefore retains independent content outside the reproduction step, limiting the circularity to partial (score 6).

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on transport coefficients inferred from modulation data and on the assumption that linear gyrokinetic simulations correctly identify the turbulence regime responsible for the intrinsic torque.

free parameters (1)
  • inferred diffusive, convective, and residual-stress coefficients
    Obtained by fitting the response of rotation to NBI modulation in both NBI-only and NBI+ECRH phases.
axioms (1)
  • domain assumption Linear gyrokinetic simulations accurately capture the transition from ITG to ITG-TEM mixed turbulence and the associated intrinsic torque direction
    Invoked to explain the observed counter-current torque and particle-pinch behavior under strong ECRH.

pith-pipeline@v0.9.0 · 5619 in / 1504 out tokens · 74157 ms · 2026-05-15T16:03:28.755936+00:00 · methodology

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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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel (J-cost uniqueness) unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    The flux-surface-averaged radial transport of toroidal angular momentum is expressed as Γφ = −mnR (χφ ∂vφ/∂r − Vc vφ) + ΠRs … The coefficient χφ represents the momentum diffusivity … The dimensionless quantity −R Vc/χφ is commonly referred to as the pinch number … residual stress contribution … intrinsic torque τint = −∂V/∂r ΠRs

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

102 extracted references · 102 canonical work pages

  1. [1]

    Angioni et al

    C. Angioni et al. 2012.Phys. Plasmas. 19. 122311

    work page 2012

  2. [2]

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

    work page 2013

  3. [3]

    Angioni et al

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

    work page 2014

  4. [4]

    F. J. Casson et al. 2015.Plasma Phys. Control. Fusion. 57. 014031

    work page 2015

  5. [5]

    Angioni et al

    C. Angioni et al. 2015.Phys. Plasmas. 22. 055902

    work page 2015

  6. [6]

    Biglari et al

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

    work page 1990

  7. [7]

    T. S. Hahm. 1994.Phys. Plasmas. 1. 2940–2944

    work page 1994

  8. [8]

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

    work page 1995

  9. [9]

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

    work page 1995

  10. [10]

    K. H. Burrell. 1997.Phys. Plasmas. 4. 1499–1518

    work page 1997

  11. [11]

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

    work page 2000

  12. [12]

    E. J. Strait et al. 1995.Phys. Rev. Lett.74. 2483–2486

    work page 1995

  13. [13]

    A. M. Garofalo et al. 2002.Phys. Rev. Lett.89. 235001

    work page 2002

  14. [14]

    Reimerdes et al

    H. Reimerdes et al. 2007.Phys. Rev. Lett.98. 055001

    work page 2007

  15. [15]

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

    work page 2008

  16. [16]

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

    work page 2008

  17. [17]

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

    work page 2011

  18. [18]

    Bardoczi et al

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

    work page 2024

  19. [19]

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

    work page 2009

  20. [20]

    Camenen et al

    Y. Camenen et al. 2009.Phys. Rev. Lett.102. 125001. 22

    work page 2009

  21. [21]

    Camenen et al

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

    work page 2011

  22. [23]

    Yoshida et al

    M. Yoshida et al. 2008.Phys. Rev. Lett.100. 105002

    work page 2008

  23. [24]

    Yoshida et al

    M. Yoshida et al. 2009.Phys. Rev. Lett.103. 065003

    work page 2009

  24. [25]

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

    work page 2009

  25. [26]

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

    work page 2011

  26. [27]

    W. M. Solomon et al. 2010.Phys. Plasmas. 17. 056108

    work page 2010

  27. [28]

    Ida et al

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

    work page 1995

  28. [29]

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

    work page 1998

  29. [30]

    W. D. Lee et al. 2003.Phys. Rev. Lett.91. 205003

    work page 2003

  30. [31]

    J. E. Rice et al. 2004.Nucl. Fusion. 44. 379–386

    work page 2004

  31. [32]

    Garbet et al

    X. Garbet et al. 2004.Plasma Phys. Control. Fusion. 46. B557–B574

    work page 2004

  32. [33]

    A. G. Peeters et al. 2007.Phys. Rev. Lett.98. 265003

    work page 2007

  33. [34]

    T. S. Hahm et al. 2007.Phys. Plasmas. 14. 072302

    work page 2007

  34. [35]

    Strintzi et al

    D. Strintzi et al. 2008.Phys. Plasmas. 15. 044502

    work page 2008

  35. [36]

    T. S. Hahm et al. 2008.Phys. Plasmas. 15. 055902

    work page 2008

  36. [37]

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

    work page 2011

  37. [38]

    Tala et al

    T. Tala et al. 2009.Phys. Rev. Lett.102. 075001

    work page 2009

  38. [39]

    Tala et al

    T. Tala et al. 2011.Nucl. Fusion. 51. 123002

    work page 2011

  39. [40]

    Tala et al

    T. Tala et al. 2016.Proceedings of 43rd EPS Conference on Plasma Physics

    work page 2016

  40. [41]

    Mantica et al

    P. Mantica et al. 2010.Phys. Plasmas. 17. 092505

    work page 2010

  41. [42]

    Tardini et al

    G. Tardini et al. 2009.Nucl. Fusion. 49. 085010

    work page 2009

  42. [43]

    Yoshida et al

    M. Yoshida et al. 2012.Nucl. Fusion. 52. 123005

    work page 2012

  43. [44]

    K. Ida. 1998.Plasma Phys. Control. Fusion. 40. 1429

    work page 1998

  44. [45]

    J. S. DeGrassie. 2009.Plasma Phys. Control. Fusion. 51. 124047

    work page 2009

  45. [46]

    Ida and J

    K. Ida and J. E. Rice. 2014.Nucl. Fusion. 54. 045001

    work page 2014

  46. [47]

    J. E. Rice. 2016.Plasma Phys. Control. Fusion. 58. 083001

    work page 2016

  47. [48]

    J. E. Rice. 2022.Springer Nature. Vol. 119

    work page 2022

  48. [49]

    C. F. B. Zimmermann et al. 2024.Phys. Plasmas. 31. 042306

    work page 2024

  49. [50]

    R. M. McDermott et al. 2011.Plasma Phys. Control. Fusion. 53. 035007

    work page 2011

  50. [51]

    R. M. McDermott et al. 2011.Plasma Phys. Control. Fusion. 53. 124013

    work page 2011

  51. [52]

    Angioni et al

    C. Angioni et al. 2011.Phys. Rev. Lett.107. 215003

    work page 2011

  52. [53]

    C. F. B. Zimmermann et al. 2022.Plasma Phys. Control. Fusion. 64. 055020

    work page 2022

  53. [54]

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

    work page 2023

  54. [55]

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

    work page 2023

  55. [56]

    Viezzer et al

    E. Viezzer et al. 2012.Review of Scientific Instruments. 83. 103501

    work page 2012

  56. [57]

    R. M. McDermott et al. 2017.Review of Scientific Instruments. 88

    work page 2017

  57. [58]

    Pereverzev and P

    G. Pereverzev and P. N. Yushmanov. 2002.MPI for Plasma Physics, Garching, Germany

    work page 2002

  58. [59]

    Fable et al

    E. Fable et al. 2013.Plasma Phys. Control. Fusion. 55. 124028. 23

    work page 2013

  59. [60]

    ASTRA-8: a modern framework for transport analysis and mod- elling in fusion devices

    G. Tardini et al. “ASTRA-8: a modern framework for transport analysis and mod- elling in fusion devices”. Submitted to Plasma Physics and Controlled Fusion. 2026

    work page 2026

  60. [61]

    E. Fable. 2015.Plasma Phys. Control. Fusion. 57. 045007

    work page 2015

  61. [62]

    Lebschy et al

    A. Lebschy et al. 2017.Nucl. Fusion. 58. 026013

    work page 2017

  62. [63]

    A. G. Peeters and C. Angioni. 2005.Phys. Plasmas. 12. 072515

    work page 2005

  63. [64]

    R. E. Waltz et al. 2007.Phys. Plasmas. 14. 056116

    work page 2007

  64. [65]

    Weiland et al

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

    work page 2009

  65. [66]

    A. G. Peeters et al. 2006.Plasma Phys. Control. Fusion. 48. B413

    work page 2006

  66. [67]

    Holod and Z

    I. Holod and Z. Lin. 2008.Phys. Plasmas. 15

    work page 2008

  67. [68]

    Holod and Z

    I. Holod and Z. Lin. 2010.Plasma Phys. Control. Fusion. 52. 035002

    work page 2010

  68. [69]

    Pankin et al

    A. Pankin et al. 2004.Comput. Phys. Commun.159. 157–184

    work page 2004

  69. [70]

    Breslau et al

    J. Breslau et al. 2018.Princeton Plasma Physics Laboratory, Princeton, New Jersey, USA

    work page 2018

  70. [71]

    An empirical approach to tokamak transport

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

    work page 1981

  71. [72]

    Poli et al

    E. Poli et al. 2018.Comput. Phys. Commun.225. 36–46

    work page 2018

  72. [73]

    Angioni et al

    C. Angioni et al. 2017.Nucl. Fusion. 57. 056015

    work page 2017

  73. [74]

    Stober et al

    J. Stober et al. 2003.Nucl. Fusion. 43. 1265–1271

    work page 2003

  74. [75]

    Fischer et al

    R. Fischer et al. 2010.Fusion Science and Technology. 58. 675–684

    work page 2010

  75. [76]

    Fischer et al

    R. Fischer et al. 2008.Plasma Phys. Control. Fusion. 50. 085009

    work page 2008

  76. [77]

    Mlynek et al

    A. Mlynek et al. 2010.Review of Scientific Instruments. 81. 033507

    work page 2010

  77. [78]

    Murmann et al

    H. Murmann et al. 1992.Review of Scientific Instruments. 63. 4941–4943

    work page 1992

  78. [79]

    Fischer et al

    R. Fischer et al. 2020.Fusion Science and Technology. 76. 879–893

    work page 2020

  79. [80]

    Angioni et al

    C. Angioni et al. 2005.Physics of Plasmas. 12. 040701

    work page 2005

  80. [81]

    Fable et al

    E. Fable et al. 2008.AIP Conference Proceedings. 1069. 64–75

    work page 2008

Showing first 80 references.