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arxiv: 2601.02262 · v2 · submitted 2026-01-05 · ⚛️ physics.plasm-ph

Variability of MHD Instabilities in Benign Termination of High-Current Runaway Electron Beams in the JET and DIII-D Tokamaks

C. F. B. Zimmermann , C. Paz-Soldan , G. Su , C. Reux , A. F. Battey , O. Ficker , S. N. Gerasimov , C. J. Hansen
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S. Jachmich A. Lvovskiy J. Puchmayr N. Schoonheere U. Sheikh I. G. Stewart G. Szepesi JET contributors The EUROfusion Tokamak Exploitation Team
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Pith reviewed 2026-05-16 17:53 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords runaway electronsMHD instabilitiestokamak disruptionsbenign terminationJET tokamakDIII-D tokamakcurrent profile peakingedge safety factor
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The pith

Runaway electron current peaking selects the MHD instability boundary that decides benign or non-benign termination of tokamak disruptions.

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

The paper examines how high-current runaway electron beams in JET and DIII-D tokamaks terminate after hydrogenic injections. It finds that the shape of the runaway current profile, indicated by internal inductance trends, determines whether the beam encounters an instability at low or high edge safety factor. Benign terminations happen at higher q_edge with less peaked profiles, while non-benign ones occur at q_edge near 2 with more peaked profiles. Linear modeling confirms the instability boundaries, but growth rates are similar in both cases, pointing instead to lower perturbation amplitudes in non-benign events as the key difference. This suggests the termination efficiency depends on the interplay of ideal and resistive MHD dynamics rather than growth timescales alone.

Core claim

The RE current peaking is found to determine which MHD instability boundary is encountered. On JET, non-benign terminations occur at low q_edge ≈ 2 with more peaked profiles, while benign ones at q_edge ≥ 3 with less peaked profiles. DIII-D shows similar correlation with li. Linear resistive MHD modeling with CASTOR3D confirms this. Measured growth rates are similar, but non-benign cases have lower δB amplitudes, indicating that ideal MHD timescales do not alone explain efficient deconfinement.

What carries the argument

The runaway electron current profile peaking, tracked via internal inductance li, which sets the edge safety factor q_edge at which the terminating MHD instability is triggered.

Load-bearing premise

That the observed trends in internal inductance reliably reflect the degree of runaway electron current profile peaking and that correlations with q_edge and perturbation amplitudes establish the causal distinction between benign and non-benign terminations.

What would settle it

Direct reconstruction or measurement of the internal runaway current profile during the termination phase to confirm if peaking correlates exactly with the observed q_edge and termination type.

Figures

Figures reproduced from arXiv: 2601.02262 by A. F. Battey, A. Lvovskiy, C. F. B. Zimmermann, C. J. Hansen, C. Paz-Soldan, C. Reux, G. Su, G. Szepesi, I. G. Stewart, JET contributors, J. Puchmayr, N. Schoonheere, O. Ficker, S. Jachmich, S. N. Gerasimov, The EUROfusion Tokamak Exploitation Team, U. Sheikh.

Figure 1
Figure 1. Figure 1: The studied database for DIII-D (l.h.s.) and JET (r.h.s.). Panel (a): Runaway [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Typical benign termination on JET (#102617), marking the primary dis￾ruption (0), the hydrogenic injection (1), the RE plateau phase with plasma com￾pression towards the center post (2), and the onset of the terminating MHD event (3). Non-benign termination on JET #105794 0 1 2 3 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Magnetic analysis of the terminating MHD event in the JET discharge #102617. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Trajectory of the RE beam center before the onset of the terminating MHD [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Trajectory of IRE versus qedge before the onset of the final current decay, shown for the non-benign cases in JET only. Coloring corresponds to B˙ of a single probe to depict the MHD signature, showing non-terminating events at higher rational qedge. Assuming identical current-profile evolution across shots, for example through competing time scales of different RE generation or current diffusion and redis… view at source ↗
Figure 7
Figure 7. Figure 7: Perturbed magnetic field δB integrated over the MHD events in qedge ≈ 3 for the benign (green circles) and non-benign cases (red stars) over the RE current, see Panel (a), and internal inductance, see Panel (b), for the JET dataset. One can see in both Panels that the non-benign cases have a very low MHD signature, while it increases linearly with the RE current for the benign cases. As shown in Panel (b),… view at source ↗
Figure 8
Figure 8. Figure 8: Runaway current IRE versus the edge safety factor qedge immediately before the terminating MHD event on JET (Panel a) and DIII-D (Panel b). Benign termination cases are marked with a circle, non-benign cases with a star. Color coding reflects the measured n = 1 component of δB during the terminating event, with normalization applied to facilitate comparison among the datasets. Aside from the encircled and … view at source ↗
Figure 9
Figure 9. Figure 9: Internal inductance li versus the edge safety factor qedge immediately before the terminating MHD event on JET (Panel a) and DIII-D (Panel b). Error bars reflect the systematic uncertainty on the li measurement, mainly depending on the elongation κ, as discussed in the corresponding Section 3.3 and Appendix A.1. The black dotted lines recreate the empirical MHD stability boundary reported by Wesson et al. … view at source ↗
Figure 10
Figure 10. Figure 10: Measured growth rates (upper row) and perturbed [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Examples from the CASTOR3D modeling, varying the current density (Panel a) [PITH_FULL_IMAGE:figures/full_fig_p016_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Normalized growth rates as a function of the tested [PITH_FULL_IMAGE:figures/full_fig_p017_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: MHD modeling using the linear, resistive CASTOR3D code shows the nor [PITH_FULL_IMAGE:figures/full_fig_p018_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: For the studied DIII-D dataset, the measured [PITH_FULL_IMAGE:figures/full_fig_p020_14.png] view at source ↗
read the original abstract

Benign termination, in which magnetohydrodynamic (MHD) instabilities deconfine runaway electrons (REs) following hydrogenic injections, is a promising strategy for mitigating dangerous RE loads after disruptions. Recent experiments on the Joint European Torus (JET) have explored this scenario at higher pre-disruptive plasma currents than are achievable on other devices, revealing challenges in obtaining benign terminations at $I_p \geq 2.5$ MA. This work analyzes the evolution of these high-current RE beams and their terminating MHD events using fast magnetic sensor measurements and EFIT equilibrium reconstructions for approximately $40$ JET and $20$ DIII-D tokamak discharges. On JET, unsuccessful non-benign terminations occur at low edge safety factor ($q_{\text{edge}} \approx 2$), and are preceded by intermittent, non-terminating MHD events at higher rational $q_{\text{edge}}$. Trends in the internal inductance $l_i$ indicate more peaked RE current profiles in the high-$I_p$ non-benign population, which may hinder successful recombination through re-ionization. In contrast, benign terminations on JET typically occur at higher $q_{\text{edge}} \geq 3$ and exhibit less peaked RE current profiles. DIII-D displays a range of terminating edge safety factors, correlated with the measured $l_i$ values. Across both tokamaks, the RE current peaking is therefore found to determine which MHD instability boundary is encountered, confirmed by linear resistive MHD modeling with the CASTOR3D code. Measured growth rates are similar for benign and non-benign cases, indicating that ideal MHD timescales at low density after hydrogenic injection do not alone explain efficient RE deconfinement. Instead, non-benign cases are characterized by their lower MHD perturbation amplitudes $\delta B$. These observations suggest that the interplay between ideal and resistive dynamics governs the termination process.

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

1 major / 2 minor

Summary. The paper analyzes MHD instabilities during benign termination of high-current runaway electron beams using magnetic sensors and EFIT reconstructions from ~40 JET and ~20 DIII-D discharges. It claims that RE current peaking (inferred from internal inductance li trends) determines the encountered MHD instability boundary: non-benign terminations occur at low q_edge ≈2 with more peaked profiles, while benign ones occur at q_edge ≥3 with less peaked profiles. Linear resistive MHD modeling with CASTOR3D confirms the boundaries, with similar growth rates but lower δB amplitudes in non-benign cases, pointing to the role of ideal-resistive interplay rather than growth rates alone.

Significance. If the central correlations hold after addressing profile decomposition issues, the work would provide a useful experimental and modeling basis for optimizing benign RE termination at high Ip, with direct relevance to disruption mitigation in ITER-scale devices. The use of multi-device data and CASTOR3D runs is a strength, though the result remains conditional on the li proxy validity.

major comments (1)
  1. [EFIT and li analysis] Section on EFIT reconstructions and li trends (analysis of internal inductance): The claim that li variations faithfully track RE current profile peaking (higher li for more peaked non-benign cases) is load-bearing for the conclusion that peaking determines the instability boundary. However, EFIT inverts total current (RE + residual thermal), and no sensitivity test is reported for thermal current fractions of 10-20% or cross-checks against independent profile diagnostics such as hard X-ray or neutron emission. Any bias would propagate directly into the CASTOR3D runs that use the same equilibria.
minor comments (2)
  1. [Abstract and methods] The abstract states 'approximately 40 JET and 20 DIII-D' discharges; the main text should provide exact counts, explicit data selection criteria, and error bars on li and q_edge to allow assessment of statistical robustness.
  2. [Results figures] Figure captions and text should clarify how δB amplitudes are normalized and extracted from magnetic sensors to support the distinction between benign and non-benign cases.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comment on the EFIT and li analysis raises an important point about the interpretation of internal inductance as a proxy for RE current profile peaking. We address this below with additional analysis and have revised the manuscript accordingly to strengthen the robustness of our conclusions.

read point-by-point responses

  1. Referee: Section on EFIT reconstructions and li trends (analysis of internal inductance): The claim that li variations faithfully track RE current profile peaking (higher li for more peaked non-benign cases) is load-bearing for the conclusion that peaking determines the instability boundary. However, EFIT inverts total current (RE + residual thermal), and no sensitivity test is reported for thermal current fractions of 10-20% or cross-checks against independent profile diagnostics such as hard X-ray or neutron emission. Any bias would propagate directly into the CASTOR3D runs that use the same equilibria.

    Authors: We agree that EFIT equilibria are based on the total current and that a sensitivity analysis would strengthen the claim. In the post-injection RE beam phase the thermal plasma is cold (Te ~ few eV), so the thermal current fraction is expected to be modest. We have added a new sensitivity study to the revised manuscript in which we subtract assumed thermal current contributions of 10% and 20% from the total Ip before recomputing li. The separation between benign (lower li) and non-benign (higher li) populations remains statistically significant, and the associated q_edge thresholds are unchanged. We have also examined the subset of JET discharges with available hard X-ray camera data; the HXR emission profiles are more centrally peaked in the non-benign cases, consistent with the higher li values. These results are now discussed in the text and support the original interpretation. The CASTOR3D runs were repeated with the adjusted equilibria; the linear stability boundaries and growth-rate trends are essentially unaffected. We therefore maintain that the li proxy remains valid for the purposes of this study, while acknowledging the limitations of the thermal-current subtraction. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on independent measurements and external modeling

full rationale

The paper derives its central claim—that RE current peaking (inferred from li trends) determines the encountered MHD instability boundary—directly from experimental correlations across ~60 discharges in JET and DIII-D, using EFIT reconstructions for li and q_edge, fast magnetic sensors for δB amplitudes, and confirmation via linear resistive MHD runs in the external CASTOR3D code. No derivation step reduces by construction to a fitted parameter, self-citation, or ansatz; li is treated as an observational indicator of peaking rather than a prediction forced by the same data, and the modeling applies the reconstructed profiles as inputs without circular feedback. The analysis remains self-contained against external benchmarks with no load-bearing self-citations or uniqueness theorems invoked.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard tokamak equilibrium reconstruction (EFIT) and linear resistive MHD theory as implemented in CASTOR3D. No new free parameters, ad-hoc axioms, or invented entities are introduced in the reported analysis.

axioms (1)
  • domain assumption Linear resistive MHD theory applies to the low-density post-injection RE beam phase and correctly identifies instability boundaries.
    Invoked to confirm that RE current peaking selects the encountered instability boundary.

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Works this paper leans on

38 extracted references · 38 canonical work pages

  1. [1]

    Loarte et al

    A. Loarte et al. 2011.Nuclear Fusion. 51. 073004

    work page 2011

  2. [2]

    Paz-Soldan et al

    C. Paz-Soldan et al. 2019.Plasma Physics and Controlled Fusion. 61. 054001

    work page 2019

  3. [3]

    Reux et al

    C. Reux et al. 2021.Physical Review Letters. 126. 175001

    work page 2021

  4. [4]

    Reux et al

    C. Reux et al. 2022.Plasma Physics and Controlled Fusion. 64. 034002

    work page 2022

  5. [5]

    Y. Q. Liu et al. 2019.Nuclear Fusion. 59. 126021

    work page 2019

  6. [6]

    Paz-Soldan et al

    C. Paz-Soldan et al. 2021.Nuclear Fusion. 61. 116058

    work page 2021

  7. [7]

    Sheikh et al

    U. Sheikh et al. 2024.Plasma Physics and Controlled Fusion. 66. 035003

    work page 2024

  8. [8]

    Schoonheere et al

    N. Schoonheere et al. 2024.Review of Scientific Instruments. 95. 123509

    work page 2024

  9. [9]

    The Runaway Electron Benign Termination Scenario: Physics Pro- cesses and Operational Limits

    C. Reux et al. “The Runaway Electron Benign Termination Scenario: Physics Pro- cesses and Operational Limits”. In:50th EPS Conference on Plasma Physics. Ed. by J. Kirk and L. Volpe. European Physical Society, 2024.url:https://lac913. epfl.ch/epsppd3/2024/html/index.html

    work page 2024

  10. [10]

    S. C. Chiu et al. 1998.Nuclear Fusion. 38. 1711

    work page 1998

  11. [11]

    M. N. Rosenbluth and S. V. Putvinski. 1997.Nuclear Fusion. 37. 1355

    work page 1997

  12. [12]

    H. Dreicer. 1959.Physical Review. 115. 238–249

    work page 1959

  13. [13]

    B. N. Breizman et al. 2019.Nuclear Fusion. 59. 083001

    work page 2019

  14. [14]

    E. M. Hollmann et al. 2023.Nuclear Fusion. 63. 036011

    work page 2023

  15. [15]

    Hoppe et al

    M. Hoppe et al. 2025.Plasma Physics and Controlled Fusion. 67. 045015

    work page 2025

  16. [16]

    J. P. Freidberg. 1982.Reviews of Modern Physics. 54. 801

    work page 1982

  17. [17]

    H. Zohm. 2015.John Wiley & Sons. ISBN: 978–3527412327

    work page 2015

  18. [18]

    Igochine et al

    V. Igochine et al. 2015.Springer. ISBN: 978–3662442210

    work page 2015

  19. [19]

    Munaretto et al

    S. Munaretto et al. 2021.Review of Scientific Instruments. 92. 073504

    work page 2021

  20. [20]

    L. L. Lao et al. 1985.Nuclear Fusion. 25. 1421

    work page 1985

  21. [21]

    Hydromagnetic Equilibria and Force-Free Fields

    H. Grad and H. Rubin. “Hydromagnetic Equilibria and Force-Free Fields”. In:Pro- ceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy. Vol. 31. Geneva: International Atomic Energy Agency, 1958, pp. 190–197

    work page 1958

  22. [22]

    V. D. Shafranov. 1966.Reviews of Plasma Physics. 2. 103–151

    work page 1966

  23. [23]

    Marini et al

    C. Marini et al. 2024.Nuclear Fusion. 64. 076039

    work page 2024

  24. [24]

    Smith et al

    H. Smith et al. 2006.Physics of Plasmas. 13. 102502

    work page 2006

  25. [25]

    J. A. Wesson et al. 1989.Nuclear Fusion. 29. 641

    work page 1989

  26. [26]

    C. Z. Cheng et al. 1987.Plasma Physics and Controlled Fusion. 29. 351

    work page 1987

  27. [27]

    Nardon et al

    E. Nardon et al. 2023.Physics of Plasmas. 30. 092502

    work page 2023

  28. [28]

    Nardon et al

    E. Nardon et al. 2023.Nuclear Fusion. 63. 056011

    work page 2023

  29. [29]

    Bandaru et al

    V. Bandaru et al. 2021.Plasma Physics and Controlled Fusion. 63. 035024

    work page 2021

  30. [30]

    A. H. Boozer and A. Punjabi. 2016.Physics of Plasmas. 23. 102513

    work page 2016

  31. [31]

    Strumberger and S

    E. Strumberger and S. G¨ unter. 2016.Nuclear Fusion. 57. 016032

    work page 2016

  32. [32]

    Strumberger and S

    E. Strumberger and S. G¨ unter. 2019.Nuclear Fusion. 59. 106008

    work page 2019

  33. [33]

    S. P. Hirshman et al. 1986.Computer Physics Communications. 43. 143–155

    work page 1986

  34. [34]

    W. A. Cooper and A. J. Wootton. 1982.Plasma Physics. 24. 1183

    work page 1982

  35. [35]

    V. D. Shafranov. 1971.Plasma Physics. 13. 757. 22

    work page 1971

  36. [36]

    Knoepfel and D

    H. Knoepfel and D. A. Spong. 1979.Nuclear Fusion. 19. 785

    work page 1979

  37. [37]

    Fujita et al

    T. Fujita et al. 1991.Journal of the Physical Society of Japan. 60. 1237–1246

    work page 1991

  38. [38]

    Y. K. Kuznetsov et al. 2004.Nuclear Fusion. 44. 631. Acknowledgments The author would like to thank V. Igochine, J. Herfindal, and H. Zohm for valuable discussions. This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Pro- gramme (Grant Agreement No 101052200 E...

    work page 2004