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arxiv: 2605.16659 · v1 · pith:VGIGGG72new · submitted 2026-05-15 · ❄️ cond-mat.mtrl-sci · physics.app-ph· physics.comp-ph

Non-linear diffusion and inhomogeneity of the magnetic field in single-turn coils: Insights from 3D multiphysics modeling

Hideaki Kobayashi , Yugaku Goyo , Yuto Ishii , Yasuhiro H. Matsuda , Kunio Takekoshi , Akihiko Ikeda This is my paper

Pith reviewed 2026-05-20 15:45 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.app-phphysics.comp-ph
keywords single-turn coilpulsed high magnetic fieldnonlinear diffusionmultiphysics simulationfinite element analysismagnetic field inhomogeneitycoil deformation
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The pith

A fully 3D multiphysics model shows that nonlinear diffusion of current, heat, and magnetic fields creates strong spatial and temporal inhomogeneities inside single-turn coils.

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

Single-turn coils produce magnetic fields above 100 tesla in pulses of only a few microseconds but destroy themselves through explosion. The paper performs finite element calculations on a complete three-dimensional geometry that includes broken cylindrical symmetry to track the coupled electrical, thermal, and mechanical evolution. The results demonstrate that electric current, temperature, and magnetic field all propagate in highly nonlinear ways driven by skin effect, rapid heating, and deformation. These nonlinear processes are the direct cause of the observed inhomogeneity of the magnetic field both in space and across the short time scale of the pulse.

Core claim

The calculated result revealed highly nonlinear diffusion of electric current, temperature, and magnetic fields, which are the sources of the inhomogeneous magnetic fields inside the single-turn coil in time and space.

What carries the argument

A fully 3D finite element multiphysics model of the single-turn coil with broken cylindrical symmetry.

If this is right

  • The magnetic field inside the coil varies strongly with position and changes rapidly during the pulse.
  • Skin effect, temperature rise, and mechanical deformation together produce the dominant inhomogeneities.
  • Two-dimensional models miss essential features of the field distribution that only appear in three dimensions.
  • The simulation identifies the internal mechanisms that govern performance limits in these destructive pulsed magnets.

Where Pith is reading between the lines

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

  • The same modeling framework could guide iterative design changes to reduce unwanted field variations before fabrication.
  • Local field measurements taken during actual coil shots would provide a direct test of the predicted nonlinear patterns.
  • Comparable three-dimensional coupled simulations may prove necessary for other short-pulse electromagnetic systems that involve rapid heating and symmetry breaking.

Load-bearing premise

The fully 3D multiphysics model with chosen material properties accurately represents the real exploding coil without reported experimental validation.

What would settle it

Direct experimental mapping of the magnetic field distribution inside the coil during the pulse that either matches or deviates from the simulated spatial and temporal patterns.

Figures

Figures reproduced from arXiv: 2605.16659 by Akihiko Ikeda, Hideaki Kobayashi, Kunio Takekoshi, Yasuhiro H. Matsuda, Yugaku Goyo, Yuto Ishii.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The photos of the single turn coils of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The finite element model of a single turn coil of the diameter [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The representative result of the calculation in the 120 T generation using the 750 kA current. The cross-sectional view of the neck [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The time evolution of the current distribution, electrical conductivity, temperature, pressure, and displacement of each finite element [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Quantitative time-evolution of electric current density, resistivity, temperature, pressure, and displacement measured at representative [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The distribution of the generated magnetic field inside the single-turn coil at 0.3 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The line profles of the spatial distribution of the generated magnetic field by the single-turn coil. The time-dependence of the magnetic [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

The single-turn coil method is a destructive pulsed magnet for generating over 100 T with a few $\mu$-second pulse duration, and it inevitably causes the coil to explode. The temporal and spatial distributions of the electric current and magnetic field are highly inhomogeneous, arising from the skin effect, rapid temperature rise, and coil deformation. To grasp the dynamic phenomena in the single-turn coil, we conducted a finite element analysis using multiphysics simulation. We employed finite element method calculations using a fully 3D model of the single-turn coil with broken cylindrical symmetry. The calculated result revealed highly nonlinear diffusion of electric current, temperature, and magnetic fields, which are the sources of the inhomogeneous magnetic fields inside the single-turn coil in time and space.

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

2 major / 1 minor

Summary. The paper presents a fully 3D multiphysics finite-element simulation of a single-turn coil for generating pulsed fields above 100 T. It reports that nonlinear diffusion of current, temperature rise, and magnetic field, together with coil deformation, produce strong spatial and temporal inhomogeneities inside the coil.

Significance. If the model faithfully reproduces the real dynamics, the work supplies useful mechanistic insight into the sources of field inhomogeneity in destructive single-turn magnets. The choice of a symmetry-broken 3D geometry is appropriate for capturing realistic behavior. However, the complete absence of experimental validation or numerical-convergence diagnostics limits the result to an untested model output rather than a demonstrated physical mechanism.

major comments (2)
  1. Abstract and results section: the central claim that nonlinear diffusion of current, temperature, and B-field are the sources of observed inhomogeneity rests entirely on forward simulation outputs. No mesh-convergence study, error estimates, or direct comparison to measured B-field traces, current waveforms, or post-shot coil geometry is reported, leaving open the possibility that the reported nonlinearities are dominated by modeling assumptions rather than physical behavior.
  2. Methods / material-properties section: the constitutive relations and temperature-dependent material parameters for the exploding coil are stated without benchmark against independent experimental data (e.g., resistivity vs. temperature curves or high-strain-rate mechanical response). Because these choices directly control the skin-effect evolution and thermal expansion, they are load-bearing for the inhomogeneity conclusion.
minor comments (1)
  1. Figure captions and axis labels should explicitly state the time instants shown and the normalization used for the magnetic-field maps to improve readability.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive and detailed review of our manuscript. We have addressed each major comment below and revised the manuscript accordingly where feasible.

read point-by-point responses

  1. Referee: Abstract and results section: the central claim that nonlinear diffusion of current, temperature, and B-field are the sources of observed inhomogeneity rests entirely on forward simulation outputs. No mesh-convergence study, error estimates, or direct comparison to measured B-field traces, current waveforms, or post-shot coil geometry is reported, leaving open the possibility that the reported nonlinearities are dominated by modeling assumptions rather than physical behavior.

    Authors: We agree that a mesh-convergence study and error estimates would strengthen the presentation of the results. In the revised manuscript we have added a new subsection in the Methods section that documents the mesh refinement procedure and shows that the reported spatial and temporal inhomogeneities in current, temperature, and magnetic field converge with increasing mesh density; quantitative error estimates based on successive refinements are now included. We also agree that direct experimental comparisons would be desirable. Because the present work is a computational study whose primary goal is to elucidate mechanisms through 3D multiphysics modeling, we did not generate new experimental data. We have expanded the Discussion to explicitly acknowledge this limitation and to outline how future combined simulation-experiment campaigns could test the predicted inhomogeneities. We maintain that the nonlinear diffusion follows directly from the standard electromagnetic, thermal, and mechanical governing equations implemented in the model, but we have added clarifying text on the modeling assumptions to address the referee's concern. revision: partial

  2. Referee: Methods / material-properties section: the constitutive relations and temperature-dependent material parameters for the exploding coil are stated without benchmark against independent experimental data (e.g., resistivity vs. temperature curves or high-strain-rate mechanical response). Because these choices directly control the skin-effect evolution and thermal expansion, they are load-bearing for the inhomogeneity conclusion.

    Authors: We acknowledge that the material models are central to the predicted behavior. The temperature-dependent resistivity, specific heat, and high-strain-rate mechanical response for copper were taken from established literature values commonly used in pulsed-magnet simulations. In the revised manuscript we have added explicit citations to the original sources of these constitutive relations and have inserted a short benchmarking paragraph that compares the adopted resistivity-versus-temperature curve to independent experimental data reported in the literature. We have further included a brief sensitivity study showing how moderate variations in the key parameters affect the magnitude of the field inhomogeneity, thereby quantifying the robustness of the conclusions to the chosen material models. revision: yes

standing simulated objections not resolved
  • Direct experimental validation against measured B-field waveforms or post-shot coil geometries, which would require laboratory experiments outside the scope of the present numerical study.

Circularity Check

0 steps flagged

No circularity: forward multiphysics FEM simulation from standard equations

full rationale

The paper sets up and solves a fully 3D finite-element multiphysics model coupling Maxwell's equations, heat conduction, and mechanical deformation for the exploding single-turn coil. The reported nonlinear diffusion of current, temperature, and B-field, together with the resulting spatial inhomogeneity, are direct numerical outputs of that solved system given the chosen geometry, material properties, and constitutive relations. No parameter is fitted to a data subset and then relabeled as a prediction; no quantity is defined in terms of itself; no uniqueness theorem or ansatz is imported via self-citation to force the result; and the central claim does not reduce to any prior author work by construction. The derivation chain is therefore self-contained as a standard forward application of FEM to coupled PDEs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The simulation depends on temperature-dependent conductivity and mechanical properties of the coil material plus boundary conditions for current injection and mechanical constraints; these are standard domain assumptions but not independently verified in the provided abstract.

axioms (2)
  • domain assumption Material properties (electrical conductivity, thermal conductivity, mechanical moduli) are known functions of temperature and can be used directly in the coupled solver.
    Invoked implicitly when setting up the multiphysics finite-element model of the exploding coil.
  • domain assumption The 3D geometry with broken cylindrical symmetry is a faithful representation of the physical single-turn coil.
    Stated in the description of the fully 3D model.

pith-pipeline@v0.9.0 · 5692 in / 1338 out tokens · 48399 ms · 2026-05-20T15:45:04.293388+00:00 · methodology

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Works this paper leans on

51 extracted references · 51 canonical work pages

  1. [1]

    In the 0.3𝜇s panel, the electric current is predominantly concentrated at the two edges of the inner surface of the single-turn coil

    The clear difference in the electric current distribution is observed between the 0.3𝜇s panel and the 1.5𝜇s, which are the early stage (50 T) and the max stage (120 T) of the mag- netic field distribution. In the 0.3𝜇s panel, the electric current is predominantly concentrated at the two edges of the inner surface of the single-turn coil. On the other hand...

    work page 2021

  2. [2]

    Nomura, Y

    T. Nomura, Y. Matsuda, S. Takeyama, A. Matsuo, K. Kindo, J. Her, and T. Kobayashi, Novel Phase of Solid Oxygen Induced by Ultrahigh Magnetic Fields, Phys. Rev. Lett.112, 247201 (2014)

    work page 2014

  3. [3]

    Nomura, Y

    T. Nomura, Y. H. Matsuda, and T. C. Kobayashi, Solid and Liquid Oxygen under Ultrahigh Magnetic Fields, Oxygen2, 152 (2022)

    work page 2022

  4. [4]

    Miyata, H

    A. Miyata, H. Ueda, Y. Ueda, H. Sawabe, and S. Takeyama, Magnetic Phases of a Highly Frustrated Magnet, ZnCr 2O4, up to an Ultrahigh Magnetic Field of 600 T, Phys. Rev. Lett.107, 207203 (2011)

    work page 2011

  5. [5]

    M. Gen, H. Suwa, S. Imajo, C. Dong, H. Ueda, M. Tachibana, A. Ikeda, K. Kindo, and Y. Kohama, Unified Description of Spin-Lattice Coupling and Thermodynamics in the Pyrochlore Heisenberg Antiferromagnet, Phys. Rev. Lett.136, 116702 (2026)

    work page 2026

  6. [6]

    Y. H. Matsuda, D. Nakamura, A. Ikeda, S. Takeyama, Y. Suga, H. Nakahara, and Y. Muraoka, Magnetic-field-induced insulator–metal transition in W-doped VO2 at 500 T, Nat. Com- mun.11, 3591 (2020)

    work page 2020

  7. [7]

    Y. H. Matsuda, K. Yamamura, Y. Ishii, A. Ikeda, H. Sawabe, H. Nakahara, and Y. Muraoka, Magnetic-field- induced insulator-metal transition in V1−𝑥 W𝑥O2 (x = 0.06, 0.12) in magnetic fields of up to 500 T, JJAP Conference Proceedings 12, 011001 (2026)

    work page 2026

  8. [8]

    Nakamura, Y

    D. Nakamura, Y. Matsuda, A. Ikeda, A. Miyake, M. Tokunaga, S. Takeyama, and T. Kanomata, Magnetoconduction in the Cor- related Semiconductor FeSi in Ultrastrong Magnetic Fields up to a Semiconductor-to-Metal Transition, Phys. Rev. Lett.127, 156601 (2021)

    work page 2021

  9. [9]

    T. T. Terashima, A. Ikeda, Y. H. Matsuda, A. Kondo, K. Kindo, and F. Iga, Magnetization Process of the Kondo Insulator YbB12 in Ultrahigh Magnetic Fields, J. Phys. Soc. Jpn.86, 054710 (2017)

    work page 2017

  10. [10]

    Nakamura, A

    D. Nakamura, A. Miyake, A. Ikeda, M. Tokunaga, F. Iga, and Y. H. Matsuda, Closing the hybridization charge gap in the Kondo semiconductor SmB 6 with an ultrahigh magnetic field, Phys. Rev. B105, L241105 (2022)

    work page 2022

  11. [11]

    Ikeda, T

    A. Ikeda, T. Nomura, Y. H. Matsuda, A. Matsuo, K. Kindo, and K. Sato, Spin state ordering of strongly correlating LaCoO3 induced at ultrahigh magnetic fields, Phys. Rev. B93, 220401(R) (2016)

    work page 2016

  12. [12]

    Ikeda, Y

    A. Ikeda, Y. H. Matsuda, and K. Sato, Two Spin-State Crystal- lizations in LaCoO3, Phys. Rev. Lett.125, 177202 (2020)

    work page 2020

  13. [13]

    Ikeda, Y

    A. Ikeda, Y. H. Matsuda, K. Sato, Y. Ishii, H. Sawabe, D. Naka- mura, S. Takeyama, and J. Nasu, Signature of spin-triplet exciton condensations in LaCoO3 at ultrahigh magnetic fields up to 600 T, Nat. Commun.14, 1744 (2023)

    work page 2023

  14. [14]

    Y. H. Matsuda, N. Abe, S. Takeyama, H. Kageyama, P. Corboz, A. Honecker, S. R. Manmana, G. R. Foltin, K. P. Schmidt, and F. Mila, Magnetization of SrCu2(BO3)2 in Ultrahigh Magnetic Fields up to 118 T, Phys. Rev. Lett.111, 137204 (2013)

    work page 2013

  15. [15]

    Nomura, P

    T. Nomura, P. Corboz, A. Miyata, S. Zherlitsyn, Y. Ishii, Y. Ko- hama, Y. H. Matsuda, A. Ikeda, C. Zhong, H. Kageyama, and F. Mila, Unveiling new quantum phases in the Shastry- Sutherland compound SrCu 2(BO3)2 up to the saturation mag- netic field, Nat. Commun.14, 3769 (2023)

    work page 2023

  16. [16]

    Kohama, F

    Y. Kohama, F. Nabeshima, A. Maeda, A. Ikeda, and Y. H. Matsuda, Direct measurement of resistivity in destructive pulsed magnetic fields, Rev. Sci. Instrum.91, 033901 (2020)

    work page 2020

  17. [17]

    Shitaokoshi, S

    T. Shitaokoshi, S. Kawachi, T. Nomura, F. F. Balakirev, and Y. Kohama, Radio frequency electrical resistance measurement under destructive pulsed magnetic fields, Rev. Sci. Instrum.94, 094706 (2023)

    work page 2023

  18. [18]

    Peng, X.-G

    S. Peng, X.-G. Zhou, Y. H. Matsuda, Q. Chen, M. Tokunaga, Y. Ishii, S. Awaji, T. Kato, T. Arita, and Y. Yoshida, Longitudinal magnetoresistance in YBa2Cu3O7 at high magnetic fields up to 100 T, Supercond. Sci. Technol.38, 075012 (2025)

    work page 2025

  19. [19]

    Takeyama, R

    S. Takeyama, R. Sakakura, Y. H. Matsuda, A. Miyata, and M. Tokunaga, Precise Magnetization Measurements by Paral- lel Self-Compensated Induction Coils in a Vertical Single-Turn Coil up to 103 T, J. Phys. Soc. Jpn.81, 014702 (2012)

    work page 2012

  20. [20]

    M. Gen, A. Ikeda, K. Aoyama, H. O. Jeschke, Y. Ishii, H. Ishikawa, T. Yajima, Y. Okamoto, X. Zhou, D. Nakamura, S. Takeyama, K. Kindo, Y. H. Matsuda, and Y. Kohama, Signa- tures of a magnetic superstructure phase induced by ultrahigh magnetic fields in a breathing pyrochlore antiferromagnet, Proc. Natl. Acad. Sci. U.S.A.120, e2302756120 (2023)

    work page 2023

  21. [21]

    Rodriguez, M

    G. Rodriguez, M. Jaime, F. Balakirev, C. H. Mielke, A. Azad, B. Marshall, B. M. La Lone, B. Henson, and L. Smilowitz, Co- herent pulse interrogation system for fiber Bragg grating sensing of strain and pressure in dynamic extremes of materials, Opt. Express.23, 14219 (2015)

    work page 2015

  22. [22]

    Ikeda, T

    A. Ikeda, T. Nomura, Y. H. Matsuda, S. Tani, Y. Kobayashi, H. Watanabe, and K. Sato, High-speed 100 MHz strain monitor using fiber Bragg grating and optical filter for magnetostric- tion measurements under ultrahigh magnetic fields, Rev. Sci. Instrum.88, 083906 (2017). 9

    work page 2017

  23. [23]

    Nomura, A

    T. Nomura, A. Hauspurg, D. I. Gorbunov, A. Miyata, E. Schulze, S. A. Zvyagin, V. Tsurkan, Y. H. Matsuda, Y. Kohama, and S. Zherlitsyn, Ultrasound measurement technique for the single- turn-coil magnets, Rev. Sci. Instrum.92, 063902 (2021)

    work page 2021

  24. [24]

    P. Chiu, Y. Ishii, and Y. H. Matsuda, Development of techniques for the dielectric constant measurement in matter in ultrahigh magnetic fields exceeding 100 T, J. Appl. Phys.137, 155903 (2025)

    work page 2025

  25. [25]

    M. Gen, A. Ikeda, S. Kawachi, T. Shitaokoshi, Y. H. Matsuda, Y. Kohama, and T. Nomura, Higher magnetic-field generation by a mass-loaded single-turn coil, Rev. Sci. Instrum.92, 033902 (2021)

    work page 2021

  26. [26]

    Ishii, W

    Y. Ishii, W. Xiaochen, O. Byungkwon, H. Yubo, Y. Urabe, H. Kobayashi, A. Ikeda, and Y. H. Matsuda, Single turn coil with a slit, JJAP Conference Proceedings12, 011016 (2026)

    work page 2026

  27. [27]

    Herlach, Pulsed magnets, Rep

    F. Herlach, Pulsed magnets, Rep. Prog. Phys.62, 859 (1999)

    work page 1999

  28. [28]

    Nakamura, A

    D. Nakamura, A. Ikeda, H. Sawabe, Y. H. Matsuda, and S. Takeyama, Record indoor magnetic field of 1200 T gener- ated by electromagnetic flux-compression, Rev. Sci. Instrum. 89, 095106 (2018)

    work page 2018

  29. [29]

    Ikeda, Y

    A. Ikeda, Y. H. Matsuda, X. Zhou, S. Peng, Y. Ishii, T. Yajima, Y. Kubota, I. Inoue, Y. Inubushi, K. Tono, and M. Yabashi, Gen- erating 77 T using a portable pulse magnet for single-shot quan- tum beam experiments, Appl. Phys. Lett.120, 142403 (2022)

    work page 2022

  30. [30]

    Ikeda, Y

    A. Ikeda, Y. Kubota, Y. Ishii, X. Zhou, S. Peng, H. Hayashi, Y. H. Matsuda, K. Noda, T. Tanaka, K. Shimbori, K. Seki, H. Kobayashi, D. Bhoi, M. Gen, K. Gautam, M. Akaki, S. Kawachi, S. Kasamatsu, T. Nomura, Y. Inubushi, and M. Yabashi, X-Ray Free-Electron Laser Observation of Giant and Anisotropic Magnetostriction in𝛽-O 2 at 110 Tesla, Phys. Rev. Lett.135...

    work page 2025

  31. [31]

    Herlach, R

    F. Herlach, R. McBroom, T. Erber, J. Murray, and R. Gearhart, Experiments with Megagauss Targets at SLAC, IEEE Transac- tions on Nuclear Science18, 809 (1971)

    work page 1971

  32. [32]

    Herlach and R

    F. Herlach and R. McBroom, Megagauss fields in single turn coils, J. Phys. E: Sci. Instrum.6, 652 (1973)

    work page 1973

  33. [33]

    Herlach, J

    F. Herlach, J. Davis, R. Schmidt, and H. Spector, Cyclotron resonance in InSb and GaAs with magnetic fields up to 140 T, Phys. Rev. B10, 682 (1974)

    work page 1974

  34. [34]

    Nakao, F

    K. Nakao, F. Herlach, T. Goto, S. Takeyama, T. Sakakibara, and N. Miura, A laboratory instrument for generating magnetic fields over 200 T with single-turn coils, J. Phys. E: Sci. Instrum. 18, 1018 (1985)

    work page 1985

  35. [35]

    Takeyama, K

    S. Takeyama, K. Amaya, T. Nakagawa, M. Ishizuka, K. Nakao, T. Sakakibara, T. Gotot, N. Miura, Y. Ajiro, and H. Kikuchi, Magnetisation measurements in ultra-high magnetic fields pro- duced by a single-turn coil system, J. Phys. E: Sci. Instrum.21, 1025 (1988)

    work page 1988

  36. [36]

    Sakakibara, T

    T. Sakakibara, T. Goto, K. Yoshimura, and K. Fukamichi, Itin- erant electron metamagnetism and spin fluctuations in nearly ferromagnetic metals Y(Co1−𝑥 Al𝑥)2, J. Phys.: Condens. Matter 2, 3381 (1990)

    work page 1990

  37. [37]

    Aruga Katori, Y

    H. Aruga Katori, Y. Ajiro, T. Asano, and T. Goto, Nonlinear Magnetization of a Quasi-One-Dimensional Triangular-Lattice Antiferromagnet CsNiCl3 up to 110 Tesla, J. Phys. Soc. Jpn.64, 3038 (1995)

    work page 1995

  38. [38]

    Portugall, N

    O. Portugall, N. Puhlmann, H. U. M¨ uller, M. Barczewski, I. Stolpe, M. Thiede, H. Scholz, M. v. Ortenberg, and F. Herlach, The design and performance of a transportable low-cost instru- ment for the generation and application of megagauss fields, J. Phys. D: Appl. Phys.30, 1697 (1997)

    work page 1997

  39. [39]

    Puhlmann, O

    N. Puhlmann, O. Portugall, H. U. M. ller, M. Barczewski, I. Stolpe, and M. v. Ortenberg, Solid state applications of a transportable low-cost megagauss generator, J. Phys. D: Appl. Phys.30, 1861 (1997)

    work page 1997

  40. [40]

    Herlach, Megagauss magnetic fields, Rep

    F. Herlach, Megagauss magnetic fields, Rep. Prog. Phys.31, 341 (1968)

    work page 1968

  41. [41]

    Miura and K

    N. Miura and K. Nakao, Computer analysis of megagauss field generation by condenser bank discharge, Jpn. J. Appl. Phys.29, 1580 (1990)

    work page 1990

  42. [42]

    Nakamura, H

    D. Nakamura, H. Sawabe, and S. Takeyama, Note: Experimental evidence of three-dimensional dynamics of an electromagneti- cally imploded liner, Rev. Sci. Instrum.85, 036102 (2014)

    work page 2014

  43. [43]

    A. Ge, S. Wang, Z. Pan, and T. Peng, Thermal–electrical cou- pling analysis based on solid–liquid phase transition theory of single-turn coil, J. Appl. Phys.134, 224902 (2023)

    work page 2023

  44. [44]

    A. Ge, N. Wang, Z. Kang, Y. Huang, Z. Liu, H. Yang, Y. Lv, L. Li, and T. Peng, Dynamic modeling of air–metal plasma mixture of single-turn coil with erosion at megaGauss magnetic field, Physics of Fluids36, 116120 (2024)

    work page 2024

  45. [45]

    A. Ge, Z. Pan, Y. Lv, and T. Peng, A self-consistent unified solid- multiphase flow shock model under complex thermodynamic states: For the application of mass-loaded single-turn coils, Physics of Fluids36, 077124 (2024)

    work page 2024

  46. [46]

    A. Ge, Q. Wang, L. Li, Y. Lv, and T. Peng, Numerical study of plasma and air heating process in single-turn coil discharges, Physics of Fluids36, 127113 (2024)

    work page 2024

  47. [47]

    A. Ge, Z. Pan, Z. Liu, H. Yang, Y. Lv, and T. Peng, Shock dynamics model based on the conductor hardening and ther- mal softening effects for single-turn coil, Phys. Scr.99, 105545 (2024)

    work page 2024

  48. [48]

    A. Ge, Z. Pan, S. Liu, H. Shang, Y. Huang, Y. Lv, and T. Peng, Modelling of the conductor vaporization process for single-turn coil, Phys. Scr.99, 075539 (2024)

    work page 2024

  49. [49]

    A. Ge, Z. Pan, S. Liu, Y. Lv, and T. Peng, The transient discharge circuit analysis of single-turn coil, J. Appl. Phys.135, 0204003 (2024)

    work page 2024

  50. [50]

    A. Ge, Z. Pan, Z. Liu, H. Yang, Y. Lv, and T. Peng, Design of magnetic field with high homogeneity for single-turn coil, Phys. Scr.100, 015515 (2025)

    work page 2025

  51. [51]

    A. Ge, Z. Kang, N. Wang, Y. Lv, L. Li, T. Peng, and J. Chen, Complete electromagnetic-thermal-dynamic-damage modelling and equation of state for tantalum single-turn coil, Phys. Scr.100, 065520 (2025)

    work page 2025