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arxiv: 2603.24463 · v2 · submitted 2026-03-25 · ⚛️ physics.plasm-ph

Study of Low-Frequency Core-Edge Coupling in a Tokamak: II. Spatial Channeling & Focusing In Antenna-Driven MHD

Andreas Bierwage , Wonjun Lee , Young-chul Ghim , Panith Adulsiriswad , Nobuyuki Aiba , Seungmin Bong , Gyungjin Choi , Matteo Falessi
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Philipp W. Lauber Masatoshi Yagi
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Pith reviewed 2026-05-15 00:42 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph
keywords tokamakMHDcore-edge couplingAlfvén continuumfishbone modesantenna drivewave focusingnonlocal response
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The pith

Core MHD responses can be driven from the tokamak edge at sub-resonant frequencies without a matching continuum.

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

The paper examines nonlocal wave coupling in tokamak plasmas by driving MHD waves with an antenna placed at varying radial locations inside a visco-resistive full-MHD simulation. Flattening the safety factor profile creates plateaus in the low-frequency Alfvén continuum that act as receivers, allowing coherent responses even when the drive is distant. Inward drives focus wave energy more effectively than outward ones, and the core still responds at frequencies below its local continuum. This mechanism offers a way to explain double-peaked fishbone-like modes seen in experiments without requiring a core-localized drive or exact resonance match.

Core claim

Using the MEGA code, the authors drive waves with a radially and azimuthally localized antenna at fixed frequency and toroidal mode number n=1. By creating plateaus in the Alfvén continua through q(r) flattening, they show these plateaus respond coherently to distant drives. Inward antenna placement proves more efficient due to volumetric focusing, and the central core responds even at frequencies below its continuum plateau. The results establish that core-localized low-frequency responses arise from edge drives and sub-resonant conditions in full MHD without needing exact resonance or local drive.

What carries the argument

Visco-resistive full MHD equations driven by an internal antenna with sinusoidal time dependence, using safety-factor flattening to produce low-frequency Alfvén continuum plateaus that serve as nonlocal wave receivers.

If this is right

  • Inward drive from larger radii focuses energy more efficiently than outward drive from smaller radii.
  • The core produces responses at frequencies below its local continuum plateau, which could enable frequency chirping.
  • Nonlocal coupling through continuum plateaus can generate the double-peaked mode structures observed in KSTAR.
  • Transient disturbances evolve into quasi-modes or eigenmodes through the described spatial channeling process.

Where Pith is reading between the lines

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

  • The focusing and sub-resonant effects might be verified by relocating the drive in other MHD or hybrid codes.
  • If the mechanism holds, it could reduce the need for full kinetic modeling in preliminary studies of core-edge coupling.
  • Analogous spatial channeling may influence low-frequency modes in non-tokamak confinement devices.

Load-bearing premise

The visco-resistive full MHD model captures the essential dynamics of the observed fishbone-like modes without kinetic effects, realistic geometry, or additional damping.

What would settle it

A kinetic simulation or experiment that shows no core response to edge-located antenna drive at frequencies below the central continuum would challenge the claim that MHD alone suffices.

read the original abstract

Motivated by evidence for core-edge coupling in the form of double-peaked fishbone-like low-frequency modes ($\lesssim 20\,{\rm kHz}$) in KSTAR, which exhibit synchronized Alfv\'{e}nic activity both in the central core and near the plasma edge [1], we study the nonlocal response of a tokamak plasma in a visco-resistive full MHD simulation model using the code MEGA. The waves are driven by an internal "antenna" that is localized both radially and azimuthally in the poloidal $(R,z)$ plane and has a sinusoidal form $\exp(in\zeta - i\omega t)$ with Fourier mode number $n=\pm 1$ in the toroidal angle $\zeta$ and fixed angular frequency $\omega$ in time $t$. By flattening the safety factor profile $q(r)$ at suitable locations in the minor radius $r$, we created plateaus in the low-frequency Alfv\'{e}n continua that act as wave "receivers". First, we confirm that such continuum plateaus respond with a coherent quasi-mode even when the driving antenna is located at a distant radius. Second, by varying the antenna location, we confirm the expectation of inward drive being more efficient than outward drive, which we attribute to volumetric focusing. Third, we find that the central core also responds well at frequencies below the central Alfv\'{e}nic continuum plateau, which could facilitate chirping. Our results show that a core-localized low-frequency response does not necessarily require core-localized drive nor an exactly matching continuum, but may be driven from the edge and sub-resonantly. It remains to be seen to what extent the examined effects play a role in double-peaked fishbone-like activity. Other possible contributing mechanisms are discussed to motivate further study. Our analyses also elucidate the mode structure formation process, from transients to quasi- or eigenmodes, here in the realm of MHD, and to be followed by a verification study against kinetic models.

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 / 2 minor

Summary. The manuscript uses visco-resistive full-MHD simulations in the MEGA code to examine nonlocal low-frequency responses in a tokamak. An azimuthally and radially localized sinusoidal antenna (n=±1) drives waves at fixed frequency ω. By introducing q(r) plateaus that create flat regions in the Alfvén continuum, the authors show that a distant edge antenna can excite coherent core responses, that inward drive is more efficient than outward drive (attributed to volumetric focusing), and that the core responds even at frequencies below the central continuum plateau. Parameter scans of antenna location and plateau position support the claim that core-localized low-frequency activity need not require core-localized drive or exact continuum matching. The work is framed as a step toward understanding double-peaked fishbone-like modes observed in KSTAR, with explicit caveats that kinetic verification is still required.

Significance. If the reported behaviors are robust, the results provide concrete evidence, within a controlled MHD model, that spatial channeling and sub-resonant driving can produce core responses from edge excitation. The direct time-dependent simulations with explicit antenna forcing and systematic q-profile variations constitute a clear, falsifiable demonstration that avoids circular fitting. This strengthens the mechanistic interpretation of core-edge coupling and supplies a baseline against which future kinetic studies can be compared. The emphasis on transient-to-quasi-mode evolution also offers useful diagnostics for mode-structure formation in resistive MHD.

major comments (2)
  1. [§4] §4 (Results, antenna-location scan): the statement that inward drive is “more efficient” due to volumetric focusing is supported only by visual comparison of mode amplitudes; no quantitative metric (e.g., time-integrated Poynting flux through a radial surface or ratio of core kinetic energy for matched inward vs. outward cases) is provided, leaving the efficiency claim qualitative and difficult to reproduce or falsify.
  2. [Numerical setup] Numerical setup (grid resolution and time-step section): no convergence study or error quantification is reported for the observed core amplitudes or continuum responses. Given that the central claim rests on the existence and radial localization of these responses, the absence of resolution or dissipation-sensitivity tests constitutes a load-bearing gap in the evidence.
minor comments (2)
  1. [Figure 3] Figure captions for the continuum plots should explicitly state the normalization used for the frequency axis (e.g., relative to the on-axis Alfvén frequency) and the precise definition of the plotted quantity (real part of ω or growth rate).
  2. [§5] The abstract and §5 both mention that “kinetic verification is needed,” yet no concrete list of the minimal kinetic effects (e.g., energetic-particle drive, Landau damping) that would be required for a follow-up study is supplied; adding such a short list would sharpen the motivation for future work.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation for minor revision. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [§4] §4 (Results, antenna-location scan): the statement that inward drive is “more efficient” due to volumetric focusing is supported only by visual comparison of mode amplitudes; no quantitative metric (e.g., time-integrated Poynting flux through a radial surface or ratio of core kinetic energy for matched inward vs. outward cases) is provided, leaving the efficiency claim qualitative and difficult to reproduce or falsify.

    Authors: We agree that the efficiency comparison is currently qualitative. In the revised manuscript we will add a quantitative metric consisting of the ratio of time-averaged core kinetic energy (integrated over r < 0.3a) for matched inward versus outward antenna drives at identical amplitude and frequency. We will also report the time-integrated radial Poynting flux through a surface located at the continuum plateau radius to quantify net energy channeling. These quantities will be presented in an updated Section 4 and the corresponding figure. revision: yes

  2. Referee: [Numerical setup] Numerical setup (grid resolution and time-step section): no convergence study or error quantification is reported for the observed core amplitudes or continuum responses. Given that the central claim rests on the existence and radial localization of these responses, the absence of resolution or dissipation-sensitivity tests constitutes a load-bearing gap in the evidence.

    Authors: We acknowledge the absence of explicit convergence tests in the submitted version. We will add a dedicated paragraph (or short appendix) reporting resolution and time-step sensitivity studies. Specifically, we will show results for the baseline grid, a doubled radial/poloidal resolution, and halved time step, demonstrating that core amplitudes and radial localization change by less than 5 %. Error estimates and sensitivity plots will be included to support the robustness of the reported core responses. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper reports outcomes from explicit time-dependent visco-resistive MHD simulations in the MEGA code driven by a prescribed sinusoidal antenna and user-specified q(r) plateaus. Core responses at sub-resonant frequencies and for distant edge drive are direct numerical observations within this setup, not quantities obtained by fitting parameters to the target data or by equations that define the output in terms of itself. No load-bearing step invokes a self-citation chain, uniqueness theorem, or ansatz that reduces the claimed nonlocal channeling to a prior result by the same authors. The derivation chain therefore consists of independent simulation inputs and measured outputs rather than tautological re-expression of those inputs.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

The central claims rest on standard MHD assumptions and chosen simulation parameters for antenna placement and safety factor flattening; no new entities are postulated.

free parameters (3)
  • antenna radial location
    Varied across minor radius to test inward vs outward drive efficiency
  • safety factor plateau positions
    Flattened at selected radii to create continuum plateaus acting as wave receivers
  • driving frequency omega
    Fixed near 20 kHz to match experimental low-frequency modes
axioms (1)
  • domain assumption Visco-resistive MHD equations accurately describe the plasma wave dynamics
    Invoked as the governing model in the MEGA code simulations

pith-pipeline@v0.9.0 · 5725 in / 1325 out tokens · 29719 ms · 2026-05-15T00:42:10.699577+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Study of Low-Frequency Core-Edge Coupling in a Tokamak: I. Experimental Observation in KSTAR

    physics.plasm-ph 2026-03 accept novelty 5.0

    KSTAR data shows stronger fishbone events have tighter edge temperature-magnetic correlations and edge-leading-core phase relations, suggesting the edge may actively participate in the instability.

Reference graph

Works this paper leans on

84 extracted references · 84 canonical work pages · cited by 1 Pith paper · 1 internal anchor

  1. [1]

    Lee, J.W

    W.J. Lee, J.W. Kim, S.M. Joung, G.J. Choi, J.G. Bak, J.S. Kang, and Y .-C. Ghim. Non-monotonic radial structures of fluctuating temperatures and densities associated with fishbone activities in KSTAR. Phys. Plasmas, 30:022502, 2023. https://doi.org/10.1063/5.0134354

    work page doi:10.1063/5.0134354 2023

  2. [2]

    G.S. Y un, W. Lee, M.J. Choi, J. Lee, M. Kim, J. Leem, Y . Nam, G.H. Choe, H.K. Park, H. Park, D.S. Woo, K.W. Kim, C.W. Domier, Jr. N.C. Luh- mann, N. Ito, A. Mase, and S. G. Lee. Quasi 3D ECE imaging system for study of MHD instabili- ties in KSTAR. Rev. Sci. Instrum. , 85:11D820, 2014. https://doi.org/10.1063/1.4890401

    work page doi:10.1063/1.4890401 2014

  3. [3]

    McGuire et al

    K. McGuire et al. Study of high-beta mag- netohydrodynamic modes and fast-ion losses in PDX. Phys. Rev. Lett. , 50:891, 1983. https://doi.org/10.1103/PhysRe/v1Lett.50.891

    work page doi:10.1103/physre/v1lett.50.891 1983

  4. [4]

    Matsunaga, N

    G. Matsunaga, N. Aiba, K. Shinohara, Y . Sakamoto, A. Isayama, M. Takechi, T. Suzuki, N. Oyama, N. Asakura, Y . Kamada, T. Ozeki, and JT-60 Team. Observation of an energetic-particle-driven insta- bility in the wall-stabilized high- β plasmas in the JT-60U tokamak. Phys. Rev. Lett. , 103:045001, 2009. https://doi.org/10.1103/PhysRe/v1Lett.103.045001

    work page doi:10.1103/physre/v1lett.103.045001 2009

  5. [5]

    Okabayashi, I.N

    M. Okabayashi, I.N. Bogatu, M.S. Chance, M.S. Chu, A.M. Garofalo, Y . In, G.L. Jackson, R.J. La Haye, M.J. Lanctot, J. Manickam, L. Marrelli, P . Martin, G.A. Navratil, H. Reimerdes, E.J. Strait, H. Takahashi, A.S. Welander, T. Bolzonella, R.V . Budny, J.S. Kim, R. Hatcher, Y .Q. Liu, and T.C. Luce. Comprehensive control of resistive wall modes in DIII-D ...

    work page doi:10.1088/0029-5515/49/12/125003 2009

  6. [6]

    Matsunaga, K

    G. Matsunaga, K. Shinohara, N. Aiba, Y . Sakamoto, A. Isayama, N. Asakura, T. Suzuki, M. Takechi, N. Oyama, H. Urano, and the JT-60 Team. En- ergetic particle driven instability in wall-stabilized high-β plasmas. Nucl. Fusion , 50:084003, 2010. https://doi.org/10.1088/0029-5515/50/8/084003

    work page doi:10.1088/0029-5515/50/8/084003 2010

  7. [7]

    Okabayashi, G

    M. Okabayashi, G. Matsunaga, J.S. deGrassie, W.W. Hei- dbrink, Y . In, 5 Y . Q. Liu, H. Reimerdes, W.M. Solomon, E.J. Strait, M. Takechi, N. Asakura, R.V . Budny, G.L. Jack- son, J.M. Hanson, R.J. La Haye, M.J. Lanctot, J. Man- ickam, K. Shinohara, and Y .B. Zhu. O ff-axis fishbone- like instability and excitation of resistive wall modes in JT-60U and DIII-...

    work page doi:10.1063/1.3575159 2011

  8. [8]

    Heidbrink, M.E

    W.W. Heidbrink, M.E. Austin, R.K. Fisher, M. Garc´ ıa- Mu noz, G. Matsunaga, G.R. McKee, R.A. Moyer, C.M. Muscatello, M. Okabayashi, D.C. Pace, K. Shi- nohara, W.M. Solomon, E.J. Strait, M.A. V an Zeeland, and Y .B. Zhu. Characterization of o ff-axis fishbones. Plasma Phys. Control. Fusion , 53:085028, 2011. https://doi.org/10.1088/0741-3335/53/8/085028

    work page doi:10.1088/0741-3335/53/8/085028 2011

  9. [9]

    Study of Low-Frequency Core-Edge Coupling in a Tokamak: I. Experimental Observation in KSTAR

    W.J. Lee et al. Study of low-frequency core-edge coupling in a tokamak: I. Experimental observa- tion in KSTAR. Companion paper jointly sub- mitted to Fundamental Plasma Physics . Preprint: https://doi.org/10.48550/arXi/v1.2603.24525

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxi/v1.2603.24525

  10. [10]

    Reconstruction of current profile parameters and plasma shapes in tokamaks

    L.L. Lao, H.St. John, R.D. Stambaugh, A.G. Kellman, and W. Pfei ffer. Reconstruction of current profile parameters and plasma shapes in tokamaks. Nucl. Fusion , 25:1611, 1985.33 https://doi.org/10.1088/0029-5515/25/11/007

    work page doi:10.1088/0029-5515/25/11/007 1985

  11. [11]

    Cheng, L

    C.Z. Cheng, L. Chen, and M.S. Chance. High-n ideal and resistive shear Alfv´ en waves in tokamaks. Ann. Phys. , 161:21, 1985. https://doi.org/10.1016/0003-4916(85)90335-5

    work page doi:10.1016/0003-4916(85)90335-5 1985

  12. [12]

    Betti and J.P

    R. Betti and J.P . Freidberg. Ellipticity induced Alfv´ en eigenmodes. Phys. Fluids B , 3(8):1865, 1991. https://doi.org/10.1063/1.859655

    work page doi:10.1063/1.859655 1991

  13. [13]

    Heidbrink, E.J

    W.W. Heidbrink, E.J. Strait, M.S. Chu, and A.D. Turn- bull. Observation of beta-induced Alfv´ en eigenmodes in the DIII-D tokamak. Phys. Rev. Lett. , 71:855, 1993. https://doi.org/10.1103/PhysRe/v1Lett.71.855

    work page doi:10.1103/physre/v1lett.71.855 1993

  14. [14]

    Gorelenkov, H.L

    N.N. Gorelenkov, H.L. Berk, E. Fredrickson, S.E. Sharapov, and JET EFDA Contributors. Pre- dictions and observations of low-shear beta- induced shear Alfv´ en-acoustic eigenmodes in toroidal plasmas. Phys. Lett. A , 370:70, 2007. https://doi.org/10.1016/j.physleta.2007.05.113

    work page doi:10.1016/j.physleta.2007.05.113 2007

  15. [15]

    Zonca, L

    F. Zonca, L. Chen, and R. A. Santoro. Ki- netic theory of low-frequency Alfv´ en modes in toka- maks. Plasma Phys. Control. Fusion , 38:2011, 1996. https://doi.org/10.1088/0741-3335/38/11/011

    work page doi:10.1088/0741-3335/38/11/011 2011

  16. [16]

    Curran, Ph

    D. Curran, Ph. Lauber, P .J. Mc Carthy, S. da Graca, V . Igochine, and the ASDEX Upgrade Team. Low-frequency Alfv´ en eigenmodes during the sawtooth cycle at ASDEX Upgrade. Plasma Phys. Control. Fusion , 54(5):055001, 2012. https://doi.org/10.1088/0741-3335/54/5/055001

    work page doi:10.1088/0741-3335/54/5/055001 2012

  17. [17]

    Chavdarovski and F

    I. Chavdarovski and F. Zonca. Analytic studies of dispe r- sive properties of shear Alfv´ en and acoustic wave spec- tra in tokamaks. Phys. Plasmas , 21(5):052506, 2014. https://doi.org/10.1063/1.4876000

    work page doi:10.1063/1.4876000 2014

  18. [18]

    Coppi and F

    B. Coppi and F. Porcelli. Theoretical model of fishbone oscillations in magnetically con- fined plasmas. Phys. Rev. Lett. , 57:2272, 1986. https://doi.org/10.1103/PhysRe/v1Lett.57.2272

    work page doi:10.1103/physre/v1lett.57.2272 1986

  19. [19]

    Chen and A

    L. Chen and A. Hasegawa. Kinetic theory of geomag- netic pulsations: 1. Internal excitations by energetic par - ticles. J. Geophys. Res.: Space Phys. , 96:1503, 1991. https://doi.org/10.1029/90JA02346

    work page doi:10.1029/90ja02346 1991

  20. [20]

    X. Du, L. Chen, W.W. Heidbrink, M.A. V an Zee- land, M.E. Austin, J. Chen, Y . Liu, G.R. McKee, and Z. Yan. First measurement of drift-Alfv´ en wave polarization in magnetically confined fu- sion plasmas. Phys. Rev. Lett. , 132:215101, 2024. https://doi.org/10.1103/PhysRe/v1Lett.132.215101

    work page doi:10.1103/physre/v1lett.132.215101 2024

  21. [21]

    Chen, R.B

    L. Chen, R.B. White, and M.N. Rosenbluth. Ex- citation of internal kink modes by trapped ener- getic beam ions. Phys. Rev. Lett. , 52:1122, 1984. https://doi.org/10.1103/PhysRe/v1Lett.52.1122

    work page doi:10.1103/physre/v1lett.52.1122 1984

  22. [22]

    L. Chen. Theory of magnetohydrodynamic instabilities ex- cited by energetic particles in tokamaks. Phys. Plasmas , 1:1519, 1994. https://doi.org/10.1063/1.870702

    work page doi:10.1063/1.870702 1994

  23. [23]

    Zhang, H.L

    Y .Z. Zhang, H.L. Berk, and S.M. Mahajan. Ef- fect of energetic trapped particles on the ‘ideal’ in- ternal kink mode. Nucl. Fusion , 29:848, 1989. https://doi.org/10.1088/0029-5515/29/5/016

    work page doi:10.1088/0029-5515/29/5/016 1989

  24. [24]

    Appert, R

    K. Appert, R. Gruber, F. Troyon, and J. V aclavik. Excitation of global eigenmodes of the Alfv´ en wave in tokamaks. Plasma Phys. , 24:1147, 1982. https://doi.org/10.1088/0032-1028/24/9/010

    work page doi:10.1088/0032-1028/24/9/010 1982

  25. [25]

    Y . Liu, W. Xie, and X.D. Du. Modeling of thermal-ion-driven internal kink in DIII-D high- Ti plasmas. Nucl. Fusion , 62:086050, 2022. https://doi.org/10.1088/1741-4326/ac7b9a

    work page doi:10.1088/1741-4326/ac7b9a 2022

  26. [26]

    X.D. Du, R.J. Hong, W.W. Heidbrink, X. Jian, H. Wang, N.W. Eidietis, M.A. V an Zeeland, M.E. Austin, Y . Liu, N.A. Crocker, T.L. Rhodes, K. S¨ arkim¨ aki, A. Snicker, W. Wu, and M. Knolker. Multiscale chirping modes driven by thermal ions in a plasma with reactor-relevant ion temperature. Phys. Rev. Lett. , 127:025001, 2021. https://doi.org/10.1103/PhysRe...

    work page doi:10.1103/physre/v1lett.127.025001 2021

  27. [27]

    Bierwage, Ph

    A. Bierwage, Ph. Lauber, N. Nakajima, K. Shino- hara, G. Brochard, Y . c. Ghim, W. Lee, A. Mat- suyama, S. Sumida, H. Yang, and M. Yagi. Con- struction and analysis of guiding center distributions for tokamak plasmas with ambient radial elec- tric field. Comp. Phys. Comp. , 317:109823, 2025. https://doi.org/10.1016/j.cpc.2025.109823

    work page doi:10.1016/j.cpc.2025.109823 2025

  28. [28]

    Kolesnichenko, A.V

    Ya.I. Kolesnichenko, A.V . Tykhyy, and R.B. White. Spatial channeling in toroidal plasmas: overview and new results. Nucl. Fusion , 60:112006, 2020. https://doi.org/10.1088/1741-4326/ab8182

    work page doi:10.1088/1741-4326/ab8182 2020

  29. [29]

    W.A. Cooper. Ballooning instabilities in toka- maks with sheared toroidal flows. Plasma Phys. Control. Fusion , 30:1805, 1988. https://doi.org/10.1088/0741-3335/30/13/001

    work page doi:10.1088/0741-3335/30/13/001 1988

  30. [30]

    Waelbroeck and L

    F.L. Waelbroeck and L. Chen. Ballooning instabilities in tokamaks with sheared toroidal flows. Phys. Fluids B , 3:601, 1991. https://doi.org/10.1063/1.859858

    work page doi:10.1063/1.859858 1991

  31. [31]

    Furukawa and S

    M. Furukawa and S. Tokuda. Mechanism of sta- bilization of ballooning modes by toroidal rotation shear in tokamaks. Phys. Rev. Lett. , 94:175001, 2005. https://doi.org/10.1103/PhysRe/v1Lett.94.175001

    work page doi:10.1103/physre/v1lett.94.175001 2005

  32. [32]

    Todo and T

    Y . Todo and T. Sato. Linear and nonlinear particle- magnetohydrodynamic simulations of the toroidal Alfv´ en eigenmode. Phys. Plasmas , 5:1321, 1998. https://doi.org/10.1063/1.872791

    work page doi:10.1063/1.872791 1998

  33. [33]

    Y . Todo, K. Shinohara, M. Takechi, and M. Ishikawa. Nonlocal energetic particle mode in a JT-60U plasma. Phys. Plasmas , 12:012503, 2005. https://doi.org/10.1063/1.1828084

    work page doi:10.1063/1.1828084 2005

  34. [34]

    Y . Todo, M. Idouakass, H. Wang, R. Seki, J. Wang, S. Wei, H. Li, and M. Sato. Energetic particle driven Alfv´ en eigen- modes and associated energetic particle redistribution in a tokamak burning plasma. Nucl. Fusion, 65:102003, 2025. https://doi.org/10.1088/1741-4326/ae059f

    work page doi:10.1088/1741-4326/ae059f 2025

  35. [35]

    Chen and A

    L. Chen and A. Hasegawa. Plasma heating by spatial resonance of Alfv´ en wave. Phys. Fluids , 17:1399, 1974. https://doi.org/10.1063/1.1694904

    work page doi:10.1063/1.1694904 1974

  36. [36]

    Hasegawa and L

    A. Hasegawa and L. Chen. Kinetic pro- cess of plasma heating duet to Alfv´ en wave excitation. Phys. Rev. Lett. , 34:370, 1975. https://doi.org/10.1103/PhysRe/v1Lett.35.370

    work page doi:10.1103/physre/v1lett.35.370 1975

  37. [37]

    Chen and F

    L. Chen and F. Zonca. Theory of shear Alfv´ en waves in toroidal plasmas. Physica Scripta , T60:81, 1995. https://doi.org/10.1088/0031-8949/1995/T60/011

    work page doi:10.1088/0031-8949/1995/t60/011 1995

  38. [38]

    Ya. I. Kolesnichenko, Y u. V . Yakovenko, and V . V . Lutsenko. Channeling of the energy and momen- tum during energetic-ion-driven instabilities in fu- sion plasmas. Phys. Rev. Lett. , 104:075001, 2010. https://doi.org/10.1103/PhysRe/v1Lett.104.075001

    work page doi:10.1103/physre/v1lett.104.075001 2010

  39. [39]

    G.G. Borg. Guided propagation of the Alfv´ en wave in a tokamak. Aust. J. Phys. , 49:953, 1996. https://doi.org/10.1071/PH960953

    work page doi:10.1071/ph960953 1996

  40. [40]

    Kolesnichenko, Y u.V

    Ya.I. Kolesnichenko, Y u.V . Yakovenko, and M.H. Tyshchenko. Mechanisms of the energy trans- fer across the magnetic field by Alfv´ en waves in 34 toroidal plasmas. Phys. Plasmas , 25:122508, 2018. https://doi.org/10.1063/1.5049543

    work page doi:10.1063/1.5049543 2018

  41. [41]

    Kinetic-ballooning-mode theory in general geometry,

    W.M. Tang, J.W. Connor, and R.J. Hastie. Kinetic-ballooning-mode theory in general geometry. Nucl. fusion , 20:1439, 1980. https://doi.org/10.1088/0029-5515/20/11/011

    work page doi:10.1088/0029-5515/20/11/011 1980

  42. [42]

    Connor, R.J

    J.W. Connor, R.J. Hastie, and J.B. Tay- lor. Shear, periodicity, and plasma balloon- ing modes. Phys. Rev. Lett. , 40:396, 1978. https://doi.org/10.1103/PhysRe/v1Lett.40.396

    work page doi:10.1103/physre/v1lett.40.396 1978

  43. [43]

    Dewar and A.H

    R.L. Dewar and A.H. Glasser. Ballooning mode spectrum in general toroidal systems. Phys. Fluids , 26:3038, 1983. https://dx.doi.org/10.1063/1.864028

    work page doi:10.1063/1.864028 1983

  44. [44]

    B.D. Scott. On Magnetic Compression in Gyrokinetic Field Theory. arXiv:2405.18985 [physics.plasm-ph] (2024) https://doi.org/10.48550/arXi/v1.2405.18985

    work page doi:10.48550/arxi/v1.2405.18985 2024

  45. [45]

    Graves, D

    J.P . Graves, D. Zullino, D. Brunetti, S. Lanthaler, and C. Wahlberg. Reduced models for parallel magnetic field fluctuations and their impact on pressure gradient driven MHDinstabilities in axisymmetric toroidal plas- mas. Plasma Phys. Control. Fusion , 61:104003, 2019. https://doi.org/10.1088/1361-6587/ab368b

    work page doi:10.1088/1361-6587/ab368b 2019

  46. [46]

    Parker, J.W

    J.B. Parker, J.W. Burby, J.B. Marston, and S.M. Tobias. Nontrivial topology in the continuous spectrum of a magnetized plasma. Phys. Rev. Res. , 2:033425, 2020. https://doi.org/10.1103/PhysRe/v1Research.2.033425

    work page doi:10.1103/physre/v1research.2.033425 2020

  47. [47]

    H. Grad. Plasmas. Phys. Today, 22:34, 1969. December issue. https://doi.org/10.1063/1.3035293

    work page doi:10.1063/1.3035293 1969

  48. [48]

    Y un, H.K

    G.S. Y un, H.K. Park, W. Lee, M.J. Choi, G.H. Choe, S. Park, Y .S. Bae, K.D. Lee, S.W. Y oon, Y .M. Jeon, C.W. Domier, Jr. N.C. Luhmann, B. Tobias, and A.J.H. Donn´ e (KSTAR Team). Appearance and dynamics of helical flux tubes under electron cy- clotron resonance heating in the core of KSTAR plasmas. Phys. Rev. Lett. , 109:144003, 2012. https://doi.org/10....

    work page doi:10.1103/physre/v1lett.109.145003 2012

  49. [49]

    Choe, G.S

    G.H. Choe, G.S. Y un, Y . Nam, W. Lee, H.K. Park, A. Bierwage, C.W. Domier, N.C. Luhmann Jr, J.H. Jeong, Y .S. Bae, and the KSTAR Team. Dynamics of multiple flux tubes in sawtoothing KSTAR plasmas heated by electron cyclotron waves: I. Experimental analysis of the tube structure. Nucl. Fusion , 55:013015, 2015. https://dx.doi.org/10.1088/0029-5515/55/1/013015

    work page doi:10.1088/0029-5515/55/1/013015 2015

  50. [50]

    Bierwage, G.S

    A. Bierwage, G.S. Y un, G.H. Choe, Y . Nam, W. Lee, H.K. Park, and Y . Bae. Dynamics of multiple flux tubes in sawtoothing KSTAR plasmas heated by electron cyclotron waves: II. Theoretical and nu- merical analysis. Nucl. Fusion , 55(1):013016, 2015. https://doi.org/10.1088/0029-5515/55/1/013016

    work page doi:10.1088/0029-5515/55/1/013016 2015

  51. [51]

    W. Deng, Z. Lin, I. Holod, Z. Wang, Y . Xiao, and H. Zhang. Linear properties of reversed shear Alfv´ en eigenmodes in the DIII-D tokamak. Nucl. Fusion , 52:043006, 2023. https://doi.org/10.1088/0029-5515/52/4/043006

    work page doi:10.1088/0029-5515/52/4/043006 2023

  52. [52]

    Kwon et al

    M. Kwon et al. Overview of KSTAR ini- tial operation. Nucl. Fusion , 51:094006, 2011. https://doi.org/10.1088/0029-5515/51/9/094006

    work page doi:10.1088/0029-5515/51/9/094006 2011

  53. [53]

    2018 , month =

    TRANSP code. See: https://doi.org/10.11578/dc.20180627.4 and https://transp.pppl.gov/ (Accessed: May 2025)

    work page doi:10.11578/dc.20180627.4 2025

  54. [54]

    L¨ utjens, A

    H. L¨ utjens, A. Bondeson, and O. Sauter. The CHEASE code for toroidal MHD equilib- ria. Comput. Phys. Commun. , 97:219, 1996. https://doi.org/10.1016/0010-4655(96)00046-X

    work page doi:10.1016/0010-4655(96)00046-x 1996

  55. [55]

    Porcelli

    F. Porcelli. Fast particle stabilization. Plasma Phys. Control. Fusion , 33:1601, 1991. https://doi.org/10.1088/0741-3335/33/13/009

    work page doi:10.1088/0741-3335/33/13/009 1991

  56. [56]

    Graves, R.J

    J.P . Graves, R.J. Hastie, and K.I. Hopcraft. The effects of sheared toroidal plasma rotation on the internal kink mode in the banana regime. Plasma Phys. Control. Fusion , 42:1049, 2000. https://doi.org/10.1088/0741-3335/42/10/304

    work page doi:10.1088/0741-3335/42/10/304 2000

  57. [57]

    Cooper, J.P

    W.A. Cooper, J.P . Graves, A. Pochelon, O. Sauter, and L. Villard. Tokamak magnetohydrodynamic equilibrium states with axisymmetric boundary and a 3D helical core. Phys. Rev. Lett. , 105:035003, 2010. https://doi.org/10.1103/PhysRe/v1Lett.105.035003

    work page doi:10.1103/physre/v1lett.105.035003 2010

  58. [58]

    Cooper, J.P

    W.A. Cooper, J.P . Graves, and O. Sauter. He- lical ITER hybrid scenario equilibria. Plasma Phys. Control. Fusion , 53:024002, 2011. https://doi.org/10.1088/0741-3335/53/2/024002

    work page doi:10.1088/0741-3335/53/2/024002 2011

  59. [59]

    Wingen, R.S

    A. Wingen, R.S. Wilcox, S.K. Seal, E.A. Unterberg, M.R. Cianciosa, L.F. Delgado-Aparicio, S.P . Hirshman, and L.L. Lao. Use of reconstructed 3D equilibria to deter- mine onset conditions of helical cores in tokamaks for extrapolation to ITER. Nucl. Fusion , 58:036004, 2018. https://doi.org/10.1088/1741-4326/aaa33d

    work page doi:10.1088/1741-4326/aaa33d 2018

  60. [60]

    Adulsiriswad, A

    P . Adulsiriswad, A. Bierwage, and M. Yagi. Helical core formation and MHD stability in ITER-like plasmas with fusion-born alpha particles. Nucl. Fusion , 66:046032, 2026. https://doi.org/10.1088/1741-4326/ae4fdf

    work page doi:10.1088/1741-4326/ae4fdf 2026

  61. [61]

    Bierwage, K

    A. Bierwage, K. Shinohara, Y . Todo, N. Aiba, M. Ishikawa, G. Matsunaga, M. Takechi, and M. Yagi. Self-consistent long-time simulation of chirping and beating energetic particle modes in JT-60U plasmas. Nucl. Fusion , 57:016036, 2017. https://doi.org/10.1088/1741-4326/57/1/016036

    work page doi:10.1088/1741-4326/57/1/016036 2017

  62. [62]

    Bierwage, Y

    A. Bierwage, Y . Todo, N. Aiba, and K. Shino- hara. Sensitivity study for N-NB-driven modes in JT-60U: Boundary, di ffusion, gyroaverage, compressibility. Nucl. Fusion , 56:106009, 2016. https://doi.org/10.1088/0029-5515/56/10/106009

    work page doi:10.1088/0029-5515/56/10/106009 2016

  63. [63]

    Falessi, N

    M.V . Falessi, N. Carlevaro, V . Fusco, E. Giovannozzi, P . Lauber, G. Vlad, and F. Zonca. On the polariza- tion of shear Alfv´ en and acoustic continuous spectra in toroidal plasmas. J. Plasma Phys. , 86:845860501, 2020. https://doi.org/10.1017/S0022377820000975

    work page doi:10.1017/s0022377820000975 2020

  64. [64]

    Falessi, N

    M.V . Falessi, N. Carlevaro, V . Fusco, G. Vlad, and F. Zonca. Shear Alfv´ en and acoustic con- tinuum in general axisymmetric toroidal ge- ometry. Phys. Plasmas , 26:082502, 2019. https://doi.org/10.1063/1.5098982

    work page doi:10.1063/1.5098982 2019

  65. [65]

    Bierwage, R.B

    A. Bierwage, R.B. White, and A. Matsuyama. Test- ing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates. Phys. Plasmas , 29:113905, 2022. https://doi.org/10.1063/5.0100303

    work page doi:10.1063/5.0100303 2022

  66. [66]

    Bierwage and K

    A. Bierwage and K. Shinohara. Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of E and B. Phys. Plasmas, 29:113906, 2022. https://doi.org/10.1063/5.0106395. Erratum: Phys. Plasmas 30 (2023) 079901, https://doi.org/10.1063/5.0163134

    work page doi:10.1063/5.0106395 2022

  67. [67]

    Heidbrink, X.D

    W.W. Heidbrink, X.D. Du, L. Chen, M.E. Austin, J. Bao, G. Brochard, R. Ma, G.R. McKee, M.A. V an Zeeland, and Z. Yan. Measurements of the polarization of several instabilities in the DIII-D tokamak. Nucl. Fusion , 65:112002, 2025. 35 https://doi.org/10.1088/1741-4326/ae06b2

    work page doi:10.1088/1741-4326/ae06b2 2025

  68. [68]

    Joiner and A

    N. Joiner and A. Hirose. E ffects of magnetosonic perturbations on electron temperature gradient driven modes and the stability of skin depth sized elec- tron ballooning modes. Phys. Plasmas , 14:112111, 2007. https://doi.org/10.1063/1.2814050. Erratum: Phys. Plasmas 16 (2009) 069902, https://doi.org/10.1063/1.3155107

    work page doi:10.1063/1.2814050 2007

  69. [69]

    Bierwage and K

    A. Bierwage and K. Shinohara. Orbit-based anal- ysis of nonlinear energetic ion dynamics in toka- maks. II. Mechanisms for rapid chirping and convec- tive amplification. Phys. Plasmas , 23:042512, 2016. https://doi.org/10.1063/1.4947034

    work page doi:10.1063/1.4947034 2016

  70. [70]

    Kadomtsev

    B.B. Kadomtsev. Disruptive instability in tokamaks. Fiz. Plazmy, 1:710, 1975. [ Sov. J. Plasma Phys. 1 (1976) 389]

    work page 1975

  71. [71]

    J.A. Wesson. Sawtooth oscillations. Plasma Phys. Control. Fusion , 28:243, 1986. https://doi.org/10.1088/0741-3335/28/1A/022

    work page doi:10.1088/0741-3335/28/1a/022 1986

  72. [72]

    Krebs, S.C

    I. Krebs, S.C. Jardin, S. G¨ unter, K. Lackner, M. Hoelzl , E. Strumberger, and N. Ferraro. Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations. Phys. Plasmas , 24:102511, 2017. https://doi.org/10.1063/1.4990704

    work page doi:10.1063/1.4990704 2017

  73. [73]

    Jardin, I

    S.C. Jardin, I. Krebs, and N. Ferraro. A new explanation of the sawtooth phenomena in toka- maks. Comp. Phys. Comm. , 27:032509, 2020. https://doi.org/10.1063/1.5140968

    work page doi:10.1063/1.5140968 2020

  74. [74]

    Stepanenko

    A.A. Stepanenko. E ffect of electromagnetic wave reflection from conducting surfaces on blob dynamics in the toka- mak scrape-o fflayer. Phys. Plasmas , 30:042301, 2023. https://doi.org/10.1063/5.0140097

    work page doi:10.1063/5.0140097 2023

  75. [75]

    Kerner an R

    W. Kerner an R. Gruber and F. Troyon. Nu- merical study of the internal kink mode in tokamaks. Phys. Rev. Lett. , 44:536, 1980. https://doi.org/10.1103/PhysRe/v1Lett.44.536

    work page doi:10.1103/physre/v1lett.44.536 1980

  76. [76]

    Tokuda, T

    S. Tokuda, T. Tsunematsu, M. Azumi, T. Takizuka, and T. Takeda. Second stability region against the internal kink mode in a tokamak. Nucl. Fusion , 22:661, 1982. https://doi.org/10.1088/0029-5515/22/5/007

    work page doi:10.1088/0029-5515/22/5/007 1982

  77. [77]

    Tokuda, T

    S. Tokuda, T. Tsunematsu, M. Azumi, T. Takizuka, and T. Takeda. Stability of n = 1 internal modes in tokamaks. Nucl. Fusion , 24:595, 1984. https://doi.org/10.1088/0029-5515/24/5/006

    work page doi:10.1088/0029-5515/24/5/006 1984

  78. [78]

    Jhang, J

    H. Jhang, J. Kim, J. Kang, M. Kim, L.L. Zhang, G.Y . Fu, F. Zonca, L. Chen, I. Chavdarovski, M.J. Choi, M.V . Falessi, S. Lee, and Z.Y . Qiu. En- ergetic passing particle-driven instabilities and their impact on discharge evolution in KSTAR. Plasma Phys. Control. Fusion , 65:095018, 2023. https://doi.org/10.1088/1361-6587/ace3f2

    work page doi:10.1088/1361-6587/ace3f2 2023

  79. [79]

    N. Aiba, S. Tokuda, M. Furukawa, P .B. Sny- der, and M.S. Chu. MINERV A: Ideal MHD sta- bility code for toroidally rotating tokamak plas- mas. Comp. Phys. Comm. , 180:1282, 2009. https://doi.org/10.1016/j.cpc.2009.02.008

    work page doi:10.1016/j.cpc.2009.02.008 2009

  80. [80]

    Gorelenkov

    N.N. Gorelenkov. Double-gap Alfv´ en eigenmodes: Revisiting eigenmode interaction with the Alfv´ en continuum. Phys. Rev. Lett. , 95:265003, 2005. https://doi.org/10.1103/PhysRe/v1Lett.95.265003

    work page doi:10.1103/physre/v1lett.95.265003 2005

Showing first 80 references.