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Optimizing 3D magnetic perturbations for edge instability control in the KSTAR tokamak

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A Correction to this article was published on 16 March 2024

This article has been updated

Abstract

A small non-axisymmetric (3D) magnetic field can offer invaluable ways for instability control in tokamaks when optimally used, as has been highlighted by the edge-localized mode (ELM) control using a resonant magnetic perturbation (RMP). While the inherent complexity due to its 3D nature constantly poses scientific challenges, recent research progresses have been increasing the prospects of universal predictive capabilities on RMP ELM suppression. A successful framework has been developed based on integrated perturbative models under international collaborations centered around the Korean Superconducting Tokamak Advanced Research (KSTAR), as will be reviewed in this article. This framework separates the interaction between 3D coils and resonant fields as the ideal magnetohydrodynamic (MHD) outer-layer process in fast time scales, from the dynamics of resonant field penetration as the narrow boundary layer process in non-ideal MHD time scales. The major profile alterations can occur only when the resonant field becomes strong enough to penetrate and bifurcate to new magnetic island topologies. This hypothesis enables simplified 3D field optimizations once the field penetration thresholds are identified. The prediction of the field penetration thresholds require non-linear MHD simulations but can be simplified by isolating it from outer-layer response, successfully explaining key parametric dependencies and accessibility conditions for RMP ELM suppression. Improved understanding has been leveraged to expand physics basis for underlying transport in fully geometry, as recent perturbative 3D simulations are revealing the complex interplays across classical and non-classical transport, between Kink and tearing mode structures, between closed- and open-field lines which are important to optimize power flux to plasma facing components. The pre-programmed predictive optimization of 3D tokamak scenarios can then be combined with an adaptive RMP control to find the optimal trade-off between stability and confinement. The above approaches under this framework are not based on the first principles but are indeed providing unique guidances for 3D tokamak design, optimization, and control.

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Data Availability

The data that support the findings introduced in this paper will be available from the corresponding author, J.-K. Park and his co-authors, upon reasonable request.

Change history

  • 04 March 2024

    The incorrect author's name “R. Fitzpatrickk” in two references has been corrected to “R. Fitzpatrick”.

  • 16 March 2024

    A Correction to this paper has been published: https://doi.org/10.1007/s41614-024-00151-w

References

  • J.-W. Ahn, R. Maingi, J.M. Canik, A.G. McLean, J.D. Lore, J.-K. Park, V.A. Soukhanovskii, T.K. Gray, A.L. Roquemore, Effect of nonaxisymmetric magnetic perturbations on divertor heat and particle flux profiles in national spherical torus experiment. Phys. Plasmas 18(5), 056108 (2011)

    Article  ADS  Google Scholar 

  • M. Bécoulet, F. Orain, P. Maget, N. Mellet, X. Garbet, E. Nardon, G.T.A. Huysmans, T. Casper, A. Loarte, P. Cahyna, A. Smolyakov, F.L. Waelbroeck, M. Schaffer, T. Evans, Y. Liang, O. Schmitz, M. Beurskens, V. Rozhansky, E. Kaveeva, Screening of resonant magnetic perturbations by flows in tokamaks. Nucl. Fusion 52, 054003 (2012)

    Article  ADS  Google Scholar 

  • M. Bécoulet, F. Orain, G.T.A. Huijsmans, S. Pamela, P. Cahyna, M. Hoelzl, X. Garbet, E. Franck, E. Sonnendrücker, G. Dif-Pradalier, C. Passeron, G. Latu, J. Morales, E. Nardon, A. Fil, B. Nkonga, A. Ratnani, V. Grandgirard, Mechanisms of edge localized mode mitigation by resonant magnetic perturbations. Phys. Rev. Lett. 113, 115001 (2014)

    Article  ADS  PubMed  Google Scholar 

  • M.G. Bell, R.E. Bell, D.A. Gates, S.M. Kaye, H. Kugel, B.P. LeBlanc, F.M. Levinton, R. Maingi, J.E. Menard, R. Raman, S.A. Sabbagh, D. Stutman, the NSTX team: New capabilities and results for the national spherical torus experiment. Nucl. Fusion 46, 565 (2006)

    Article  Google Scholar 

  • A.H. Boozer, Quasi-helical symmetry in stellarators. Plasma Phys. Control. Fusion 37, 103–117 (1995)

    Article  ADS  Google Scholar 

  • A.H. Boozer, Error field amplification and rotation damping in tokamak plasmas. Phys. Rev. Lett. 86, 5059–5061 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  • A.H. Boozer, Physics of magnetically confined plasmas. Rev. Mod. Phys. 76, 1071 (2004)

    Article  ADS  CAS  Google Scholar 

  • A.H. Boozer, Perturbation to the magnetic field strength. Phys. Plasmas 13, 044501 (2006)

    Article  ADS  Google Scholar 

  • A.H. Boozer, Stellarators and the path from iter to demo. Plasma Phys. Control. Fusion 50, 124005 (2008)

    Article  ADS  Google Scholar 

  • A.H. Boozer, Control of non-axisymmetric toroidal plasmas. Plasma Phys. Control. Fusion 52, 104001 (2010)

    Article  ADS  Google Scholar 

  • A. Bortolon, W.W. Heidbrink, G.J. Kramer, J.-K. Park, E.D. Fredrickson, J.D. Lore, M. Podesta, Mitigation of alfven activity in a tokamak by externally applied static 3d fields. Phys. Rev. Lett. 110, 265008 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  • R.J. Buttery, M.D. Benedetti, D.A. Gates, Y. Gribov, T.C. Hender, R.J. La Haye, P. Leahy, J.A. Leuer, A.W. Morris, A. Santagiustina, J.T. Scoville, B. J. D. Tubbing, the JET Team, the COMPASS-D Research Team, the DIII-D Team: Error field mode studies on jet, compass-d and diii-d, and implications for iter. Nucl. Fusion 39, 1827–1835 (1999)

  • J.D. Callen, Effects of 3d magnetic perturbations on toroidal plasmas. Nucl. Fusion 51, 094026 (2011)

    Article  ADS  Google Scholar 

  • J.M. Canik, R. Maingi, T.E. Evans, R.E. Bell, S.P. Gerhardt, B.P. LeBlanc, J. Manickam, J.E. Menard, T.H. Osborne, J.-K. Park, S.F. Paul, P.B. Snyder, S.A. Sabbagh, H.W. Kuget, E.A. Unterberg, the NSTX Research Team: Elm triggering with 3d magnetic fields in nstx. Phys. Rev. Lett. 104, 045001 (2009)

    Article  ADS  Google Scholar 

  • M.J. Choi, J.-M. Kwon, J. Kim, T. Rhee, J.-G. Bak, G. Shin, H.-S. Kim, H. Jhang, G.S.Y. K. Kim, M.W. Kim, S.K. Kim, H.H. Kaang, J.-K. Park, H.H. Lee, Y. In, J. Lee, M. Kim, B.-H. Park, H. Park, Stochastic fluctuation and transport of tokamak edge plasmas with the resonant magnetic perturbation field. Physics of Plasmas 29(12), (2022)

  • M.J. Choi, J. Kim, J.-M. Kwon, H.K. Park, Y. In, W. Lee, K.D. Lee, G.S. Yun, J. Lee, M. Kim, W.-H. Ko, J.H. Lee, Y.S. Park, Y.-S. Na, N.C. Luhmann, B.H. Park, Multiscale interaction between a large scale magnetic island and small scale turbulence. Nucl. Fusion 57(12), 126058 (2017)

    Article  ADS  Google Scholar 

  • A.J. Cole, R. Fitzpatrick, Drift-magnetohydrodynamical model of error-field penetration in tokamak plasmas. Phys. Plasmas 13, 032503 (2006)

    Article  ADS  Google Scholar 

  • A.J. Cole, C.C. Hegna, J.D. Callen, Neoclassical toroidal viscosity and error-field penetration in tokamaks. Phys. Plasmas 15, 056102 (2008)

    Article  ADS  Google Scholar 

  • J.W. Connor, A review of models for elms. Plasma Phys. Control. Fusion 40, 191–213 (1998)

    Article  ADS  CAS  Google Scholar 

  • J.W. Connor, R.J. Hastie, Scaling laws for plasma confinement. Nucl. Fusion 13, 221 (1973)

    Article  Google Scholar 

  • T.E. Evans, Resonant magnetic perturbations of edge-plasmas in toroidal confinement devices. Plasma Phys. Control. Fusion 57, 123001 (2015)

    Article  ADS  Google Scholar 

  • T.E. Evans, R.A. Moyer, P.R. Thomas, J.G. Watkins, T.H. Osborne, J.A. Boedo, E.J. Doyle, M.E. Fenstermacher, K.H. Finken, R.J. Groebner, M. Groth, J.H. Harris, R.J. La Haye, C.J. Lasnier, S. Masuzaki, N. Ohyabu, D.G. Pretty, T.L. Rhodes, H. Reimerdes, D.L. Rudakov, M.J. Schaffer, G. Wang, L. Zeng, Suppression of large edge-localized modes in high-confinement diii-d plasmas with a stochastic magnetic boundary. Phys. Rev. Lett. 92, 235003 (2004)

    Article  ADS  CAS  PubMed  Google Scholar 

  • T.E. Evans, R.A. Moyer, J.G. Watkins, T.H. Osborne, P.R. Thomas, M. Becoulet, J.A. Boedo, E.J. Doyle, M.E. Fenstermacher, K.H. Finken, R.J. Groebner, M. Groth, J.H. Harris, G.L. Jackson, R.J. LaHaye, C.J. Lasnier, S. Masuzaki, N. Ohyabu, D.G. Pretty, H. Reimerdes, T.L. Rhodes, D.L. Rudakov, M.J. Schaffer, M.R. Wade, G. Wang, W.P. West, L. Zeng, Suppression of large edge-localized modes with edge resonant magnetic fields in high confinement diii-d plasmas. Nucl. Fusion 45, 595 (2005)

    Article  ADS  CAS  Google Scholar 

  • T.E. Evans, R.A. Moyer, K.H. Burrell, M. Fenstermacher, I. Joseph, A.W. Leonard, T.H. Osborne, G.D. Porter, M.J. Schaffer, P.B. Snyder, P.R. Thomas, J.G. Watkins, W.P. West, Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas. Nat. Phys. 2, 419–423 (2006)

    Article  CAS  Google Scholar 

  • T.E. Evans, M.E. Fenstermacher, A. Moyer, T.H. Osborne, J.G. Watkins, P. Gohil, I. Joseph, M.J. Schaffer, L.R. Baylor, M. Bécoulet, J.A. Boedo, K.H. Burrell, J.S. deGrassie, K.H. Finken, T. Jernigan, M.W. Jakubowski, C.J. Lasnier, M. Lehnen, A.W. Leonard, J. Lonnroth, E. Nardon, V. Parail, O. Schmitz, B. Unterberg, W.P. West, Rmp elm suppression in diii-d plasmas with iter similar shapes and collisionalities. Nucl. Fusion 48, 024002 (2008)

    Article  ADS  Google Scholar 

  • Y. Feng, F. Sardei, J. Kisslinger, P. Grigull, A 3d monte carlo code for plasma transport in island divertors. J. Nucl. Mater. 241–243, 930 (1997)

    Article  ADS  Google Scholar 

  • M.E. Fenstermacher, T.E. Evans, T.H. Osborne, M.J. Schaffer, M.P. Aldan, J.S. deGrassie, P. Gohil, I. Joseph, R.A. Moyer, P.B. Snyder, R.J. Groebner, M. Jakubowski, A.W. Leonard, O. Schmitz, the DIII-D Team: Effect of island overlap on edge localized mode suppression by resonant magnetic perturbations in diii-d. Phys. Plasmas 15, 056122 (2008)

    Article  ADS  Google Scholar 

  • G.M. Fishpool, P.S. Haynes, Field error instabilities in jet. Nucl. Fusion 34, 109 (1994)

    Article  ADS  CAS  Google Scholar 

  • R. Fitzpatrick, Interaction of tearing modes with external structures in cylindrical geometry. Nucl. Fusion 33, 1049 (1993)

    Article  ADS  CAS  Google Scholar 

  • R. Fitzpatrick, Nonlinear error-field penetration in low density ohmically heated tokamak plasmas. Plasma Phys. Control. Fusion 54, 094002 (2012)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, A neoclassical drift-magnetohydrodynamical fluid model of the interaction of a magnetic island chain with a resonant error-field in a high temperature tokamak plasma. Phys. Plasmas 25, 042503 (2018)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, Nonlinear neoclassical two-fluid theory of response of tokamak plasma to resonant error-field. Phys. Plasmas 25, 082513 (2018)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, T.C. Hender, The interaction of resonant magnetic perturbations with rotating plasmas. Phys. Fluids B 3, 644–673 (1991)

    Article  ADS  CAS  Google Scholar 

  • R. Fitzpatrick, F.L. Waelbroeck, Two-fluid magnetic island dynamics in slab geometry. Phys. Plasmas 12, 022307 (2005)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, F.L. Waelbroeck, Drift-tearing magnetic islands in tokamak plasmas. Phys. Plasmas 15, 012502 (2008)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, F.L. Waelbroeck, Effect of flow damping on drift-tearing magnetic islands in tokamak plasmas. Phys. Plasmas 16, 072507 (2009)

    Article  ADS  Google Scholar 

  • R. Fitzpatrick, Scaling of forced magnetic reconnection in the hall-magnetohydrodynamic taylor problem. Phys. Plasmas 11, 937 (2004)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • R. Fitzpatrick, An improved neoclassical drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in tokamak plasmas. Phys. Plasmas 23, 052506 (2016)

    Article  ADS  Google Scholar 

  • H. Frerichs, D. Reiter, O. Schmitz, T.E. Evans, Y. Feng, Three-dimensional edge transport simulations for diii-d plasmas with resonant magnetic perturbations. Nucl. Fusion 50, 034004 (2010)

    Article  ADS  Google Scholar 

  • S. Gu, C. Paz-Soldan, Y.Q. Liu, Y. Sun, B.C. Lyons, D.A. Ryan, D. Weisberg, N. Leuthold, M. Willensdorfer, W. Suttrop, J.-K. Park, N.C. Logan, M.W. Shafer, H.H. Wang, Q. Ma, A. Kirk, B. Tal, M. Griener, the ASDEX Upgrade, the EUROfusion MST1 Teams: Influence of triangularity on the plasma response to resonant magnetic perturbations. Nucl. Fusion 62, 076031 (2022)

    Article  ADS  CAS  Google Scholar 

  • R. Hager, C.S. Chang, N.M. Ferraro, R. Nazikian, Gyrokinetic understanding of the edge pedestal transport driven by resonant magnetic perturbations in a realistic divertor geometry. Phys. Plasmas 27, 062301 (2020)

    Article  ADS  CAS  Google Scholar 

  • T.S. Hahm, Y.J. Kim, P.H. Diamond, G.J. Choi, Anisotropic exb shearing rate in a magnetic island. Phys. Plasmas 28(2), 022302 (2021)

    Article  ADS  CAS  Google Scholar 

  • D.M. Harting, Y. Liang, S. Jachmich, R. Koslowski, G. Arnoux, S. Devaux, T. Eich, E. Nardon, D. Reiter, H. Thomsen, Strike point splitting in the heat and particle flux profiles compared with the edge magnetic topology in a n=2 resonant magnetic perturbation field at jet. Nuc. Fusion 52(5), 054009 (2012)

    Article  ADS  Google Scholar 

  • R.J. Hawryluk, D.J. Campbell, G. Janeschitz, P.R. Thomas, R. Albanese, R. Ambrosino, C. Bachmann, L. Baylor, M. Becoulet, I. Benfatto, J. Bialek, A. Boozer, A. Brooks, R. Budny, T. Casper, M. Cavinato, J.-J. Cordier, V. Chuyanov, E. Doyle, T. Evans, G. Federici, M. Fenstermacher, H. Fujieda, K. Gal, A. Garofalo, L. Garzotti, D. Gates, Y. Gribov, P. Heitzenroeder, T.C. Hender, N. Holtkamp, D. Humphreys, I. Hutchinson, K. Ioki, J. Johner, G. Johnson, Y. Kamada, A. Kavin, C. Kessel, R. Khayrutdinov, G. Kramer, A. Kukushkin, K. Lackner, I. Landman, P. Lang, Y. Liang, J. Linke, B. Lipschultz, A. Loarte, G.D. Loesser, C. Lowry, T. Luce, V. Lukash, S. Maruyama, M. Mattei, J. Menard, M. Merola, A. Mineev, N. Mitchell, E. Nardon, R. Nazikian, B. Nelson, C. Neumeyer, J.-K. Park, R. Pearce, R.A. Pitts, A. Polevoi, A. Portone, M. Okabayashi, P.H. Rebut, V. Riccardo, J. Roth, S. Sabbagh, G. Saibene, G. Sannazzaro, M. Schaffer, M. Shimada, A. Sen, A. Sips, C.H. Skinner, P. Snyder, R. Stambaugh, E. Strait, M. Sugihara, E. Tsitrone, J. Urano, M. Valovic, M. Wade, J. Wesley, R. White, D.G. Whyte, S. Wu, M. Wykes, L. Zakharov, Principal physics developments evaluated in the iter design review. Nucl. Fusion 49, 065012 (2009)

    Article  ADS  Google Scholar 

  • R.D. Hazeltine, M. Kotschenreuther, P.J. Morrison, A four-field model for tokamak plasma dynamics. Phys. Fluids 28, 2466 (1985)

    Article  ADS  CAS  Google Scholar 

  • P. Helander, C.D. Beidler, T.M. Bird, M. Drevlak, Y. Feng, R. Hatzky, F. Jenko, R. Kleiber, J.H.E. Proll, Y. Turkin, P. Xanthopoulos, Plasma Phys. Control. Fusion 54, 124009 (2012)

    Article  ADS  Google Scholar 

  • T.C. Hender, R. Fitzpatrick, A.W. Morris, P.G. Carolan, R.D. Durst, T. Eddlington, J. Ferreira, S.J. Fielding, P.S. Haynes, J. Hugill, I.J. Jenkins, R.J. La Haye, B.J. Parham, D.C. Robinson, T.N. Todd, M. Valovic, G. Vayakis, Effect of resonant magnetic perturbations on compass-c tokamak discharges. Nucl. Fusion 32, 2091 (1992)

    Article  ADS  CAS  Google Scholar 

  • W.A. Hornsby, P. Migliano, R. Buchholz, S. Grosshauser, A. Weikl, D. Zarzoso, F.J. Casson, E. Poli, A.G. Peeters, The non-linear evolution of the tearing mode in electromagnetic turbulence using gyrokinetic simulations. Plasma Phys. Control. Fusion 58(1), 014028 (2015)

    Article  ADS  Google Scholar 

  • Q. Hu, R. Nazikian, B.A. Grierson, N.C. Logan, J.-K. Park, C. Paz-Soldan, Q. Yu, Phys. Plasmas 26, 120702 (2019)

    Article  ADS  Google Scholar 

  • Q. Hu, N.C. Logan, J.-K. Park, C. Paz-Soldan, R. Nazikian, Q. Yu, Nonlinear modeling of the scaling law for the m/n = 3/2 error field penetration threshold. Nucl. Fusion 60, 076006 (2020)

    Article  ADS  CAS  Google Scholar 

  • Q. Hu, R. Nazikian, B.A. Grierson, N.C. Logan, D.M. Orlov, C. Paz-Soldan, Q. Yu, Wide operational windows of edge-localized mode suppression by resonant magnetic perturbations in the diii-d tokamak. Phys. Rev. Lett. 125, 045001 (2020)

    Article  ADS  CAS  PubMed  Google Scholar 

  • Q. Hu, R. Nazikian, B.A. Grierson, N.C. Logan, C. Paz-Soldan, Q. Yu, The role of edge resonant magnetic perturbations in edge-localized-mode suppression and density pump-out in low-collisionality diii-d plasmas. Nucl. Fusion 60, 076001 (2020)

    Article  ADS  CAS  Google Scholar 

  • Q.M. Hu, J.-K. Park, N.C. Logan, S.M. Yang, B.A. Grierson, R. Nazikian, Q. Yu, Nonlinear two-fluid modeling of plasma response to rmps for the elm control in the iter baseline. Nucl. Fusion 61, 106006 (2021)

    Article  ADS  CAS  Google Scholar 

  • Q.M. Hu, R. Nazikian, N.C. Logan, J.-K. Park, C. Paz-Soldan, S.M. Yang, B.A. Grierson, Y. In, Y.M. Jeon, M. Kim, S.K. Kim, D.M. Orlov, G.Y. Park, Q. Yu, Predicting operational windows of elms suppression by resonant magnetic perturbations in the diii-d and kstar tokamaks. Phys. Plasmas 28, 052505 (2021)

    Article  ADS  CAS  Google Scholar 

  • B. Hudson, T. Evans, C. Petty, P. Synder, Dependence of resonant magnetic perturbation experiments on the diii-d plasma shape. Nucl. Fusion 50, 064005 (2010)

    Article  ADS  Google Scholar 

  • G.T.A. Huijsmans, A. Loarte, Non-linear mhd simulation of elm energy deposition. Nucl. Fusion 53, 123023 (2013)

    Article  ADS  Google Scholar 

  • K. Ida, T. Kobayashi, M. Ono, T.E. Evans, G.R. McKee, M.E. Austin, Hysteresis relation between turbulence and temperature modulation during the heat pulse propagation into a magnetic island in diii-d. Phys. Rev. Lett. 120, 245001 (2018)

    Article  ADS  CAS  PubMed  Google Scholar 

  • Y. In, J.-K. Park, Y.M. Jeon, J. Kim, G.Y. Park, J.-W. Ahn, A. Loarte, W.H. Ko, H.H. Lee, J.W. Yoo, J.W. Juhn, S.W. Yoon, H. Park, Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks. Nucl. Fusion 57, 116054 (2017)

    Article  ADS  Google Scholar 

  • Y. In, Y.M. Jeon, J.-K. Park, A. Loarte, J.-W. Ahn, J.H. Lee, H.H. Lee, G.Y. Park, K. Kim, W.H. Ko, T. Rhee, J. Kim, S.W. Yoon, H. Park, 3D Physics Task Force in KSTAR: Tamed stability and transport using controlled non-axisymmetric fields in kstar. Nucl. Fusion 59, 056009 (2019)

    Article  ADS  CAS  Google Scholar 

  • A. Ishizawa, Y. Kishimoto, Y. Nakamura, Multi-scale interactions between turbulence and magnetic islands and parity mixture - a review. Plasma Phys. Control. Fusion 61, 056006 (2019)

    Article  Google Scholar 

  • M.W. Jakubowski, T.E. Evans, M.E. Fenstermacher, M. Groth, C.J. Lasnier, A.W. Leonard, O. Schmitz, J.G. Watkins, T. Eich, W. Fundamenski, R.A. Moyer, R.C. Wolf, L.B. Baylor, J.A. Boedo, K.H. Burrell, H. Frerichs, J.S. de Grassie, P. Gohil, I. Joseph, S. Mordijck, M. Lehnen, C.C. Petty, R.I. Pinsker, D. Reiter, T.L. Rhodes, U. Samm, M.J. Schaffer, P.B. Snyder, H. Stoschus, T. Osborne, B. Unterberg, E. Unterberg, W.P. West, Overview of the results on divertor heat loads in RMP controlled h-mode plasmas on DIII-d. Nucl. Fusion 49(9), 095013, (2009)

  • Y.M. Jeon et al., Suppression of edge localized modes in high-confinement kstar plasmas by non-axisymmetric magnetic perturbations. Phys. Rev. Lett. 109, 035004 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  • S.K. Kim, S. Pamela, O. Kwon, M. Becoulet, G.T.A. Huijsmans, Y. In, M. Hoelzl, J.H. Lee, M. Kim, G.Y. Park, H.S. Kim, Y.H. Lee, G.J. Choi, C.Y. Lee, A. Kirk, A. Thornton, JOREK team, Y.-S. Na, Nonlinear modeling of the effect of n=2 resonant magnetic field perturbation on peeling-ballooning modes in kstar. Nucl. Fusion 60, 026009 (2020)

  • S.K. Kim, S. Pamela, O. Kwon, G. Huijsmans, Y. In, J. Lee, M.W. Kim, Y.-S. Na, On effect of n=2 rmp to edge pedestal in kstar with nonlinear mhd simulation. In: Proceedings of the 28th IAEA Fusion Energy Conference, p. 2. IAEA (2021)

  • K. Kim, J.-K. Park, A.H. Boozer, Numerical verification of bounce-harmonic resonances in neoclassical toroidal viscosity for tokamaks. Phys. Rev. Lett. 110, 185004 (2013)

    Article  ADS  PubMed  Google Scholar 

  • S.K. Kim, R. Shousha, S.H. Hahn, A.O. Nelson, J. Wai, S.M. Yang, J.-K. Park, R. Nazikian, N.C. Logan, Y.M. Jeon, Y. In, J.H. Lee, J. Kim, C.Y. Lee, Y.-S. Na, E. Kolemen, Optimization of 3d controlled elm-free state with recovered global confinement for kstar with n = 1 resonant magnetic field perturbation. Nucl. Fusion 62, 026043 (2022)

    Article  ADS  Google Scholar 

  • A. Kirk, E. Nardon, R. Akers, M. Becoulet, G.D. Temmerman, B. Dudson, B. Hnat, Y.Q. Liu, R. Martin, P. Tamain, D. Taylor, the MAST team: resonant magnetic perturbation experiments on mast using external and internal coils for elm control. Nucl. Fusion 50, 034008 (2010)

    Article  ADS  Google Scholar 

  • A. Kirk, J. Harrison, Y. Liu, E. Nardon, I.T. Chapman, P. Denner, the MAST Team: observation of lobes near the x point in resonant magnetic perturbation experiments in mast. Phys. Rev. Lett. 108, 255003 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  • A. Kirk, I.T. Chapman, Y. Liu, P. Cahyna, P. Denner, G. Fishpool, C.J. Ham, J.R. Harrison, Y. Liang, E. Nardon, S. Saarelma, R. Scannell, A.J. Thornton, the MAST team: Understanding edge-localized mode mitigation by resonant magnetic perturbations on mast. Nucl. Fusion 53, 043007 (2013)

    Article  ADS  CAS  Google Scholar 

  • A. Kirk, W. Suttrop, I.T. Chapman, Y. Liu, A.J.T. Rscannell, L. BarreraOrte, P. Cahyna, T. Eich, R. Fischer, C. Fuchs, C. Ham, J.R. Harrison, M.W. Jakubowski, B. Kurzan, S. Pamela, M. Peterka, D. Ryan, S. Saarelma, B. Sieglin, M. Valovic, M. Willensdorfer, MAST and ASDEX Upgrade Teams: Effect of resonant magnetic perturbations on low collisionality discharges in mast and a comparison with asdex upgrade. Nucl. Fusion 55, 043011 (2015)

    Article  ADS  Google Scholar 

  • J.-M. Kwon, S. Ku, M.-J. Choi, C.S. Chang, R. Hager, E.S. Yoon, H.H. Lee, H.S. Kim, Gyrokinetic simulation study of magnetic island effects on neoclassical physics and micro-instabilities in a realistic kstar plasma. Phys. Plasmas 25(5), 052506 (2018)

    Article  ADS  Google Scholar 

  • R.J. La Haye, R. Fitzpatrick, T.C. Hender, A.W. Morris, J.T. Scoville, T.N. Todd, Non-linear instability to low m, n=1 error fields in diii-d as a function of plasma fluid rotation and beta. Phys. Fluids B 4, 2098 (1992)

    ADS  Google Scholar 

  • M.J. Lanctot, H. Reimerdes, A.M. Garofalo, M.S. Chu, Y.Q. Liu, E.J. Strait, G.L. Jackson, R.J. La Haye, M. Okabayashi, T.H. Osborne, M.J. Schaffer, Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria. Phys. Plasmas 17, 030701 (2010)

    Article  ADS  Google Scholar 

  • M.J. Lanctot, H. Reimerdes, A.M. Garofalo, M.S. Chu, J.M. Hanson, Y.Q. Liu, G.A. Navratil, I.N. Bogatu, Y. In, G.L. Jackson, R.J.L. Haye, M. Okayabashi, J.-K. Park, M.J. Schaffer, O. Schmitz, E.J. Strait, A.D. Turnbull, Measurement and modeling of three-dimensional equilibria in diii-d. Phys. Plasmas 18, 056121 (2011)

    Article  ADS  Google Scholar 

  • M.J. Lanctot, J.-K. Park, P. Piovesan, Y. Sun, R.J. Buttery, L. Frassubetti, B.A. Grierson, J.M. Hanson, S.R. Haskey, Y. In, Y.M. Jeon, R.J. La Haye, N.C. Logan, L. Marrelli, D.M. Orlov, C. Paz-Soldan, H.H. Wang, E.J. Strait, JET Contributors: Impact of toroidal and poloidal mode spectra on the control of non-axisymmetric fields in tokamaks. Phys. Plasmas 24, 056117 (2017)

    Article  ADS  Google Scholar 

  • S.A. Lazerson, J.-K. Park, N.C. Logan, A.H. Boozer, Numerical optimization of three-dimensional coils for nstx-u. Plasma Phys. Control. Fusion 57, 104001 (2015)

    Article  ADS  Google Scholar 

  • G.S. Lee et al., The kstar project: An advanced steady state superconducting tokamak experiment. Nucl. Fusion 40, 575–582 (2000)

    Article  ADS  CAS  Google Scholar 

  • J. Lee, G.S. Yun, M.J. Choi, J.-M. Kwon, Y.M. Jeon, W. Lee, N.C. Luhmann Jr., H.K. Park, Nonlinear interaction of edge-localized modes and turbulent eddies in toroidal plasma under n = 1 magnetic perturbation. Phys. Rev. Lett. 117, 075001 (2016)

    Article  ADS  PubMed  Google Scholar 

  • Y. Liang, H.R. Koslowski, P.R. Thomas, E. Nardon, B. Alper, P. Andrew, Y. Andrew, G. Arnoux, Y. Baranov, M. Bécoulet, M. Beurskens, T. Biewer, M. Bigi, K. Crombe, E. De La Luna, P. de Vries, W. Fundamenski, S. Gerasimov, C. Giroud, M.P. Gryaznevich, N. Hawkes, S. Hotchin, D. Howell, S. Jachmich, V. Kiptily, L. Moreira, V. Parail, S.D. Pinches, E. Rachlew, O. Zimmermann, Active control of type-i edge-localized modes with n=2 perturbation fields in the jet tokamak. Phys. Rev. Lett. 98, 265004 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  • Y. Liu, B.C. Lyons, S. Gu, A. Kirk, L. Li, C. Paz-Soldan, Shafer, M.W., Turnbull, A.D.: Influence of up-down asymmetry in plasma shape on rmp response. Plasma Phys. Control. Fusion 63, 065003 (2021)

  • Y. Liu, A. Kirk, L. Li, Y. In, R. Nazikian, Y. Sun, W. Suttrop, B. Lyons, D. Ryan, S. Wang, X. Yang, L. Zhou, EUROfusionMST1 team: Comparative investigation of elm control based on toroidal modelling of plasma response to rmp fields. Phys. Plasmas 24, 056111 (2017)

    Article  ADS  Google Scholar 

  • Y. Liu, C. Paz-Soldan, L. Li, Y. Sun, Role of 3d neoclassical particle flux in density pump-out during elm control by rmp in diii-d. Nucl. Fusion 60, 036018 (2020)

    Article  ADS  CAS  Google Scholar 

  • A. Loarte, G. Huijsmans, S. Futatani, L.R. Baylor, T.E. Evans, D.M. Orlov, O. Schmitz, M. Becoulet, P. Cahyna, Y. Gribov, A. Kavin, A. Sashala Naik, D.J. Campbell, T. Casper, E. Daly, H. Frerichs, A. Kischner, R. Laengner, S. Lisgo, R.A. Pitts, G. Saibene, A. Wingen, Progress on the application of elm control schemes to iter scenarios from the non-active phase to dt operation. Nucl. Fusion 54, 033007 (2014)

    Article  ADS  CAS  Google Scholar 

  • N.C. Logan, J.-K. Park, K. Kim, Z.R. Wang, J.W. Berkery, Neoclassical toroidal viscosity in perturbed equilibria with general tokamak geometry. Plasma Phys. 20, 122507 (2013)

    Article  Google Scholar 

  • N.C. Logan, J.-K. Park, Q. Hu, C. Paz-Soldan, T. Markovic, H.H. Wang, Y. In, L. Piron, P. Piovesan, C.E. Myers, M. Marascheck, S.M. Wolfe, E.J. Strait, S. Munaretto, Empirical scaling of the n=2 error field penetration threshold in tokamaks. Nucl. Fusion 60, 086010 (2020)

    Article  ADS  CAS  Google Scholar 

  • N.C. Logan, C. Zhu, J.-K. Park, S.M. Yang, Q. Hu, Physics basis for design of 3d coils in tokamaks. Nucl. Fusion 61, 076010 (2021)

    Article  ADS  CAS  Google Scholar 

  • J.D. Lore, A.R. Briesemeister, N.M. Ferraro, H. Frerichs, B. Lyons, A. McLean, J.-K. Park, M.W. Shafer, Pedestal-to-wall 3d fluid transport simulations on DIII-d. Nucl. Fusion 57(5), 056025 (2017)

    Article  ADS  Google Scholar 

  • J.L. Luxon, M.J. Schaffer, G.L. Jackson, J.A. Leuer, A. Nagy, J.T. Scoville, E.J. Strait, Tbr. Nucl. Fusion 43, 1813 (2003)

    Article  ADS  CAS  Google Scholar 

  • T. Markovic, M. Peterka, A. Loarte, J.-K. Park, Y. Gribov, J. Havlicek, R. Panek, P. Hacek, M. Hron, M. Imrisek, K. Kovarik, L. Kripner, K. Mitosinkova, M. Sos, M. Tomes, J. Varju, P. Vondracek, V. Weinzettl, the COMPASS team http://ohttp://ocs.ciemat.es/EPS2018ABS/pdf/O3.108.pdf. in Proceedings of the 45th EPS Conference (2018)

  • G.R. McKee, Z. Yan, C. Holland, R.J. Buttery, T.E. Evans, R.A. Moyer, S. Mordijck, R. Nazikian, T.L. Rhodes, O. Schmitz, M.R. Wade, Increase of turbulence and transport with resonant magnetic perturbations in ELM-suppressed plasmas on DIII-d. Nucl. Fusion 53(11), 113011 (2013)

    Article  ADS  Google Scholar 

  • J.E. Menard, R.E. Bell, D.A. Gates, S.P. Gerhardt, J.-K. Park, S.A. Sabbagh, J.W. Berkery, A. Egan, J. Kallman, S.M. Kaye, B. LeBlanc, Y.Q. Liu, A. Sontag, D. Swanson, H. Yuh, W. Zhu, the NSTX research team: progress in understanding error-field physics in nstx spherical torus plasmas. Nucl. Fusion 50, 045008 (2010)

    Article  ADS  Google Scholar 

  • R.A. Moyer, T.E. Evans, T.H. Osborne, P.R. Thomas, M. Becoulet, J.H. Harris, K.-H. Finken, J.A. Boedo, E.J. Doyle, M.E. Fenstermacher, P. Gohil, R.J. Groebner, M. Groth, G.L. Jackson, R.J. LaHaye, C.J. Lasnier, A.W. Leonard, G.R. McKee, H. Reimerdes, T.L. Rhodes, D.L. Rudakov, M.J. Schaffer, P.B. Snyder, M.R. Wade, G. Wang, J.G. Watkins, W.P. West, L. Zeng, Edge localized mode control with an edge resonant magnetic perturbation. Phys. Plasmas 12, 056119 (2005)

    Article  ADS  Google Scholar 

  • R.A. Moyer, C. Paz-Soldan, R. Nazikian, D.M. Orlov, N.M. Ferraro, B.A. Grierson, M. Knölker, B.C. Lyons, G.R. McKee, T.H. Osborne, T.L. Rhodes, O. Meneghini, S. Smith, T.E. Evans, M.E. Fenstermacher, R.J. Groebner, J.M. Hanson, R.J.L. Haye, T.C. Luce, S. Mordijck, W.M. Solomon, F. Turco, Z. Yan, L. Zeng, DIII-D Team: Validation of the model for elm suppression with 3d magnetic fields using low torque iter baseline scenario discharges in diii-d. Phys. Plasmas 24, 102501 (2017)

    Article  ADS  Google Scholar 

  • R. Nazikian, W. Suttrop, A. Kirk, T. Evans, B.A. Grierson, R. McDermott, C. Paz-Soldan, D. Orlov, M. Willensdorfer. First observation of elm suppression in asdex-upgrade in a similarity experiment with diii-d. In: Proceedings of the 26th IAEA Fusion Energy Conference, pp. 1. IAEA (2016)

  • R. Nazikian, C. Paz-Soldan, J.D. Callen, J.S. deGrassie, D. Eldon, T.E. Evans, N.M. Ferraro, B.A. Grierson, R.J. Groebner, S.R. Haskey, C.C. Hegna, J.D. King, N.C. Logan, G.R. McKee, R.A. Moyer, M. Okabayashi, D.M. Orlov, T.H. Osborne, J.-K. Park, T.L. Rhodes, M.W. Shafer, P.B. Snyder, W.M. Solomon, E.J. Strait, M.R. Wade, Pedestal bifurcation and resonant field penetration at the threshold of edge-localized mode suppression in the diii-d tokamak. Phys. Rev. Lett. 114, 105002 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  • C. Nürenberg, R. Zille, Quasihelically symmetric toroidal stellarators. Phys. Lett. A 129, 113 (1988)

    Article  ADS  Google Scholar 

  • R. Orain, M. Hölzl, E. Viezzer, M. Dunne, M. Bécoulet, P. Cahyna, G.T.A. Huijsmans, J. Morales, M. Willensdorfer, W. Suttrop, A. Kirk, S. Pamela, S. Günter, K. Lackner, E. Strumberger, A. Lessig, the ASDEX Upgrade team, the EUROfusion MST1 Team: Non-linear modeling of the plasma response to rmps in asdex upgrade. Nucl. Fusion 57, 022013 (2017)

    Article  ADS  Google Scholar 

  • G. Park, Y. In, J.-K. Park, W.H. Ko, J. Lee, M. W. G.W.S. Kim, S.-H. Hahn, S.K. Kim, S.M. Yang, Q. Hu, T. Rhee, M.J. Choi, K. Kim, H.H. Lee, Y.M. Jeon, W.-C. Kim, S.W. Yoon, Overview of recent progress in 3d field physics in kstar. J. Korean Phys. Soc. 80, 759 (2022)

  • J.-K. Park, N.C. Logan, Self-consistent perturbed equlibrium with neoclassical toroidal torque in tokamaks. Phys. Plasmas 24, 032505 (2017)

    Article  ADS  Google Scholar 

  • J.-K. Park, M.J. Schaffer, J.E. Menard, A.H. Boozer, Control of asymmetric magnetic perturbations in tokamaks. Phys. Rev. Lett. 99, 195003 (2007)

    Article  ADS  PubMed  Google Scholar 

  • J.-K. Park, A.H. Boozer, J.E. Menard, Spectral asymmetry due to magnetic coordinates. Phys. Plasmas 15, 064501 (2008)

    Article  ADS  Google Scholar 

  • J.-K. Park, A.H. Boozer, J.E. Menard, Non-ambipolar transport by trapped particles in tokamaks. Phys. Rev. Lett. 102, 065002 (2009)

    Article  ADS  PubMed  Google Scholar 

  • G. Park, C.S. Chang, I. Joseph, R.A. Moyer, Plasma transport in stochastic magnetic field caused by vacuum resonant magnetic perturbations at diverted tokamak edge. Phys. Plasmas 17, 102503 (2010)

    Article  ADS  Google Scholar 

  • J.-K. Park, Y.M. Jeon, J.E. Menard, W.H. Ko, S.G. Lee, Y.S. Bae, M. Joung, K.-I. You, K.-D. Lee, N.C. Logan, K. Kim, J.S. Ko, S.W. Yoon, S.H. Hahn, J.H. Kim, W.C. Kim, Y.-K. Oh, J.-G. Kwak, Rotational resonance of nonaxisymmetric magnetic braking in the kstar tokamak. Phys. Rev. Lett. 111, 095002 (2013)

    Article  ADS  PubMed  Google Scholar 

  • J.-K. Park, Y.M. Jeon, Y. In, J.-W. Ahn, R. Nazikian, G. Park, J. Kim, H.H. Lee, W.H. Ko, N.C. Logan, Z. Wang, E.A. Feibush, J.E. Menard, M.C. Zarnstorff, 3d field phase-space control in tokamak plasmas. Nat. Phys. 14, 1223–1228 (2018)

    Article  CAS  Google Scholar 

  • J.-K. Park, S.M. Yang, N.C. Logan, Q. Hu, C. Zhu, M.C. Zarnstorff, R. Nazikian, C. Paz-Soldan, Y.M. Jeon, W.H. Ko, Quasisymmetric optimization of nonaxisymmetry in tokamaks. Phys. Rev. Lett. 126, 125001 (2021)

    Article  ADS  CAS  PubMed  Google Scholar 

  • C. Paz-Soldan, M.J. Lanctot, N.C. Logan, D. Shiraki, R.J. Buttery, J.M. Hanson, R.J. La Haye, J.-K. Park, W.M. Solomon, E.J. Strait, The importance of matched poloidal spectra to error field correction in diii-d. Phys. Plasmas 21, 072503 (2014)

    Article  ADS  Google Scholar 

  • C. Paz-Soldan, R. Nazikian, S.R. Haskey, N.C. Logan, E.J. Strait, N.M. Ferraro, J.M. Hanson, J.D. King, M.J. Lanctot, R.A. Moyer, M. Okabayashi, J.-K. Park, M.W. Shafer, B.J. Tobias, Observation of a multimode plasma response and its relationship to density pumpout and edge-localized mode suppression. Phys. Rev. Lett. 114, 105001 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  • C. Paz-Soldan, R. Nazikian, L. Cui, B.C. Lyons, D.M. Orlov, A. Kirk, N.C. Logan, T.H. Osborne, W. Suttrop, D.B. Weisberg, The effect of plasma shape and neutral beam mix on the rotation threshold for rmp-elm suppression. Nucl. Fusion 59, 056012 (2019)

    Article  ADS  CAS  Google Scholar 

  • E. Poli, A. Bottino, A.G. Peeters, Behaviour of turbulent transport in the vicinity of a magnetic island. Nucl. Fusion 49, 075010 (2009)

    Article  ADS  Google Scholar 

  • T. Rhee, J. Kim, K. Kim, J. Kang, M. Podesta, Y.-S. Park, B.-H. Park, Simulation study of fast ion losses associated with the rotating n = 1 resonant magnetic perturbations in kstar. Nucl. Fusion 62, 066028 (2022)

    Article  ADS  CAS  Google Scholar 

  • P.H. Rutherford, Nonlinear growth of the tearing mode. Phys. Fluid 16, 1903 (1973)

    Article  ADS  Google Scholar 

  • M.J. Schaffer, J.E. Menard, M.P. Aldan, J.M. Bialek, T.E. Evans, R.A. Moyer, Study of in-vessel nonaxisymmetric elm suppression coil concepts for iter. Nucl. Fusion 48, 024004 (2008)

    Article  ADS  Google Scholar 

  • O. Schmitz, T.E. Evans, M.E. Fenstermacher, A. McLean, J. Boedo, N.H. Brooks, H. Frerichs, M. Jakubowski, R. Laengner, C.L. Lasnier, A. Loarte, R.A. Moyer, D. Orlov, H. Reimerdes, D. Reiter, U. Samm, H. Stoschus, E.A. Unterberg, J.G. Watkins, The influence of three-dimensional stochastic magnetic boundaries on plasma edge transport and the resulting plasma wall interaction. J. Nucl. Mater. 415(1, Supplement), 886–893 (2011)

    Article  Google Scholar 

  • J.T. Scoville, R.J. LaHaye, Multi-mode error field correction on the diii-d tokamak. Nucl. Fusion 43, 250 (2003)

    Article  ADS  CAS  Google Scholar 

  • M.W. Shafer, C. Paz-Soldan, T.E. Evans, N. Ferraro, B. Lyons, T. Osborne, A. Turnbull. Limits of rmp elm suppression in double null plasmas. In: Proceedings of the 28th IAEA Fusion Energy Conference, pp. 1–930. IAEA (2021)

  • K.C. Shaing, Neoclassical flows and transport in non-axisymmetric toroidal plasmas. Phys. Fluids 26, 3315–3326 (1983)

    Article  ADS  CAS  Google Scholar 

  • K.C. Shaing, Symmetry-breaking induced transport in the vicinity of a magnetic island. Phys. Rev. Lett. 87, 245003 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  • K.C. Shaing, Magnetohydrodynamic-activity-induced toroidal momentum dissipation in collisionless regimes in tokamaks. Phys. Plasmas 10, 1443 (2003)

    Article  ADS  CAS  Google Scholar 

  • K.C. Shaing, P. Cahyna, M. Becoulet, J.-K. Park, S.A. Sabbagh, M.S. Chu, Collisional boundary layer analysis for neoclassical toroidal plasma viscosity in tokamaks. Phys. Plasmas 15, 082506 (2008)

    Article  ADS  Google Scholar 

  • K.C. Shaing, K. Ida, S.A. Sabbagh, Neoclassical plasma viscosity and transport processes in non-axisymmetric neoclassical plasma viscosity and transport processes in non-axisymmetric tori. Nucl. Fusion 55, 125001 (2015)

    Article  ADS  Google Scholar 

  • T. Shoji, H. Tamai, Y. Miura, M. Mori, H. Ogawa, A.W. Leonard, T. Jensen, A.W. Hyatt, A.M. Howald, G. Fuchs, N. Ohyabu, N. Asakura, T. Fujita, M. Shimada, S. Tsuji, H. Maeda, H. Aikawa, K. Hoshino, S. Kasai, T. Kawakami, H. Kawashima, M. Maeno, T. Matsuda, T. Ogawa, T. Seike, N. Suzuki, K. Uehara, T. Yamamoto, T. Yamauchi, T. Hamano, K. Hasegawa, A. Honda, M. Kazawa, Y. Kashiwa, K. Kikuchi, H. Okano, E. Sato, N. Seki, T. Shibata, T. Shiina, S. Suzuki, T. Tani, T. Tokutake, Y. Tomiyama, T. Yamasato, Effects of ergodization on plasma confinement in jft-2m. Journal of Nucl. Materials 196–198, 296–300 (1992)

    Article  ADS  Google Scholar 

  • R. Shousha, S.K. Kim, K.G. Erickson, S.H. Hahn, A.O. Nelson, S.M. Yang, J.-K. Park, J. Wai, Y.M. Jeon, J.H. Lee, J. Jang, D. Seo, E. Kolemen, Design and experimental demonstration of feedback adaptive rmp elm controller toward complete long pulse elm suppression on kstar. Phys. Plasmas 29, 032514 (2022)

  • P.B. Snyder, K.H. Burrell, H.R. Wilson, M.S. Chu, M.E. Fenstermacher, A.W. Leonard, R.A. Moyer, T.H. Osborne, M. Umansky, W.P. West, X.Q. Xu, Stability and dynamics of the edge pedestal in the low collisionality regime: physics mechanisms for steady-state elm-free operation. Nucl. Fusion 47, 961–968 (2007)

    Article  ADS  CAS  Google Scholar 

  • Y. Sun, Y. Liang, K.C. Shaing, H.R. Koslowski, C. Wiegmann, T. Zhang, Neoclassical toroidal plasma viscosity torque in collisionless regimes in tokamaks. Phys. Rev. Lett. 105, 145002 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  • Y. Sun, Y. Liang, K.C. Shaing, Y.Q. Liu, H.R. Koslowski, S. Jachmich, B. Alper, A. Alfier, O. Asunta, P. Buratti, G. Corrigan, E. Delabie, C. Giroud, M.P. Gryaznevich, D. Harting, T. Hender, E. Nardon, V. Naulin, V. Parail, T. Tala, C. Wiegmann, S. Wiesen, T. Zhang, JET-EFDA contributors: Non-resonant magnetic braking on jet and textor. Nucl. Fusion 52, 083007 (2012)

    Article  ADS  Google Scholar 

  • Y. Sun, Y. Liang, Y.Q. Liu, S. Gu, X. Yang, W. Guo, T. Shi, M. Jia, L. Wang, B. Lyu, C. Zhou, A. Liu, Q. Zang, H. Liu, N. Chu, H.H. Wang, T. Zhang, J. Qian, L. Xu, K. He, D. Chen, B. Shen, X. Gong, X. Ji, S. Wang, M. Qi, Y. Song, Q. Yuan, Z. Sheng, G. Gao, P. Fu, B. Wan, Nonlinear transition from mitigation and suppression of the edge localized mode with resonant magnetic perturbations in the east tokamak. Phys. Rev. Lett. 117, 115001 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  • W. Suttrop, T. Eich, J.C. Fuchs, S. Gunter, A. Janzer, A. Herrmann, A. Kallenbach, P.T. Lang, T. Lunt, M. Maraschek, R.M. McDermott, A. Mlynek, T. Putterich, M. Rott, T. Vierle, E. Wolfrum, Q. Yu, I. Zammuto, H. Zohm, ASDEX Upgrade Team: First observation of edge localized modes mitigation with resonant and nonresonant magnetic perturbations in asdex upgrade. Phys. Rev. Lett. 106, 225004 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  • W. Suttrop, A. Kirk, R. Nazikian, N. Leuthold, E. Strumberger, M. Willensdorfer, M. Cavedon, M. Dunne, R. Fischer, S. Fietz, J.C. Fuchs, Y.Q. Liu, R.M. McDermott, F. Orain, D.A. Ryan, E. Viezzer, The ASDEX Upgrade Team, The DIII-D Team, The Eurofusion MST1 Team: Experimental studies of high-confinement mode plasma response to non-axisymmetric magnetic perturbations in asdex upgrade. Plasma Phys. Control. Fusion 59, 014049 (2017)

    Article  ADS  Google Scholar 

  • W. Suttrop, A. Kirk, V. Bobkov, M. Cavedon, M. Dunne, R.M. McDermott, H. Meyer, R. Nazikian, C. Paz-Soldan, D.A. Ryan, E. Viezzer, M. Willensdorfer, The ASDEX Upgrade, MST1 Teams: Experimental conditions to suppress edge localised modes by magnetic perturbations in the asdex upgrade tokamak. Nucl. Fusion 58, 096031 (2018)

    Article  ADS  Google Scholar 

  • S. Taimourzadeh, L. Shi, Z. Lin, R. Nazikian, I. Holod, D. Spong, Effects of rmp-induced changes of radial electric fields on microturbulence in diii-d pedestal top. Nucl. Fusion 59, 046005 (2019)

    Article  ADS  Google Scholar 

  • M.A. Van Zeeland, N.M. Ferraro, B.A. Grierson, W.W. Heidbrink, G.J. Kramer, C.J. Lasnier, D.C. Pace, S.L. Allen, X. Chen, T.E. Evans, M. García-Mun̈oz, J.M. Hanson, M.J. Lanctot, L.L. Lao, W.H. Meyer, R.A. Moyer, R. Nazikian, D.M. Orlov, C. Paz-Soldan, A. Wingen, Fast ion transport during applied 3d magnetic perturbations on diii-d. Nucl. Fusion 55, 073028 (2015)

  • M.R. Wade, R. Nazikian, J.S. deGrassie, T.E. Evans, N.M. Ferraro, R.A. Moyer, D.M. Orlov, R.J. Buttery, M.E. Fenstermacher, A.M. Garofalo, M.A. Lanctot, G.R. McKee, T.H. Osborne, M.A. Shafer, W.M. Solomon, P.B. Snyder, W. Suttrop, A. Wingen, E.A. Unterberg, L. Zeng, Advances in the physics understanding of elm suppression using resonant magnetic perturbations in diii-d. Nucl. Fusion 55, 023002 (2015)

    Article  ADS  CAS  Google Scholar 

  • F.L. Waelbroeck, Shielding of resonant magnetic perturbations in the long mean-free path regime. Phys. Plasmas 10, 4040 (2003)

    Article  ADS  CAS  Google Scholar 

  • F.L. Waelbroeck, I. Joseph, E. Nardon, M. Bécoulet, R. Fitzpatrick, Role of singular layers in the plasma response to resonant magnetic perturbations. Nucl. Fusion 52, 074004 (2012)

    Article  ADS  Google Scholar 

  • F. Wagner, G. Fussmann, T. Grave, M. Keilhacker, M. Kornherr, K. Lackner, K. McCormick, E.R. Muller, A. Stabler, G. Becker, K. Bernhardi, U. Ditte, A. Eberhagen, O. Gehre, J. Gernhardt, v. G. Gierke, E. Glock, O. Gruber, G. Haas, M. Hesse, G. Janeschitz, F. Karger, S. Kissel, O. Kluber, G. Lisitano, H.M. Mayer, D. Meisel, V. Mertens, H. Murrnann, W. Poschenrieder, H. Rapp, H. Rohr, F. Ryter, F. Schneider, G. Siller, P. Smeulders, F. Soldner, E. Speth, K.-H. Steuer, Z. Szymanski, O. Vollmer, Development of an edge transport barrier at the h-mode transition of asdex. Phys. Rev. Lett. 53, 1453 (1984)

  • R.E. Waltz, N.M. Ferraro, Theory and simulation of quasilinear transport from external magnetic field perturbations in a diii-d plasma. Phys. Plasmas 22, 042507 (2015)

    Article  ADS  Google Scholar 

  • M. Willensdorfer, V. Mitterauer, G. Suarez, W. Suttrop, M.R. Cianciosa, M. Dunne, R. Fischer, M. Hoelzl, T. Gleiter, D. Wendler. Internal Plasma Response Measurements at the pedestal top in ELM suppressed plasmas in ASDEX Upgrade. 2022 APS invited talk, GL02.00005

  • S.M. Wolfe, I.H. Hutchinson, R.S. Granetz, J. Rice, A. Hubbard, A. Lynn, P. Phillips, T.C. Hender, D.F. Howell, R.J. La Haye, J.T. Scoville, Nonaxisymmetric field effects on alcator c-mod. Phys. Plasmas 12, 056110 (2005)

    Article  ADS  Google Scholar 

  • Y. Xu, L. Li, Y. Hu, Y. Liu, W. Guo, L. Ye, X. Xiao, Numerical simulations of nbi fast ion loss with rmps on the east tokamak. Nucl. Fusion 60, 086013 (2020)

    Article  ADS  CAS  Google Scholar 

  • S.M. Yang, J.-K. Park, N.C. Logan, C. Zhu, Q. Hu, Y.M. Jeon, Y. In, W.H. Ko, S.K. Kim, Y.H. Lee, Y.S. Na, Localizing resonant magnetic perturbations for edge localized mode control in kstar. Nucl. Fusion 60, 096023 (2020)

    Article  ADS  CAS  Google Scholar 

  • Q. Yu, S. G̈unter, Y. Kikuchi, K.H. Finken, Numerical modelling of error field penetration. Nucl. Fusion 48, 024007 (2008)

  • W. Zhu, S.A. Sabbagh, R.E. Bell, J.M. Bialek, B.P. LeBlanc, S.M. Kaye, F.M. Levinton, J.E. Menard, K.C. Shaing, A.C. Sontag, H. Yuh, Observation of plasma toroidal-momentum dissipation by neoclassical toroidal viscosity. Phys. Rev. Lett. 96, 225002 (2006)

    Article  ADS  CAS  PubMed  Google Scholar 

  • C. Zhu, S.R. Hudson, Y. Song, Y. Wan, New method to design stellarator coils without the winding surface. Nucl. Fusion 58, 016008 (2018)

    Article  ADS  Google Scholar 

  • H. Zohm, Edge localized modes (elms). Plasma Phys. Control. Fusion 38, 105–128 (1996)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

The author would like to acknowledge a number of US collaborators who are participating in the project named "Physics Basis, Optimization, and Control for Integrated 3D Edge Long-Pulse Tokamak Scenarios" and offering the materials used in this particle. They are Qiming Hu, Seong Moo Yang, Caoxiang Zhu in Princeton Plasma Physics Laboratory, SangKeyun Kim, Richardo Shousha, Egemen Kolemen in Princeton University, Jonathan Van Blarcum, Heinke Frerichs in University of Wisconsin - Madison, Nikolas Logan in Lawrence Livermore National Laboratory, Shuai Gu, Tyler Cotes, Yueqiang Liu in General Atomics, Nils Leuthold, Carlos Paz-Soldan in Columbia University, Dmitri Orlov in University of California - San Diego, Javier Hernandez Nicolau, Zhihong Lin in University of California - Urvine. The cooperations by KSTAR collaborations are also greatly appreciated, particularly by Yongkyoon In, Jinyoung Heo in Ulsan National Institute of Science and Technology, Gunyoung Park, Wonha Ko, Young-Mu Jeon in Korean Institute of Fusion Energy. In particular, the author and collaborators are much indebted to Todd E. Evans who was collaborating in the project but unfortunately passed away, as the mentor for all with unparalleled scientific impact for the field discussed in this article. This work was supported by DOE Contract No. DE-AC02-09CH11466 for Princeton Plasma Physics Laboratory (PPPL), by R&D Program of “KSTAR Experimental Collaboration and Fusion Plasma Research (EN2201-13)" through the Korea Institute of Fusion Energy (KFE) funded by Korea Ministry of Science and ICT (MSIT), by the National Research Foundation (NRF) grant No. RS-2023-00281272 funded by MSIT, and also by the New Faculty Startup Fund from Seoul National University.

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Park, JK. Optimizing 3D magnetic perturbations for edge instability control in the KSTAR tokamak. Rev. Mod. Plasma Phys. 8, 1 (2024). https://doi.org/10.1007/s41614-023-00137-0

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