A small relaxation of the axisymmetric magnetic field of a tokamak into a non-axisymmetric three-dimensional (3D) configuration can be effective to control magnetohydrodynamic instabilities, such as edge-localized modes. However, a major challenge to the concept of 3D tokamaks is that there are virtually unlimited possible choices for a 3D magnetic field, and most of them will only destabilize or degrade plasmas by symmetry breaking. Here, we demonstrate the phase-space visualization of the full 3D field-operating windows of a tokamak, which allows us to predict which configurations will maintain high confinement without magnetohydrodynamic instabilities in an entire region of plasmas. We test our approach at the Korean Superconducting Tokamak Advanced Research (KSTAR) facility, whose 3D coils with many degrees of freedom in the coil space make it unique for this purpose. Our experiments show that only a small subset of coil configurations can accomplish edge-localized mode suppression without terminating the discharge with core magnetohydrodynamic instabilities, as predicted by the perturbative 3D expansion of plasma equilibrium and the optimizing principle of local resonance. The prediction provided excellent guidance, implying that our method can substantially improve the efficiency and fidelity of the 3D optimization process in tokamaks.

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The authors would like to thank all the KSTAR team members for their support and assistance to our studies. We also wish to acknowledge Alberto Roarte, in the ITER organization, for illuminating discussions of the results and applications. This work was supported by DOE contract DE-AC02-76CH03073 (PPPL) and also by the Korean Ministry of Science and Technology for the KSTAR project.

Author information


  1. Princeton Plasma Physics Laboratory, Princeton, NJ, USA

    • Jong-Kyu Park
    • , Raffi Nazikian
    • , Nikolas C. Logan
    • , Zhirui Wang
    • , Eliot A. Feibush
    • , Jonathan E. Menard
    •  & Michael C. Zarnstroff
  2. National Fusion Research Institute, Daejeon, South Korea

    • YoungMu Jeon
    • , Yongkyoon In
    • , Gunyoung Park
    • , Jaehyun Kim
    • , HyungHo Lee
    • , WonHa Ko
    •  & Hyun-Seok Kim
  3. Oak Ridge National Laboratory, Oak Ridge, TN, USA

    • Joon-Wook Ahn


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J.-K.P. carried out the 3D simulations and led the experimental validations. Y.M.J., Y.I., J.-W.A., G.Y.P. and J.K. participated in all the experimental procedures from the initial design to the final execution. R.N. and N.C.L. contributed to the clarification of the issues and the presentation of the results. H.H.L., W.H.K. and H.-S.K. provided reconstructed profiles and plasma equilibria in experiments. Z.W. carried out MARS calculations for benchmark, and E.A.F. visualized the 3D MHD-free window in the coil configuration space. J.E.M. and M.C.Z. offered general guidance to the research.

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The authors declare no competing interests.

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Correspondence to Jong-Kyu Park.

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