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3D field phase-space control in tokamak plasmas

Abstract

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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Fig. 1: MHD-stable tokamak operation with 3D fields.
Fig. 2: KSTAR 3D coils and fields.
Fig. 3: Stable 3D field-operating window in the n = 1 coil phase space.
Fig. 4: Validation of predicted 3D field-operating window.
Fig. 5: Plasma amplification and response to 3D fields.
Fig. 6: Stable 3D field-operating windows in the n = 2 coil phase space.

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References

  1. Ikeda, K. Progress in the ITER physics basis. Nucl. Fusion 47, S1–S17 (2007).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Buttery, R. J. et al. Error field mode studies on JET, COMPASS-D and DIII-D, and implications for ITER. Nucl. Fusion 39, 1827–1835 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Paz-Soldan, C. et al. The importance of matched poloidal spectra to error field correction in DIII-D. Phys. Plasmas 21, 072503 (2014).

    Article  ADS  Google Scholar 

  6. Evans, T. E. et al. 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  Google Scholar 

  7. Evans, T. E. et al. Edge stability and transport control with resonant magnetic perturbations in collisionless tokamak plasmas. Nat. Phys. 2, 419–423 (2006).

    Article  Google Scholar 

  8. Evans, T. E. et al. RMP ELM suppression in DIII-D plasmas with ITER similar shapes and collisionalities. Nucl. Fusion 48, 024002 (2008).

    Article  ADS  Google Scholar 

  9. Liang, Y. et al. Active control of type-I edge-localized modes with n =1 perturbation fields in the JET tokamak. Phys. Rev. Lett. 98, 265004 (2007).

    Article  ADS  Google Scholar 

  10. Suttrop, W. et al. First observation of edge localized modes mitigation with resonant and nonresonant magnetic perturbations in ASDEX Upgrade. Phys. Rev. Lett. 106, 225004 (2011).

    Article  ADS  Google Scholar 

  11. Kirk, A. et al. Observation of lobes near the X point in resonant magnetic perturbation experiments in MAST. Phys. Rev. Lett. 108, 255003 (2012).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Nazikian, R. et al. 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  Google Scholar 

  14. Sun, Y. et al. 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  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Snyder, P. et al. 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  Google Scholar 

  18. Hawryluk, R. et al. Principal physics developments evaluated in the ITER design review. Nucl. Fusion 49, 065012 (2009).

    Article  ADS  Google Scholar 

  19. Loarte, A. et al. 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  Google Scholar 

  20. Schmitz, O. et al. Enhancement of helium exhaust by resonant magnetic perturbation fields at LHD and TEXTOR. Nucl. Fusion 56, 106011 (2016).

    Article  ADS  Google Scholar 

  21. Kolmogorov, A. N. On the preservation of conditionally periodic motions under small variations of the Hamilton function. Dokl. Akad. Nauk SSSR 98, 527–530 (1954).

    MathSciNet  MATH  Google Scholar 

  22. Arnol’d, V. I. Small denominators and problems of stability of motion in classical and celestial mechanics. Russ. Math. Surveys 18, 85–191 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  23. Möser, J. On invariant curves of area-preserving mappings of an annulus. Machr. Akad. Wiss. Goett. II, Math.-Phys. Kl. 2a, 1–20 (1962).

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Troyon, F. et al. MHD-limits to plasma confinement. Plasma Phys. Control. Fusion 26, 209–215 (1984).

    Article  ADS  Google Scholar 

  27. Fenstermacher, M. E. et al. 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 

  28. Park, G., Chang, C. S., Joseph, I. & Moyer, R. A. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Callen, J. D., Hegna, C. C. & Cole, A. J. Magnetic-flutter-induced pedestal plasma transport. Nucl. Fusion 53, 113015 (2013).

    Article  ADS  Google Scholar 

  32. Bécoulet, M. et al. Mechanisms of edge localized mode mitigation by resonant magnetic perturbations. Phys. Rev. Lett. 113, 115001 (2014).

    Article  ADS  Google Scholar 

  33. Wade, M. R. et al. Advances in the physics understanding of ELM suppression using resonant magnetic perturbations in DIII-D. Nucl. Fusion 55, 023002 (2015).

    Article  ADS  Google Scholar 

  34. Paz-Soldan, C. et al. 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  Google Scholar 

  35. Orain, R. et al. Non-linear modeling of the plasma response to RMPs in ASDEX Upgrade. Nucl. Fusion 57, 022013 (2017).

    Article  ADS  Google Scholar 

  36. In, Y., Park, J.-K., Jeon, J. M., Kim, J. & Okabayashi, M. Extremely low intrinsic non-axisymmetric field in KSTAR and its implications. Nucl. Fusion 55, 043004 (2015).

    Article  ADS  Google Scholar 

  37. Park, J.-K., Boozer, A. H. & Glasser, A. H. Computation of three-dimensional tokamak and spherical torus equilibria. Phys. Plasmas 14, 052110 (2007).

    Article  ADS  Google Scholar 

  38. Callen, J. D. et al. Model of n=2 RMP ELM Suppression in DIII-D Report UW-CPTC 16-4 (University of Wisconsin–Madison Center for Plasma Theory and Computation, 2016); http://www.cptc.wisc.edu

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

    Article  ADS  Google Scholar 

  40. Shaing, K. C. & Callen, J. D. Neoclassical flows and transport in nonaxisymmetric toroidal plasmas. Phys. Fluids 26, 3315–3326 (1983).

    Article  ADS  Google Scholar 

  41. Lanctot, M. J. et al. Validation of the linear ideal magnetohydrodynamic model of three-dimensional tokamak equilibria. Phys. Plasmas 17, 030701 (2010).

    Article  ADS  Google Scholar 

  42. Wang, Z. R., Lanctot, M. J., Liu, Y. Q., Park, J.-K. & Menard, J. E. Three-dimensional drift kinetic response of high-beta plasmas in the DIII-D tokamak. Phys. Rev. Lett. 114, 145005 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  44. Lee, S. G. et al. Validation of toroidal rotation and ion temperature in KSTAR plasmas. Fusion Sci. Technol. 69, 555–559 (2016).

    Article  Google Scholar 

  45. In, Y. et al. Enhanced understanding of non-axisymmetric intrinsic and controlled field impacts in tokamaks. Nucl. Fusion 57, 116054 (2017).

    Article  ADS  Google Scholar 

  46. Liu, Y., Chu, M. S., Chapman, I. T. & Hender, T. C. Toroidal self-consistent modeling of drift kinetic effects on the resistive wall mode. Phys. Plasmas 15, 112503 (2008).

    Article  ADS  Google Scholar 

  47. Gribov, Y. et al. Error fields expected in ITER and their correction. In Proc. 24th IAEA Fusion Energy Conference ITR/P5–29 (IAEA, Vienna, 2012).

  48. Liu, Y. et al. Comparative investigation of ELM control based on toroidal modelling of plasma response to RMP fields. Phys. Plasmas 24, 056111 (2017).

    Article  ADS  Google Scholar 

  49. Waltz, R. E. & Ferraro, N. M. 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 

  50. Lee, J. et al. 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  Google Scholar 

  51. Park, J.-K., Schaffer, M. J., Haye, R. J. La, Scoville, T. J. & Menard, J. E. Error field correction in DIII-D ohmic plasmas with either handedness. Nucl. Fusion 51, 023003 (2011).

    Article  ADS  Google Scholar 

  52. Park, J.-K., Schaffer, M. J., La Haye, R. J., Scoville, T. J. & Menard, J. E. Corrigendum: Error field correction in DIII-D ohmic plasmas with either handedness. Nucl. Fusion 52, 089501 (2012).

    Article  Google Scholar 

  53. Lanctot, M. J. et al. 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 

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Acknowledgements

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.

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Contributions

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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Correspondence to Jong-Kyu Park.

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Park, JK., Jeon, Y., In, Y. et al. 3D field phase-space control in tokamak plasmas. Nature Phys 14, 1223–1228 (2018). https://doi.org/10.1038/s41567-018-0268-8

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