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Simulation of hard X-ray time evolution in plasma tokamak by using the NARX-GA hybrid neural network

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Abstract

The NARX-GA hybrid neural network was applied to simulate the time evolution of runaway electrons (REs) in the plasma tokamak. This particular type of artificial neural network was created specifically for time series prediction. The NARX-GA network was built using inputs from some plasma diagnostic signals (loop voltage, hard X-ray) collected during all phases of plasma tokamak discharges. The network output predicts the time evolution of hard X-ray (HXR) signals up to 500 μs, which can be achieved with high accuracy (MSE = \(3.76\times {10}^{-5}\)). The real-time application of this methodology can pave the way for prompt REs control action. The confinement time increases as the REs generation decreases, and their destructive effects on the tokamak wall decrease as well. Early prediction of RE behavior is critical in attempting to mitigate their potentially dangerous effects.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. The data that support the findings of this study are available upon reasonable request from the authors.

References

  1. B.N. Breizman, P. Aleynikov, E.M. Hollmann, M. Lehnen, Nucl. Fusion 59, 083001 (2019)

    Google Scholar 

  2. M. Bakhtiari, G.J. Kramer, M. Takechi, H. Tamai, Y. Miura, Y. Kusama, Y. Kamada, Phys. Rev. Lett. 94, 2 (2005)

    Google Scholar 

  3. R.D. Gill, Nucl. Fusion 33, 1613 (1993)

    Google Scholar 

  4. R.D. Gill, B. Alper, A.W. Edwards, L.C. Ingesson, M.F. Johnson, D.J. Ward, Nucl. Fusion 40, 163 (2000)

    Google Scholar 

  5. L. Novotny, J. Cerovsky, P. Dhyani, O. Ficker, M. Havranek, M. Hejtmanek, Z. Janoska, V. Kafka, S. Kulkov, M. Marcisovska, M. Marcisovsky, G. Neue, P. Svihra, V. Svoboda, L. Tomasek, M. Tunkl, V. Vrba, J. Instrum. 15, C07015 (2020)

    Google Scholar 

  6. A. Dal Molin, L. Fumagalli, M. Nocente, D. Rigamonti, M. Tardocchi, L. Giacomelli, E. Panontin, A. Lvovskiy, C. Paz-Soldan, N.W. Edietis, G. Gorini, Rev. Sci. Instrum. 92, 043517 (2021)

    Google Scholar 

  7. A. Shevelev, V. Kiptily, I. Chugunov, E. Khilkevitch, D. Gin, D. Doinikov, V. Naidenov, V. Plyusnin, AIP Conf. Proc. 1612, 125 (2014)

    Google Scholar 

  8. L.G. Eriksson, P. Helander, F. Andersson, D. Anderson, M. Lisak, Phys. Rev. Lett. 92, 205004 (2004)

    Google Scholar 

  9. S. Mirnov, J. Wesley, N. Fujisawa, Y. Gribov, O. Gruber, T. Hender, N. Ivanov, S. Jardin, J. Lister, F. Perkins, M. Rosenbluth, N. Sauthoff, T. Taylor, S. Tokuda, K. Yamazaki, R. Yoshino, A. Bondeson, J. Conner, E. Fredrickson, D. Gates, R. Granetz, R. La Haye, J. Neuhauser, F. Porcelli, F.W. Perkins, D.E. Post, N.A. Uckan, M. Azumi, D.J. Campbell, N. Ivanov, N. Sauthoff, M. Wakatani, W.M. Nevins, M. Shimada, J. Van Dam, MHD stability operational limits and disruptions. Nucl. Fusion 39, 2251–2389 (1999)

    Google Scholar 

  10. A.H. Boozer, Nucl. Fusion 57, 056018 (2017)

    Google Scholar 

  11. R.D. Gill, B. Alper, M. De Baar, T.C. Hender, M.F. Johnson, V. Riccardo, Nucl. Fusion 42, 1039 (2002)

    Google Scholar 

  12. O.N. Jarvis, G. Sadler, J.L. Thompson, Nucl. Fusion 28, 1981 (1988)

    Google Scholar 

  13. V.V. Plyusnin, V. Riccardo, R. Jaspers, B. Alper, V.G. Kiptily, J. Mlynar, S. Popovichev, E. De La Luna, F. Andersson, Nucl. Fusion 46, 277 (2006)

    Google Scholar 

  14. J.A. Wesson, R.D. Gill, M. Hugon, F.C. Schöller, J.A. Snipes, D.J. Ward, D.V. Bartlett, D.J. Campbell, P.A. Duperrex, A.W. Edwards, R.S. Granetz, C. Lowry, N.A.O. Gottardi, T.C. Hender, E. Lazzaro, P.J. Lomas, N. Lopes Cardozo, K.F. Mast, M.F.F. Nave, N.A. Salmon, P. Smeulders, P.R. Thomas, B.J.D. Tubbing, M.F. Turner, A. Weller, Nucl. Fusion 29, 641 (1989)

    Google Scholar 

  15. C. Reux, V. Plyusnin, B. Alper, D. Alves, B. Bazylev, E. Belonohy, A. Boboc, S. Brezinsek, I. Coffey, J. Decker, P. Drewelow, S. Devaux, P.C. De Vries, A. Fil, S. Gerasimov, L. Giacomelli, S. Jachmich, E.M. Khilkevitch, V. Kiptily, R. Koslowski, U. Kruezi, M. Lehnen, I. Lupelli, P.J. Lomas, A. Manzanares, A. Martin De Aguilera, G.F. Matthews, J. Mlynář, E. Nardon, E. Nilsson, C. Perez Von Thun, V. Riccardo, F. Saint-Laurent, A.E. Shevelev, G. Sips, C. Sozzi, Nucl. Fusion 55, 093013 (2015)

    Google Scholar 

  16. R. Nygren, T. Lutz, D. Walsh, G. Martin, M. Chatelier, T. Loarer, D. Guilhem, J. Nucl. Mater. 241–243, 522 (1997)

    Google Scholar 

  17. A.H. Boozer, Phys. Plasmas 22, 032504 (2015)

    Google Scholar 

  18. M. Lehnen, K. Aleynikova, P.B. Aleynikov, D.J. Campbell, P. Drewelow, N.W. Eidietis, Y. Gasparyan, R.S. Granetz, Y. Gribov, N. Hartmann, E.M. Hollmann, V.A. Izzo, S. Jachmich, S.H. Kim, M. Kočan, H.R. Koslowski, D. Kovalenko, U. Kruezi, A. Loarte, S. Maruyama, G.F. Matthews, P.B. Parks, G. Pautasso, R.A. Pitts, C. Reux, V. Riccardo, R. Roccella, J.A. Snipes, A.J. Thornton, P.C. De Vries, J. Nucl. Mater. 463, 39 (2015)

    Google Scholar 

  19. E.M. Hollmann, P.B. Aleynikov, T. Fülöp, D.A. Humphreys, V.A. Izzo, M. Lehnen, V.E. Lukash, G. Papp, G. Pautasso, F. Saint-Laurent, J.A. Snipes, Phys. Plasmas 22, 021802 (2015)

    Google Scholar 

  20. M. Lehnen, S.A. Bozhenkov, S.S. Abdullaev, M.W. Jakubowski, Phys. Rev. Lett. 100, 255003 (2008)

    Google Scholar 

  21. M. Gobbin, M. Valisa, R.B. White, D. Cester, L. Marrelli, M. Nocente, P. Piovesan, L. Stevanato, M.E. Puiatti, M. Zuin, Nucl. Fusion 57, 016014 (2017)

    Google Scholar 

  22. S. Munaretto, B.E. Chapman, M.D. Nornberg, J. Boguski, A.M. DuBois, A.F. Almagri, J.S. Sarff, Phys. Plasmas 23, 056104 (2016)

    Google Scholar 

  23. E.M. Hollmann, N. Commaux, N.W. Eidietis, T.E. Evans, D.A. Humphreys, A.N. James, T.C. Jernigan, P.B. Parks, E.J. Strait, J.C. Wesley, J.H. Yu, M.E. Austin, L.R. Baylor, N.H. Brooks, V.A. Izzo, G.L. Jackson, M.A. Van Zeeland, W. Wu, Phys. Plasmas 17, 056117 (2010)

    Google Scholar 

  24. O. Ficker, E. MacUsova, J. Mlynar, D. Bren, A. Casolari, J. Cerovsky, M. Farnik, O. Grover, J. Havlicek, A. Havranek, M. Hron, M. Imrisek, M. Jerab, J. Krbec, P. Kulhanek, V. Linhart, M. Marcisovsky, T. Markovic, D. Naydenkova, R. Panek, M. Sos, P. Svihra, V. Svoboda, M. Tomes, J. Urban, J. Varju, M. Vlainic, P. Vondracek, V. Vrba, V. Weinzettl, D. Carnevale, J. Decker, M. Gobbin, M. Gospodarczyk, G. Papp, Y. Peysson, V.V. Plyusnin, M. Rabinski, C. Reux, Nucl. Fusion 59, 096036 (2019)

    Google Scholar 

  25. D. Shiraki, N. Commaux, L.R. Baylor, C.M. Cooper, N.W. Eidietis, E.M. Hollmann, C. Paz-Soldan, S.K. Combs, S.J. Meitner, Nucl. Fusion 58, 056006 (2018)

    Google Scholar 

  26. M.R. Ghanbari, M. Ghoranneviss, S. Mohammadi, R. Arvin, Radiat. Eff. Defects Solids 168, 664 (2013)

    Google Scholar 

  27. Y. Liu, C. Paz-Soldan, E. MacUsova, T. Markovic, O. Ficker, P.B. Parks, C.C. Kim, L.L. Lao, L. Li, Phys. Plasmas 27, 102507 (2020)

    Google Scholar 

  28. M. Landreman, A. Stahl, T. Fülöp, Comput. Phys. Commun. 185, 847 (2014)

    MathSciNet  Google Scholar 

  29. K. Insulander Björk, G. Papp, O. Embreus, L. Hesslow, T. Fülöp, O. Vallhagen, A. Lier, G. Pautasso, A. Bock, J. Plasma Phys. 59, 112014 (2020)

    Google Scholar 

  30. M. Ariola, A. Pironti, Magnetic Control of Tokamak Plasmas (Springer, London, 2008)

    MATH  Google Scholar 

  31. W. William, W.S. William, W.S. Wei, Time-Series Analysis—Univariate and Multivariate Methods (Addison Wesley, Boston, 2005), p. 634

    Google Scholar 

  32. S.H. Saadat, M. Salem, M. Ghoranneviss, P. Khorshid, J. Plasma Phys. 78, 99 (2012)

    Google Scholar 

  33. M. Hagan, H. Demuth, M. Beale, O. De Jesus, Neural Network Design (PWS Pub. Co., Boston, 1996)

    Google Scholar 

  34. A. Alavi, S. Saadat, M.R. Ghanbari, S.E. Alavi, A. Kadkhodaie, Phys. Scr. 96, 125625 (2021)

    Google Scholar 

  35. D. Rastovic, J. Fusion Energy 34, 207 (2015)

    Google Scholar 

  36. F. Matos, V. Menkovski, F. Felici, A. Pau, F. Jenko, Nucl. Fusion 60, ab6c7a (2020)

    Google Scholar 

  37. R.M. Churchill, B. Tobias, Y. Zhu, Phys. Plasmas 27, 062510 (2020)

    Google Scholar 

  38. W. Zheng, Q.Q. Wu, M. Zhang, Z.Y. Chen, Y.X. Shang, J.N. Fan, Y. Pan and J-TEXT team, Plasma Phys. Control. Fusion 62(4), 045012 (2020)

  39. K.L. Van De Plassche, J. Citrin, C. Bourdelle, Y. Camenen, F.J. Casson, V.I. Dagnelie, F. Felici, A. Ho, S. Van Mulders, Phys. Plasmas 27, 022310 (2020)

    Google Scholar 

  40. B. Yang, Z. Liu, X. Song, X. Li, Y. Li, Plasma Phys. Control. Fusion 62, 075004 (2020)

    Google Scholar 

  41. A.N.V. Nicolaos, B. Karayiannis, Artificial Neural Networks: Learning Algorithms, Performance Evaluation, and Applications (Springer, Berlin, 1992)

    MATH  Google Scholar 

  42. J. McCall, J. Comput. Appl. Math. 184, 205 (2005)

    MathSciNet  Google Scholar 

  43. A. Thengade, R. Dondal, MPGI Natl. Multi Conf. Int. J. Comput. Appl. 2012, 975 (2012)

    Google Scholar 

  44. K. Guo, Neural Comput. Appl. 32, 1679 (2020)

    Google Scholar 

  45. H. Wei, H. Bao, X. Ruan, Nano Energy 71, 104619 (2020)

    Google Scholar 

  46. M. Jawad, S.M. Ali, B. Khan, C.A. Mehmood, U. Farid, Z. Ullah, S. Usman, A. Fayyaz, J. Jadoon, N. Tareen, A. Basit, M.A. Rustam, I. Sami, J. Eng. 2018, 721 (2018)

    Google Scholar 

  47. L. Liu, H. Moayedi, A.S.A. Rashid, S.S.A. Rahman, H. Nguyen, Eng. Comput. 36, 421 (2020)

    Google Scholar 

  48. Y. Zhou, Y. Wang, K. Wang, L. Kang, F. Peng, L. Wang, J. Pang, Appl. Energy 260, 114169 (2020)

    Google Scholar 

  49. H. Liang, J. Zou, K. Zuo, M.J. Khan, Mech. Syst. Signal Process. 142, 106708 (2020)

    Google Scholar 

  50. A. Al Mamun, M. Sohel, N. Mohammad, M.S. Haque Sunny, D.R. Dipta, E. Hossain, IEEE Access 8, 134911 (2020)

    Google Scholar 

  51. M.A. Albadr, S. Tiun, M. Ayob, F. Al-Dhief, Symmetry (Basel). 12, 1 (2020)

    Google Scholar 

  52. Y. Sun, B. Xue, M. Zhang, G.G. Yen, J. Lv, IEEE Trans. Cybern. 50, 3840 (2020)

    Google Scholar 

  53. K. Itoh, S.I. Itoh, Plasma Phys. Control. Fusion 38, 1 (1996)

    Google Scholar 

  54. H. Dreicer, Phys. Rev. 115, 238 (1959)

    MathSciNet  Google Scholar 

  55. H. Dreicer, Phys. Rev. 117, 329 (1960)

    MathSciNet  Google Scholar 

  56. Y.A. Sokolov, JETP Lett. 29, 4 (1979)

    Google Scholar 

  57. R. Jayakumar, H.H. Fleischmann, S.J. Zweben, Phys. Lett. A 172, 447 (1993)

    Google Scholar 

  58. M.N. Rosenbluth, S.V. Putvinski, Nucl. Fusion 37, 1355 (1997)

    Google Scholar 

  59. D. Graupe, Principles of Artificial Neural Networks (WORLD SCIENTIFIC, Singapore, 2007)

    MATH  Google Scholar 

  60. Z.Y. Chen, W.C. Kim, A.C. England, S.W. Yoon, K.D. Lee, Y.S. Lee, J.W. Yoo, Y.W. Yu, Y.K. Oh, J.G. Kwak, M. Kwon, Phys. Lett. Sect. A Gen. At. Solid State Phys. 375, 2569 (2011)

    Google Scholar 

  61. S. García, J. Luengo, F. Herrera, Data Preprocessing in Data Mining (Springer International Publishing, Cham, 2015)

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

    Amir Alavi, Shervin Saadat, Mohamad Reza Ghanbari, Seyed Enayatallah Alavi & Ali Kadkhodaie

  2. Department of Basic Sciences, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    Mohamad Reza Ghanbari

  3. Department of Computer Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

    Seyed Enayatallah Alavi

  4. Earth Sciences Department, Faculty of Natural Sciences, University of Tabriz, Tabriz, Iran

    Ali Kadkhodaie

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  1. Amir Alavi
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Contributions

All authors contributed to the study conception and design. Data collection and analysis were performed by AA, SS, MRG, SEA, and AK. The first draft of the manuscript was written by AA, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Shervin Saadat.

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Alavi, A., Saadat, S., Ghanbari, M.R. et al. Simulation of hard X-ray time evolution in plasma tokamak by using the NARX-GA hybrid neural network. Eur. Phys. J. D 76, 199 (2022). https://doi.org/10.1140/epjd/s10053-022-00511-6

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