1)

Institute of Science and Technology Research, Chubu University, Aichi 487-8501, Japan

2)

Research Center for Plasma Turbulence, Kyushu University, Kasuga 816-8580, Japan

3)

National Institute for Fusion Science, Toki 509-5292, Japan

4)

Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan

5)

Department of Innovative Energy Science and Engineering, Graduate School of Engineering, Chubu University, Aichi 487-8501, Japan

6)

Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

Abstract

As a result of the progresses in the study of plasma turbulence, the picture of ‘multiple-scale turbulence’ is widely accepted, and the ‘nonlinear excitation, nonlocal interaction, probabilistic transition’ views have been developed. Along the paths of these progresses, importance of new problem, i.e., the symmetry-breaking of turbulence structure (such as up-down asymmetry, excitation of streamer, etc.) is gradually recognized. In this topical review article, we revisit these issues, and illuminate the possibilities that the new progresses (which will be brought about by studying the symmetry-breaking of turbulence) are expected. Examining theoretical predictions and preceding experimental achievements, new advancements, which will be realized, are explained. The experimental study of symmetry-breaking of turbulence structure ultimately requires to measure fluctuations (at all scales) over the whole plasma cross-section simultaneously. In addition, new type of demands can be imposed in measuring of fluctuations over the whole plasma cross-section simultaneously. One of such demands is the accuracy of the measurement position. Problems in this aspect are also discussed. This concise review is used to identify what will be discovered and how it will be reached in future experiments, in the subject of the symmetry-breaking of turbulence structure.

Keywords

plasma turbulence, toroidal plasma, plasma diagnostics, symmetry-breaking

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References

• [1] K. Itoh, S.-I. Itoh and A. Fukuyama, Transport and Structural Formation in Plasmas (IOP, England, 1999).
• [2] A. Yoshizawa, S.-I. Itoh and K. Itoh, Plasma and Fluid Turbulence (IOP, England, 2002).
• [3] P.H. Diamond, S.-I. Itoh and K. Itoh, Physical Kinetics of Turbulent Plasmas (Cambridge University Press, planned publication, 2010).
• [4] J.A. Krommes and C.-B. Kim, Phys. Rev. E 62, 8508 (2000).
• [5] A. Smolyakov, P.H. Diamond and V.I. Shevchenko, Phys. Plasmas 7, 1349 (2000).
• [6] L. Chen and Z. Lin, Phys. Plasmas 7, 3129 (2000).
• [7] A. Das, A. Sen, S. Mahajan and P. Kaw, Phys. Plasmas 8, 5104 (2001).
• [8] G. Manfredi, C.M. Roach and R.O. Dendy, Plasma Phys. Control. Fusion 43, 825 (2001).
• [9] N. Miyato, Y. Kishimoto and J. Li, Phys. Plasmas 11, 5557 (2004).
• [10] Y. Idomura, S. Tokuda and Y. Kishimoto, Nucl. Fusion 45, 1571 (2005).
• [11] M. Yagi, S. Yoshida, S.-I. Itoh, H. Naitou, H. Nagahara, J.-N. Leboeuf, K. Itoh, T. Matsumoto, S. Tokuda and M. Azumi, Nucl. Fusion 45, 900 (2005).
• [12] H. Sugama and T.-H. Watanabe, Phys. Plasmas 13, 012501 (2006).
• [13] T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006).
• [14] K. Miki, Y. Kishimoto, N. Miyato and J.Q. Li, Phys. Rev. Lett. 99, 145003 (2007).
• [15] A. Ishizawa and N. Nakajima, Phys. Plasmas 14, 040702 (2007).
• [16] M. Yagi, S.-I. Itoh, K. Itoh and P.H. Diamond, Cotnrib. Plasma Phys. 48, 13 (2008).
• [17] Y. Todo, H.L. Berk and B.N. Breizman, Nucl. Fusion 50, 084016 (2010).
• [18] M. Muraglia, O. Agullo, S. Benkadda, M. Yagi, X. Garbet and A. Sen, Phys. Rev. Lett. 107, 095003 (2011).
• [19] M. Nakata, T.-H. Watanabe and H. Sugama, Phys. Plasmas 19, 022303 (2012).
• [20] L. Chen and F. Zonca, Phys. Rev. Lett. 109, 145002 (2012).
• [21] S. Maeyama, Y. Idomura, T.-H.Watanabe, M. Nakata, M. Yagi, N. Miyato, A. Ishizawa and M. Nunami, Phys. Rev. Lett. 114, 255002 (2015).
• [22] H. Wang, Y. Todo, T. Ido and M. Osakabe, Phys. Plasmas 22, 092507 (2015).
• [23] S.-I. Itoh and K. Itoh, Plasma Phys. Control. Fusion 43, 1055 (2001).
• [24] P.H. Diamond, S.-I. Itoh, K. Itoh and T.S. Hahm, Plasma Phys. Control. Fusion 47, R35 (2005).
• [25] E.-J. Kim and P.H. Diamond, Phys. Rev. Lett. 90, 185006 (2003).
• [26] L. Chone, P. Beyer, Y. Sarazin, G. Fuhr, C. Bourdelle and S. Benkadda, Nucl. Fusion 55, 073010 (2015).
• [27] G.Y. Park, S.S. Kim, H. Jhang, P.H. Diamond, T. Rhee and X.Q. Xu, Phys. Plasmas 22, 032505 (2015).
• [28] A. Strugarek, Y. Sarazin, D. Zarzoso, J. Abiteboul, A.S. Brun, T. Cartier-Michaud, G. Dif-Pradalier, X. Garbet, Ph. Ghendrih, V. Grandgirard, G. Latu, C. Passeron and O. Thomine, Phys. Rev. Lett. 111, 145001 (2013).
• [29] C.S. Chang, S. Ku, G.R. Tynan, R. Haager, R.M. Churhill, I. Cziegler, M. Greenwald, A.E. Hubbard and J.W. Hughes, Phys. Rev. Lett. 118, 175001 (2017).
• [30] T. Estrada, T. Happel, C. Hidalgo, E. Ascasibar and E. Blanco, EPL 92, 35100 (2010).
• [31] S.J. Zweben, R.J. Maqueda, R. Hager, K. Hallatschek, S.M. Kaye, T. Munsat, F.M. Poli, A.L. Roquemore, Y. Sechrest and D.P. Stotler, Phys. Plasmas 17, 102502 (2010).
• [32] G.D. Conway, C. Angioni, F. Ryter, P. Sauter, J. Vicente and ASDEX Upgrade Team, Phys. Rev. Lett. 106, 065001 (2011).
• [33] L. Schmitz, L. Zeng, T.L. Rhodes, J.C. Hillsheim, E.J. Doyle, R.J. Groebner, W.A. Peebles, K.H. Burrell and G. Wang, Phys. Rev. Lett. 108, 155002 (2012).
• [34] G.S. Xu, B.N. Wan, H.Q. Wang, H.Y. Guo, H.L. Zhao, A.D. Liu, V. Naulin, P.H. Diamond, G.R. Tynan, M. Xu, R. Chen, M. Jiang, P. Liu, N. Yan, W. Zhang, L. Wang, S.C. Liu and S.Y. Ding, Phys. Rev. Lett. 107, 125001 (2011).
• [35] T. Estrada, C. Hidalgo, T. Happel and P.H. Diamond, Phys. Rev. Lett. 107, 245004 (2011).
• [36] J. Cheng, J.Q. Dong, K. Itoh, L.W. Yan, M. Xu, K.J. Zhao, W.Y. Hong, Z.H. Huang, X.Q. Ji, W.L. Zhong, D.L. Yu, S.-I. Itoh, L. Nie, D.F. Kong, T. Lan, A.D. Liu, X.L. Zou, Q.W. Yang, X.T. Ding, X.R. Duan, Y. Liu and HL-2A Team, Phys. Rev. Lett. 110, 265002 (2013).
• [37] I. Cziegler, A.E. Hubbard, J.W. Hughes, J.L. Terry and G.R. Tynan, Phys. Rev. Lett. 118, 105003 (2017).
• [38] K. Itoh, S.-I. Itoh and A. Fujisawa, Plasma Fusion Res. 8, 1102168 (2013).
• [39] S.-I. Itoh and K. Itoh, Sci. Rep. 2, 860 (2012).
• [40] K. Itoh, S.-I. Itoh, M. Sasaki and Y. Kosuga, Nucl. Fusion 57, 056031 (2017).
• [41] C. Hidalgo, E. Sanchez, T. Estrada, B. Branas and Ch.P. Ritz, Phys. Rev. Lett. 71, 3127 (1993).
• [42] P.H. Diamond, M.N. Rosenbluth, E. Sanchez, C. Hidalgo, B. Van Milligen, T. Estrada, B. Branas, M. Hirsch, H.J. Hartfuss and B.A. Carreras, Phys. Rev. Lett. 84, 4842 (2000).
• [43] G.R. Tynan, R.A. Moyer, M.J. Burin and C. Holland, Phys. Plasmas 8, 2691 (2001).
• [44] G.R. Tynan, M.J. Burin, C. Holland, G. Antar and N. Crocker, Phys. Plasmas 11, 5195 (2004).
• [45] A. Fujisawa, Plasma Phys. Control. Fusion 53, 124015 (2011).
• [46] A. Fujisawa, K. Itoh, H. Iguchi, K. Matsuoka, S. Okamura, A. Shimizu, T. Minami, Y. Yoshimura, K. Nagaoka, C. Takahashi, M. Kojima, H. Nakano, S. Ohsima, S. Nishimura, M. Isobe, C. Suzuki, T. Akiyama, K. Ida, K. Toi, S.-I. Itoh and P.H. Diamond, “Identification of Zonal Flows in a Toroidal Plasma”, Phys. Rev. Lett. 93, 165002 (2004) http://dx.doi.org/10.1103/PhysRevLett.93.165002
• [47] Y. Nagashima, K. Hoshino, A. Ejiri, K. Shionohara, Y. Takase, K. Tsuzuki, K. Uehara, H. Kawashima, H. Ogawa, T. Ido, Y. Kusama and Y. Miura, Phys. Rev. Lett. 95, 095002 (2005).
• [48] T. Yamada, S.-I. Itoh, T. Maruta, N. Kasuya, Y. Nagashima, S. Shinohara, K. Terasaka, M. Yagi, S. Inagaki, Y. Kawai, A. Fujisawa and K. Itoh, “Anatomy of plasma turbulence”, Nature Phys. 4, 721 (2008) http://dx.doi.org/10.1038/nphys1029
• [49] A. Fujisawa, K. Itoh, A. Shimizu, H. Nakano, S. Ohshima, H. Iguchi, K. Matsuoka, S. Okamura, T. Minami, Y. Yoshimura, K. Nagaoka, K. Ida, K. Toi, C. Takahashi, M. Kojima, S. Nishimura, M. Isobe, C. Suzuki, T. Akiyama, Y. Nagashima, S.-I. Itoh and P.H. Diamond, Phys. Rev. Lett. 98, 165001 (2007).
• [50] S. Inagaki, T. Tokuzawa, K. Itoh, K. Ida, S.-I. Itoh, N. Tamura, S. Sakakibara, N. Kasuya, A. Fujisawa, S. Kubo, T. Shimozuma, T. Ido, S. Nishimura, H. Arakawa, T. Kobayashi, K. Tanaka, Y. Nagayama, K. Kawahata, S. Sudo, H. Yamada, A. Komori and LHD Experiment Group, “Observation of Long-Distance Radial Correlation in Toroidal Plasma Turbulence”, Phys. Rev. Lett. 107, 115001 (2011) http://dx.doi.org/10.1103/PhysRevLett.107.115001
• [51] H. Arakawa, S. Inagaki, M. Sasaki, Y. Kosuga, T. Kobayashi, N. Kasuya, Y. Nagashima, T. Yamada, M. Lesur, A. Fujisawa, S.-I. Itoh and K. Itoh, Eddy, Sci. Rep. 6, 33371 (2016).
• [52] S. Inagaki, T. Tokuzawa, N. Tamura, S.-I. Itoh, T. Kobayashi, K. Ida, T. Shimozuma, S. Kubo, K. Tanaka, T. Ido, A. Shimizu, H. Tsuchiya, N. Kasuya, Y. Nagayama, K. Kawahata, S. Sudo, H. Yamada, A. Fujisawa, K. Itoh and the LHD Experiment Group, Nucl. Fusion 53, 113006 (2013).
• [53] K. Ida, Z. Shi, H.J. Sun, S. Inagaki, K. Kamiya, J.E. Rice, N. Tamura, P.H. Diamond, G. Dif-Pradalier and X.L. Zou, Nucl. Fusion 55, 013022 (2015).
• [54] S.-I. Itoh, S. Inagaki, J. Dong and K. Itoh, Plasma Fusion Res. 11, 2503086 (2016).
• [55] P.A. Politzer, Phys. Rev. Lett. 84, 1192 (2000).
• [56] F. Kin, K. Itoh, A. Fujisawa, Y. Kosuga, M. Sasaki, T. Yamada, S. Inagaki, S.-I. Itoh, T. Kobayashi, Y. Nagashima, N. Kasuya, H. Arakawa, K. Yamasaki and K. Hasamada, Phys. Plasmas 25, 062304 (2018).
• [57] B. Coppi, Nucl. Fusion 42, 1 (2002).
• [58] P.H. Diamond, Y. Kosuga, O.D. Gurcan, C.J. McDevitt, T.S. Hahm, N. Fedorczak, J.E. Rice, W.X. Wang, S. Ku, J.M. Kwon, G. Dif-Pradalier, J. Abiteboul, L. Wang, W.H. Ko, Y.J. Shi, K. Ida, W. Solomon, H. Jhang, S.S. Kim, S. Yi, S.H. Ko, Y. Sarazin, R. Singh, and C.S. Chang, Nucl. Fusion 53, 104019 (2013).
• [59] A.G. Peeters, C. Angioni, A. Bortolon, Y. Camenen, F.J. Casson, B. Duval, L. Fiederspiel, W.A. Hornsby, Y. Idomura, T. Hein, N. Kluy, P. Mantica, F.I. Parra, A.P. Snodin, G. Szepesi, D. Strinstzi, T. Tala, G. Tardini, P. de Vries and J. Weiland, Nucl. Fusion 51, 094027 (2011).
• [60] O.D. Gurcan and P.H. Diamond, Phys. Plasmas 14, 042306 (2007).
• [61] O.D. Gurcan, P.H. Diamond, P. Hennequin, C.J. McDevitt, X. Garbet and C. Bourdelle, Phys. Plasmas 17, 112309 (2010).
• [62] Y. Camenen, Y. Idomura, S. Jolliet and A.G. Peeters, Nucl. Fusion 51, 073039 (2011).
• [63] Y. Idomura, Phys. Plasmas 21, 022517 (2014).
• [64] T. Stoltzfus-Dueck, A.N. Karpushov, O. Sauter, B.P. Duval, B. Labit, H. Reimerdes, W.A.J. Vijvers, the TCV team and Y. Camenen, Phys. Rev. Lett. 114, 245001 (2015).
• [65] X. Garbet, Y. Asahi, P. Donnel, C. Ehrlacher, G. Dif-Pradalier, P. Ghendrih, V. Grandgirard and Y. Sarazin, New J. Phys. 19, 015011 (2017).
• [66] M.N. Rosenbluth, R.D. Hazeltine and F.L. Hinton, Phys. Fluids 15, 116 (1972); F.L. Hinton and R.D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976).
• [67] D. Pfirsch and A. Schlüter, MPI/PA/7/62 Max-Planck Institut für Physik und Astrophysik, München (1962).
• [68] R.J. Bickerton, J.W. Connor and J.B. Taylor, Nature Physical Science 229, 110 (1971).
• [69] M.C. Zarnstorff and S.C. Prager, Phys. Fluids 29, 298 (1986).
• [70] M. Kikuchi and M. Azumi, Plasma Phys. Control. Fusion 37, 1215 (1995).
• [71] B.B. Kadomtsev and O.P. Pogutse: Reviews of Plasma Physics 5, ed. by M.A. Leontovich (Consultant Bureau, New York 1970).
• [72] A.H. Glasser, E.A. Frieman and S. Yoshikawa, “Stabilization of the collisionless trapped-particle instability by shaping of the tokamak cross section”, Phys. Fluids 17, 181 (1974) http://dx.doi.org/10.1063/1.1694585
• [73] A. Fujisawa, A. Ouroua, J.W. Heard, T.P. Crowley, P.M. Schoch, K.A. Connor, R.L. Hickok and A.J. Wootton, “Ballooning characteristics in density fluctuations observed with the 2MeV heavy ion beam probe on the TEXT-U tokamak”, Nucl. Fusion 36, 375 (1996) http://dx.doi.org/10.1088/0029-5515/36/3/I10
• [74] K. Ida and J. Rice, Nucl. Fusion 54, 045001 (2014).
• [75] T.E. Stringer, Phys. Rev. Lett. 22, 770 (1969).
• [76] A.B. Hassam and J.F. Drake, “Spontaneous poloidal spin up of tokamak plasmas: Reduced equations, physical mechanism, and sonic regimes”, Phys. Plasmas 5, 4022 (1993) http://dx.doi.org/10.1063/1.860622
• [77] K. Itoh and S.-I. Itoh, Plasma Phys. Control. Fusion 38, 1 (1996).
• [78] K. Hallatschek, Plasma Phys. Control. Fusion 49, B137 (2007).
• [79] T. Kobayashi, K. Itoh, T. Ido, K. Kamiya, S.-I. Itoh, Y. Miura, Y. Nagashima, A. Fujisawa, S. Inagaki, K. Ida and K. Hoshino, Phys. Rev. Lett. 111, 035002 (2013).
• [80] T. Pütterich, E. Wolfrum, R. Dux and C.F. Maggi, Phys. Rev. Lett. 102, 025001 (2009).
• [81] F.L. Waelbroeck and L. Chen, Phys. Fluids B 3, 601 (1991).
• [82] K. Itoh, K. Hallatschek and S.-I. Itoh, “Excitation of Geodesic Acoustic Mode in Toroidal Plasmas”, Plasma Phys. Control. Fusion 47, 451 (2005) http://dx.doi.org/10.1088/0741-3335/47/3/004
• [83] K.C. Shaing, R.D. Hazeltine and H. Sanuki, Phys. Fluids B 4, 404 (1992).
• [84] N. Kasuya and K. Itoh, Phys. Rev. Lett. 94, 195002 (2005).
• [85] N. Kasuya, K. Itoh and Y. Takase, J. Plasma Fusion Res. 81, 553 (2005).
• [86] Y. Camenen, A.G. Peeters, C. Angioni, F.J. Casson, W.A. Hornsby, A.P. Snodin and D. Strintzi, Phys. Rev. Lett. 102, 125001 (2009).
• [87] Y. Kosuga, S.-I. Itoh, P.H. Diamond and K. Itoh, Plasma Phys. Control. Fusion 55, 125001 (2013).
• [88] S.-I. Itoh, ‘cross-ferroic turbulence’, presented at Meeting of Phys. Soc. Jpn. (Kansai Univ., 2015) 17aCN-10c.
• [89] S. Inagaki, T. Kobayashi, Y. Kosuga, S.-I. Itoh, T. Mitsuzono, Y. Nagashima, H. Arakawa, T. Yamada, Y. Miwa, N. Kasuya, M. Sasaki, M. Lesur, A. Fujisawa and K. Itoh, Sci. Rep. 6, 22189 (2016).
• [90] F. Wagner, G. Becker, K. Behringer, D. Campbell, A. Eberhagen, W. Engelhardt, G. Fussmann, O. Gehre, J. Gernhardt, G.v. Gierke, G. Haas, M. Huang, F. Karger, M. Keilhacker, O. Klüber, M. Kornherr, K. Lackner, G. Lisitano, G.G. Lister, H.M. Mayer, D. Meisel, E.R. Müller, H. Murmann, H. Niedermeyer, W. Poschenrieder, H. Rapp, H. Röhr, F. Schneider, G. Siller, E. Speth, A. Stäbler, K.H. Steuer, G. Venus, O. Vollmer and Z. Yü, Phys. Rev. Lett. 49, 1408 (1982).
• [91] T. Kobayashi, K. Itoh, T. Ido, K. Kamiya, S.-I. Itoh, Y. Miura, Y. Nagashima, A. Fujisawa, S. Inagaki, K. Ida and K. Hoshino, Sci. Rep. 6, 30720 (2016).
• [92] D.G. Whyte, A.E. Hubbard, J.W. Hughes, B. Lipschultz, J.E. Rice, E.S. Marmar, M. Greenwald, I. Cziegler, A. Dominguez, T. Golfinopoulos, N. Howard, L. Lin, R.M. McDermott, M. Porkolab, M.L. Reinke, J. Terry, N. Tsujii, S. Wolfe, S. Wukitch, Y. Lin and the Alcator C-Mod Team, Nucl. Fusion 50, 105005 (2010).
• [93] S.-I. Itoh, K. Itoh, H. Zushi and A. Fukuyama, Plasma Phys. Control. Fusion 40, 879 (1998).
• [94] K. Ida, T. Kobayashi, K. Itoh, M. Yoshinuma, T. Tokuzawa, T. Akiyama, C. Moon, H. Tsuchiya, S. Inagaki and S.-I. Itoh, Sci. Rep. 6, 36217 (2016).
• [95] J. Cheng, J.Q. Dong, K. Itoh, S.-I. Itoh, L.W. Yan, J.Q. Xu, M. Jiang, K.J. Zhao, Z.H. Huang, D.L. Yu, K. Ida, S. Inagaki, T. Kobayashi, X.Q. Ji, Z.B. Shi, W.L. Zhong, X.L. Zou, X.T. Ding, A. Fujisawa, Y. Kosuga, Y. Nagashima, M. Sasaki, T. Yamada, M.K. Han, Y. Liu, Q.W. Yang, M. Xu, X.R. Duan, Y. Liu and HL-2A team, “Streamer - A Trigger of Edge Localized Modes in Toroidal Plasmas”, submitted to Phys. Rev. Lett.
• [96] J.E. Lee, G.S. Yun, W. Lee, M.H. Kim, M. Choi, J. Lee, M. Kim, H.K. Park, J.G. Bak, W.H. Ko, and Y.S. Park, Sci. Rep. 7, 45075 (2017).
• [97] P.H. Diamond and T.S. Hahm, Phys. Plasmas 2, 3640 (1995).
• [98] T.S. Hahm, L. Wang, W.X. Wang, E.S. Yoon and F.X. Duthoit, Nucl. Fusion 53, 072002 (2013).
• [99] X. Garbet, Y. Sarazin, F. Imbeaux, P. Ghendrih and C. Bourdelle, Phys. Plasmas 14, 122305 (2007).
• [100] S. Sugita, K. Itoh, S.-I. Itoh, M. Yagi, G. Fuhr, P. Beyer and S. Benkadda, Plasma Phys. Control. Fusion 54, 125001 (2012).
• [101] G. Dif-Pradalier, P.H. Diamond, V. Grandgirard, Y. Sarazin, J. Abiteboul, X. Garbet, Ph. Ghendrih, A. Strugarek, S. Ku and C.S. Chang, Phys. Rev. E 82, 025401 (2010).
• [102] K. Itoh and S.-I. Itoh, Plasma Phys. Control. Fusion 58, 045017 (2016).
• [103] G. Dif-Pradalier, G. Hornung, Ph. Ghendrih, Y. Sarazin, F. Clairet, L. Vermare, P.H. Diamond, J. Abiteboul, T. Cartier-Michaud, C. Ehrlacher, D. Estève, X. Garbet, V. Grandgirard, Ö.D. Gürcan, P. Hennequin, Y. Kosuga, G. Latu, P. Maget, P. Morel, C. Norscini, R. Sabot and A. Storelli, “Finding the Elusive E × B Staircase in Magnetized Plasmas”, Phys. Rev. Lett. 114, 085004 (2015) http://dx.doi.org/10.1103/PhysRevLett.114.085004
• [104] S.-I. Itoh, K. Itoh, A. Fukuyama and M. Yagi, Phys. Rev. Lett. 76, 920 (1996).
• [105] P.K. Kaw, E.J. Valeo and P.H. Rutherford, Phys. Rev. Lett. 43, 1398 (1979).
• [106] M. Yagi, S.-I. Itoh, K. Itoh, M. Azumi, P.H. Diamond, A. Fukuyama and T. Hayashi, “Nonlinear Drive of Tearing Mode by Microscopic Plasma Turbulence”, Plasma Fusion Res. 2, 025 (2007) http://dx.doi.org/10.1585/pfr.2.025
• [107] A. Ishizawa and F.L. Waelbroeck, Phys. Plasmas 20, 122301 (2013).
• [108] R. Fitzpatrick, Phys. Plasmas 2, 825 (1995).
• [109] F.L. Waelbroeck, F. Militello, R. Fitzpatrick and W. Horton, Plasma Phys. Control. Fusion 51, 015015 (2009).
• [110] W.A. Hornsby, M. Siccinio, A.G. Peeters, E. Poli, A.P. Snodin, F.J. Casson, Y. Camenen and G. Szepesi, Plasma Phys. Control. Fusion 53, 054008 (2011).
• [111] K. Ida, T. Kobayashi, T.E. Evans, S. Inagaki, M.E. Austin, M.W. Shafer, S. Ohdachi, Y. Suzuki, S.-I. Itoh and K. Itoh, “Self-regulated oscillation of transport and topology of magnetic island in toroidal plasmas”, Sci. Rep. 5, 16165 (2015) http://dx.doi.org/10.1038/srep16165
• [112] K. Zhao, Y. Nagashima, P. Diamond, J. Dong, K. Itoh, S.-I. Itoh, L. Yan, J. Cheng, A. Fujisawa, S. Inagaki, Y. Kosuga, M. Sasaki, Z. Huang, D. Yu, Q. Li, X.Q. Ji, X. Song, Y. Huang, Y. Liu, Q. Yang, X. Ding and X. Duan, Nucl. Fusion 57, 076036 (2017).
• [113] L. Giannone, J. Baldzuhn, R. Burhenn, P. Grigull, U. Stroth, F. Wagner, R. Brakel, C. Fuchs, H.J. Hartfuss, K. McCormick, A. Weller, C. Wendland, NBI Team, W7-AS Team, K. Itoh and S.-I. Itoh, “Physics of the density limit in the W7-AS stellarator”, Plasma Phys. Control. Fusion 42, 603 (2000) http://dx.doi.org/10.1088/0741-3335/42/6/301
• [114] B. Lipschultz, B. LaBombard, E.S. Marmar, M.M. Pickrel, J.L. Terry, R. Watterson and S.M. Wolfe, “Marfe: an edge plasma phenomenon”, Nucl. Fusion 24, 977 (1984) http://dx.doi.org/10.1088/0029-5515/24/8/002
• [115] T. Nishitani and S. Ishida, “Radiative Thermal Instability in Peripheral Plasma (marfe)” (in Japanese) Kakuyugo-Kenkyu 61, 137 (1989).
• [116] S.-I. Itoh, K. Itoh, Y. Nagashima and Y. Kosuga, Plasma Fusion Res. 12, 1101003 (2017).
• [117] Ch.P. Ritz, R.V. Bravenec, P.M. Schoch, R.D. Bengtson, J.A. Boedo, J.C. Forster, K.W. Gentle, Y. He, R.L. Hickok, Y.J. Kim, H. Lin, P.E. Phillips, T.L. Rhodes, W.L. Rowan, P.M. Valanju and A.J. Wootton, Phys. Rev. Lett. 62, 1844 (1989).
• [118] A.J. Wootton, Phys. Plasmas 2, 2879 (1990).
• [119] T. Kobayashi, K. Itoh, T. Ido, K. Kamiya, S.-I. Itoh, Y. Miura, Y. Nagashima, A. Fujisawa, S. Inagaki, K. Ida, N. Kasuya and K. Hoshino, “Dynamics of edge limit cycle oscillation in the JFT-2M Tokamak”, Nucl. Fusion 54, 073017 (2014) http://dx.doi.org/10.1088/0029-5515/54/7/073017
• [120] S. Inagaki, T. Tokuzawa, T. Kobayashi, S.-I. Itoh, K. Itoh, K. Ida, A. Fujisawa, S. Kubo, T. Shimozuma, N. Tamura, N. Kasuya, H. Tsuchiya, Y. Nagayama and LHD Experiment Group, “Study of Non-linear Coupling of Fluctuations at Long Distance in LHD”, Nucl. Fusion 54, 114014 (2014) http://dx.doi.org/10.1088/0029-5515/54/11/114014
• [121] S. Inagaki, K. Itoh, T. Yamada, S.-I. Itoh, T. Tokuzawa, A. Fujisawa, N. Kasuya, M. Sasaki, Y. Nagashima and H. Arakawa, Plasma Fusion Res. 8, 1201171 (2013).
• [122] K. Itoh, K.J. Zhao, J.Q. Dong, S.-I. Itoh, A. Fujisawa, S. Inagaki, M. Sasaki, Y. Nagashima, Y. Kosuga, J. Cheng and T. Kobayashi, Plasma Fusion Res. 11, 1402002 (2016).
• [123] K. Itoh, S.-I. Itoh, Y. Nagashima, T. Yamada and A. Fujisawa, J. Phys. Soc. Jpn. 87, 025002 (2018).
• [124] Y. Nagashima, K. Itoh, A. Fujisawa, K. Shinohara, S.-I. Itoh, T. Ido, M. Yagi, K. Hoshino, A. Ejiri, Y. Takase, K. Uehara and Y. Miura, “Boundary of the geodesic acoustic eigenmode in the vicinity of the magnetic separatrix”, Plasma Phys. Control. Fusion 51, 065019 (2009) http://dx.doi.org/10.1088/0741-3335/51/6/065019
• [125] T. Ido, Y. Miura, K. Kamiya, Y. Hamada, K. Hoshino, A. Fujisawa, K. Itoh, S.-I. Itoh, A. Nishizawa, H. Ogawa, Y. Kusama and JFT-2M group, Plasma Phys. Control. Fusion 48, S41 (2006).
• [126] S.-I. Itoh, K. Itoh, M. Sasaki, A. Fujisawa, T. Ido and Y. Nagashima, Plasma Phys. Control. Fusion 49, L7 (2007).
• [127] Y. Nagashima, K. Itoh, S.-I. Itoh, A. Fujisawa, M. Yagi, K. Hoshino, K. Shinohara, A. Ejiri, Y. Takase, T. Ido, K. Uehara, Y. Miura and JFT-2M group, Plasma Phys. Control. Fusion 49, 1611 (2007).
• [128] K.J. Zhao, Y. Nagashima, P.H. Diamond, J.Q. Dong, L.W. Yan, J. Cheng, M. Xu, G.R. Tynan, K. Itoh, S.-I. Itoh, A. Fujisawa, S. Inagaki, Z.X. Wang, L. Wei, Z.H. Huang, W.Y. Hong, Q. Li, X.Q. Ji, M. Huang, X.M. Song, Y. Huang, Yi. Liu, Q.W. Yang, X.T. Ding, X.R. Duan and HL-2A team, Phys. Rev. Lett. 117, 145002 (2016).
• [129] K. Ida, Y. Sakamoto, H. Takenaga, N. Oyama, K. Itoh, M. Yoshinuma, S. Inagaki, T. Kobuchi, A. Isayama, T. Suzuki, T. Fujita, G. Matsunaga, Y. Koide, M. Yoshida, S. Ide, Y. Kamada and JT-60 team, Phys. Rev. Lett. 101, 055003 (2008).
• [130] K. Ida, Y. Sakamoto, M. Yoshinuma, S. Inagaki, T. Kobuchi, G. Matsunaga and Y. Koide, Rev. Sci. Instrum. 79, 053506 (2008).
• [131] S.-I. Itoh, J. Plasma Fusion Res. 83, 241 (2007) (in Japanese).
• [132] S.-I. Itoh, J. Plasma Fusion Res. 86, 334 (2010) (in Japanese).
• [133] S.-I. Itoh, S. Inagaki, A. Fujisawa and K. Itoh, J. Plasma Fusion Res. 90, 793 (2014) (in Japanese).
• [134] S.-I. Itoh, R. Kodama, A. Fujisawa, M. Sato, K. Tanaka, R. Hatakeyama and K. Itoh, J. Plasma Fusion Res. 87, 371 (2011) (in Japanese).
• [135] A. Fujisawa, K. Itoh, S.-I. Itoh, Y. Uesugi, N. Ohno, T. Kaneko, R. Kodama, M. Shiratani, K. Tanaka, R. Hatakeyama, S. Hamaguchi and H. Yoneda, J. Plasma Fusion Res. 90, 177 (2014) (in Japanese).
• [136] Science Council of Japan, Committee for Scientific Community, Subcommittee for Large Research Projects, Japanese Master Plan of Large Research Projects 2011 -A Table of 46 Selected Projects (28 September 2011).
• [137] Road Map 2014 by MEXT Japan, http://www.mext.go.jp/b_menu/shingi/gijyutu/gijyutu4/toushin/_icsFiles/afieldfile/2015/11/17/1351171_1_1.pdf
• [138] K. Matsuoka, Design of toroidal machine for plasma-turbulence research, Reports of Research Institute for Applied Mechanics Kyushu University 141 (2011) p.51-85.
• [139] Specially-promoted research (2017-2021) “Plasma Turbulence Obseravation System (PLATO) for puzzling out the principles of structural formation and functional expression in turbulent plasmas”.
• [140] A. Fujisawa, Y. Nagashima and S. Inagaki, Plasma Fusion Res. 10, 1201080 (2015).
• [141] A. Fujisawa, Y. Nagashima, S. Inagaki, T. Onchi, S. Ohshima and A. Shimizu, Plasma Phys. Control. Fusion 58, 025005 (2016).
• [142] T. Ohkawa, Kakuyugo-Kenkyu 32, 672 (1974) (in Japanese).