Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T06:47:27.481Z Has data issue: false hasContentIssue false

Ion kinetic effects on linear pressure driven magnetohydrodynamic instabilities in helical plasmas

Published online by Cambridge University Press:  11 June 2020

M. Sato*
Affiliation:
National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi, Toki, Gifu509-5292, Japan
Y. Todo
Affiliation:
National Institute for Fusion Science, National Institutes of Natural Sciences, 322-6 Oroshi, Toki, Gifu509-5292, Japan
*
Email address for correspondence: masahiko@nifs.ac.jp

Abstract

The linear MHD (magnetohydrodynamic) stability for high beta plasmas in the inward shifted Large Helical Device (LHD) configurations has been investigated for a wide range of magnetic Reynolds numbers $S$ using numerical simulations based on the kinetic MHD model with kinetic thermal ions where the beta is the ratio of the plasma pressure to the magnetic pressure. It is found that the dependence of the linear growth rate of the resistive ballooning modes on the $S$ number changes from $\unicode[STIX]{x1D6FE}\propto S^{-1/3}$ to $\unicode[STIX]{x1D6FE}\propto S^{-1}$ by the kinetic thermal ion effects so that the resistive ballooning modes are significantly suppressed as the $S$ number increases. For a high $S$ number comparable to experimental values, the most unstable modes are interchange modes. The kinetic thermal ion effects change the most unstable interchange mode from the ideal mode to the resistive mode. This transition of the interchange modes by kinetic thermal ion effects is consistent with the shift of the marginal stability boundary for the ideal interchange modes observed in the LHD experiments.

Type
Research Article
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aydemir, A. Y. 1994 A unified Monte Carlo interpretation of particle simulations and applications to non-neutral plasmas. Phys. Plasmas 1, 822.CrossRefGoogle Scholar
Bateman, G. & Nelson, D. B. 1978 Resistive-ballooning-mode equation. Phys. Rev. Lett. 41, 1804.CrossRefGoogle Scholar
Boozer, A. H. 1980 Guiding center drift equations. Phys. Fluids 23, 904.CrossRefGoogle Scholar
Chen, L. & Zonca, F. 2016 Physics of Alvén waves and energetic particles in burning plasmas. Rev. Mod. Phys. 88, 015008.Google Scholar
Dimits, A. M. & Lee, W. W. 1993 Partially linearized algorithms in gyrokinetic particle simulation. J. Comput. Phys. 107, 309.CrossRefGoogle Scholar
Gorelenkov, N. N., Cheng, C. Z. & Fu, G. Y. 1999 Fast particle finite orbit width and Larmor radius effects on low-$n$ toroidicity induced Alfvén eigenmode excitation. Phys. Plasmas 6, 2802.CrossRefGoogle Scholar
Komori, A., Yamada, H., Sakakibara, S., Kaneko, O., Kawahata, K., Mutoh, T., Ohyabu, N., Imagawa, S., Ida, K., Nagayama, Y. et al. 2009 Development of net-current free heliotron plasmas in the Large Helical Device. Nucl. Fusion 49, 104015.CrossRefGoogle Scholar
Lee, W. W. 1987 Gyrokinetic particle simulation model. J. Comput. Phys. 72, 243.CrossRefGoogle Scholar
Mikhailovskii, A. B., Shirokov, M. S., Konovalov, S. V. & Tsypin, V. S. 2004 Suppression of toroidal Alfvén eigenmodes by the density gradient of hot ions in tokamaks. Dokl. Phys. 49, 505.CrossRefGoogle Scholar
Miura, H., Hamaba, F. & Ito, A. 2017 Two-fluid sub-grid-scale viscosity in nonlinear simulation of ballooning modes in a heliotron device. Nucl. Fusion 57, 076034.CrossRefGoogle Scholar
Miura, H. & Nakajima, N. 2010 Influences of ballooning modes with moderate wave number on MHD equilibrium in LHD. Nucl. Fusion 50, 054006.CrossRefGoogle Scholar
Nakajima, N., Hudson, S. R., Hegna, C. C. & Nakamura, Y. 2006 Boundary modulation effects on MHD instabilities in heliotrons. Nucl. Fusion 46, 177.CrossRefGoogle Scholar
Nakajima, N., Nührenberg, C. & Nührenberg, J. 2004 Growth rates and structures of MHD modes in stellarator/heliotron. J. Plasma Fusion Res. Ser. 6, 45.Google Scholar
Ohdachi, S., Sakamoto, R., Miyazawa, J., Morisaki, T., Masuzaki, S., Yamada, H., Watanabe, K. Y., Jacobo, V. R., Nakajima, N., Watanabe, F. et al. 2010 Density collapse events observed in the Large Helical Device. Contrib. Plasma Phys. 50, 552.CrossRefGoogle Scholar
Ohdachi, S., Watanabe, K. Y., Tanaka, K., Suzuki, Y., Takemura, Y., Sakakibara, S., Du, X. D., Bando, T., Narushima, Y., Sakamoto, R. et al. 2017 Observation of the ballooning mode that limits the operation space of the high-density super-dense-core plasma in the LHD. Nucl. Fusion 57, 066042.CrossRefGoogle Scholar
Ohyabu, N., Morisaki, T., Masuzaki, S., Sakamoto, R., Kobayashi, M., Miyazawa, J., Shoji, M., Komori, A. & Motomima, O. 2006 Observation of stable superdense core plasmas in the Large Helical Device. Phys. Rev. Lett. 97, 055002.CrossRefGoogle ScholarPubMed
Parker, S. E. & Lee, W. W. 1993 A fully nonlinear characteristic method for gyrokinetic simulation. Phys. Fluids B5, 77.CrossRefGoogle Scholar
Sakakibara, S., Watanabe, K. Y., Suzuki, Y., Narushima, Y., Ohdachi, S., Nakajima, N., Watanabe, F., Garcia, L., Weller, A., Toi, K. et al. 2008 MHD study of the reactor-relevant high-beta regime in the Large Helical Device. Plasma Phys. Control. Fusion 50, 124014.CrossRefGoogle Scholar
Sakamoto, R., Yamada, H., Ohyabu, N., Kobayashi, M., Miyazawa, J., Ohdachi, S., Morisaki, T., Masuzaki, S., Yamada, I., Harihara, K. et al. 2007 Pellet injection and internal diffusion barrier formation in Large Helical Device. Plasma Fusion Res. 2, 047.CrossRefGoogle Scholar
Sánchez, R., Jiménez, J. A., García, L. & Varias, A. 1997 Compressibility effects on ideal and resistive balloonig stability in the TJ-II heliac device. Nucl. Fusion 37, 1363.CrossRefGoogle Scholar
Sato, M., Nakajima, N., Watanabe, K. Y. & Todo, Y. 2017 Characteristics of MHD instabilities for high beta plasmas in inward shifted LHD configurations. Nucl. Fusion 57, 126023.CrossRefGoogle Scholar
Sato, M. & Todo, Y. 2019 Effect of precession drift motion of trapped thermal ions on ballooning modes in helical plasmas. Nucl. Fusion 59, 094003.CrossRefGoogle Scholar
Schwab, C. 1993 Ideal magnetohydrodynamics: global mode analysis of three-dimensional plasma configurations. Phys. Fluids B5, 3195.CrossRefGoogle Scholar
Sharapov, S. E., Mikhailovskii, A. B. & Huysmans, G. T. A. 2004 Effects of nonresonant hot ions with large orbits on Alfvén cascades and on magnetohydrodynamic instabilities in tokamaks. Phys. Plasmas 11, 2286.CrossRefGoogle Scholar
Suzuki, Y., Nakajima, N., Watanabe, K. Y., Nakamura, Y. & Hayashi, T. 2006 Development and application of HINT2 to helical system plasmas. Nucl. Fusion 46, L19.CrossRefGoogle Scholar
Todo, Y. 2017 A new magnetohydrodynamic hybrid simulation model with thermal and energetic ions. In The 26th International Toki Conference (Toki, Japan, 5–8 December 2017) O9.Google Scholar
Todo, Y., Nakajima, N., Sato, M. & Miura, H. 2010 Simulation study of ballooning modes in the Large Helical Device. Plasma Fusion Res. 5, S2062.CrossRefGoogle Scholar
Todo, Y., Shinohara, K., Takechi, M. & Ishikawa, M. 2005 Nonlocal energetic particle mode in a JT-60U plasma. Phys. Plasmas 12, 012503.CrossRefGoogle Scholar
Ueda, R., Watanabe, K. Y., Matsumoto, Y., Itagaki, M., Sato, M. & Oikawa, S. 2014 Characteristics of magnetic island formation due to resistive interchange instability in helical plasma. Phys. Plasmas 21, 052502.CrossRefGoogle Scholar
Watanabe, K. Y., Sakakibara, S., Narushima, Y., Funaba, H., Narihara, K., Tanaka, K., Yamaguchi, T., Toi, K., Ohdachi, S., Kaneko, O. et al. 2005 Effects of global MHD instability on operational high beta-regime in LHD. Nucl. Fusion 45, 1247.CrossRefGoogle Scholar
Yamada, H.for the LHD Experiment Group 2011 Overview of results from the Large Helical Device. Nucl. Fusion 51, 094021.CrossRefGoogle Scholar