Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-19T22:41:22.167Z Has data issue: false hasContentIssue false
  • English
  • Français

Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

Part of: ITER International School 2014 Focus on Fusion

Published online by Cambridge University Press:  27 February 2015

A. Ishizawa ,
S. Maeyama ,
T.-H. Watanabe ,
H. Sugama  and
N. Nakajima
A. Ishizawa*
Affiliation:
National Institute for Fusion Science, Toki, 509-5292, Japan
S. Maeyama
Affiliation:
Japan Atomic Energy Agency, Kashiwa, 277-8587Japan
T.-H. Watanabe
Affiliation:
Nagoya University, Nagoya 464-8602Japan
H. Sugama
Affiliation:
National Institute for Fusion Science, Toki, 509-5292, Japan
N. Nakajima
Affiliation:
National Institute for Fusion Science, Toki, 509-5292, Japan
*
†Email address for correspondence: ishizawa@nifs.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 2 , April 2015 , 435810203
Check for updates
Copyright
Copyright © Cambridge University Press 2015 

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

REFERENCES

Antonsen, T. M. and Lane, B. 1980 Phys. Fluids 23, 1205.CrossRefGoogle Scholar
Applegate, D. J., Roach, C. M., Connor, J. W., Cowley, S. C., Dorland, W., Hastie, R. J. and Joiner, N. 2007 Plasma Phys. Control. Fusion 49, 1113.Google Scholar
Beer, M. A., Cowley, S. C. and Hammett, G. W. 1995 Phys. Plasmas 2, 2687.Google Scholar
Biskamp, D. 2000 Magnetic Reconnection in Plasmas. Cambridge: Cambridge University Press.Google Scholar
Brizard, A. J. and Hahm, T. S. 2007 Rev. Mod. Phys. 79, 421.Google Scholar
Candy, J. 2005 Phys. Plasmas 12, 072307.CrossRefGoogle Scholar
Candy, J. and Waltz, R. E. 2003a J. Comput. Phys. 186, 545.Google Scholar
Candy, J. and Waltz, R. E. 2003b Phys. Rev. Lett. 91, 045001.Google Scholar
Chen, L. 2008 Plasma Phys. Control. Fusion 50, 124001.Google Scholar
Clemmow, P. C. and Dougherty, J. P. 1969 Electrodynamics of Particles and Plasmas. Redwood City: Addison-Wesley.Google Scholar
Davidson, P. A. 2004 Turbulence. Oxford: Oxford University Press.Google Scholar
Diamond, P. H., Itoh, S.-I. and Itoh, K. 2010 Modern Plasma Physics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Dimits, A. M.et al. 2000 Phys. Plasmas 7, 969.Google Scholar
Doerk, H., Jenko, F., Pueschel, M. J. and Hatch, D. R. 2011 Phys. Rev. Lett. 106, 155003.Google Scholar
Ferrando-Margalet, S., Sugama, H. and Watanabe, T.-H. 2007 Phys. Plasmas 14, 122505.Google Scholar
Freidberg, J. 2007 Plasma Physics and Fusion Energy. Cambridge: Cambridge University Press.Google Scholar
Fried, B. D. and Conte, S. D. 1961 The Plasma Dispersion Function. New York: Academic Press.Google Scholar
Frieman, E. A. and Chen, L. 1982 Phys. Fluids 25, 502.CrossRefGoogle Scholar
Gorler, T.et al. 2008 Phys. Rev. Lett. 100, 185002.CrossRefGoogle Scholar
Guttenfelder, W.et al. 2011 Phys. Rev. Lett. 106, 155004.Google Scholar
Guttenfelder, W., Candy, J., Kaye, S. M., Nevins, W. M., Bell, R. E., Hammett, G. W., LeBlanc, B. P. and Yuh, H. 2012 Phys. Plasmas 19, 022506.CrossRefGoogle Scholar
Hahm, T. S., Lee, W. W. and Brizard, A. 1988 Phys. Fluids 31, 1940.CrossRefGoogle Scholar
Hatch, D. R., Pueschel, M. J., Jenko, F., Nevins, W. M., Terry, P. W. and Doerk, H. 2012 Phys. Rev. Lett. 108, 235002.Google Scholar
Hazeltine, R. D. and Meiss, J. D. 2003 Plasma Confinement. Dover: Dover Pub.Google Scholar
Helander, P. and Sigmar, D. J. 2002 Collisional Transport in Magnetized Plasmas. Cambridge: Cambridge University Press.Google Scholar
Hirose, A. 1994 Phys. Rev. Lett. 72, 3993.Google Scholar
Hornsby, W. A., Peeters, A. G., Siccinio, M. and Poli, E. 2012 Phys. Plasmas 19, 032308.Google Scholar
Hornsby, W. A., Siccinio, M., Peeters, A. G., Poli, E., Snodin, A. P., Casson, F. J., Camenen, Y. and Szepesi, G. 2011 Plasma Phys. Control. Fusion 53, 054008.CrossRefGoogle Scholar
Horton, W. 2012 Turbulent Transport in Magnetized Plasmas. Singapore: World Scientific.Google Scholar
Ishizawa, A., Maeyama, S., Watanabe, T.-H., Sugama, H. and Nakajima, N. 2013 Nuclear Fusion 53, 053007.Google Scholar
Ishizawa, A. and Watanabe, T.-H. 2013 Phys. Plasmas 20, 102116.Google Scholar
Ishizawa, A., Watanabe, T.-H. and Nakajima, N. 2011 Plasma Fusion Res. 6, 2403087.Google Scholar
Ishizawa, A., Watanabe, T.-H., Sugama, H., Maeyama, S. and Nakajima, N. 2014 Phys. Plasmas 21, 055905.Google Scholar
Jenko, F. 2000 Comput. Phys. Commun. 125, 196.Google Scholar
Jenko, F. and Dorland, W. 2001 Plasma Phys. Controll. Fusion 43, A141.Google Scholar
Jenko, F., Dorland, W., Kotschenreuther, M. and Rogers, B. N. 2000 Phys. Plasmas 7, 1904.Google Scholar
Kaneko, O., Yamada, H., Inagaki, S. and LHD Experiment Group 2013 Nuclear Fusion 53, 104015.Google Scholar
Kim, J. Y., Horton, W. and Dong, J. Q. 1993 Phys. Fluids B 5, 4030.CrossRefGoogle Scholar
Kotschenreuther, M., Rewoldt, G. and Tang, W. M. 1995 Comput. Phys. Commun. 88, 128.Google Scholar
Maeyama, S., Idomura, Y., Nakata, M., Yagi, M. and Miyato, N. 2014 IAEA-FEC TH/1-1.Google Scholar
Maeyama, S., Ishizawa, A., Watanabe, T.-H., Nakajima, N., Tsuji-Iio, S. and Tsutsui, H. 2013 Comput. Phys. Commun. 184, 2462.CrossRefGoogle Scholar
Maeyama, S., Ishizawa, A., Watanabe, T.-H., Nakata, M., Miyato, N., Yagi, M. and Idomura, Y. 2014 Phys. Plasmas 21, 052301.CrossRefGoogle Scholar
Maeyama, S., Ishizawa, A., Watanabe, T.-H., Nakata, M., Miyato, N. and Idomura, Y. 2014 Plasma Fusion Res. 9, 1203020.Google Scholar
Nakata, M., Watanabe, T.-H. and Sugama, H. 2012 Phys. Plasmas 19, 022303.Google Scholar
Numata, R., Dorland, W., Howes, G. G., Loureiro, N. F., Rogers, B. N. and Tatsuno, T. 2011 Phys. Plasmas 18, 112106.Google Scholar
Ohdachi, S., Tanaka, K., Watanabe, K. Y. and LHD Experiment Group 2010 Cont. Plasma Phys. 50, 552.Google Scholar
Peeters, A. G., Angioni, C. and the ASDEX Upgrade Team 2005 Phys. Plasmas 12, 072515.Google Scholar
Peeters, A. G., Camenen, Y., Casson, F. J., Hornsby, W. A., Snodina, A. P., Strintzi, D. and Szepesia, G. 2009 Comput. Phys. Commun. 180, 2650.CrossRefGoogle Scholar
Poli, E., Bottino, A. and Peeters, A. G. 2009 Nucl. Fusion 49, 075010.Google Scholar
Pueschel, M. J., Gorler, T., Jenko, F., Hatch, D. R. and Cianciara, A. J. 2013aPhys. Plasmas 20, 102308.Google Scholar
Pueschel, M. J. and Jenko, F. 2010 Phys. Plasmas 17, 062307.Google Scholar
Pueschel, M. J., Jenko, F., Told, D. and Buchner, J. 2011 Phys. Plasmas 18, 112102.Google Scholar
Pueschel, M. J., Kammerer, M. and Jenko, F. 2008 Phys. Plasmas 15, 102310.Google Scholar
Pueschel, M. J., Terry, P. W. and Hatch, D. R. 2014 Phys. Plasmas 21, 055901.Google Scholar
Pueschel, M. J., Terry, P. W., Jenko, F., Hatch, D. R., Nevins, W. M., Gorler, T. and Told, D. 2013b Phys. Rev. Lett. 110, 155005.Google Scholar
Rechester, A. B. and Rosenbluth, M. N. 1978 Phys. Rev. Lett. 40, 38.Google Scholar
Schekochihin, A. A., Cowley, S. C., Dorland, W., Hammett, G. W., Howes, G. G., Quataert, E. and Tatsuno, T. 2009 Astrophys. J. Suppl. Ser. 182, 310.CrossRefGoogle Scholar
Sugama, H., Okamoto, M., Horton, W. and Wakatani, M. 1996 Phys. Plasmas 3, 2379.Google Scholar
Sugama, H. and Watanabe, T.-H. 2004 Phys. Plasmas 11, 3068.Google Scholar
Sugama, H., Watanabe, T.-H. and Nunami, M. 2009 Phys. Plasmas 16 112503.Google Scholar
Sugama, H., Watanabe, T.-H., Nunami, M. and Nishimura, S. 2011 Plasma Phys. Control. Fusion 53, 024004.Google Scholar
Tang, W. M., Connor, J. W. and Hastie, R. J. 1980 Nucl. Fusion 20, 1439.Google Scholar
Terry, P. W., Pueschel, M. J., Carmody, D. and Nevins, W. M. 2013 Phys. Plasmas 20, 112502.Google Scholar
Terry, P. W.et al. 2014 IAEA-FEC, OV/5-1.Google Scholar
Told, D., Jenko, F., Xanthopoulous, P., Horton, L. D., Wolfrum, E. and ASDEX Upgrade Team 2008 Phys. Plasmas 15, 102306.Google Scholar
Waltz, R. E. 2010 Phys. Plasmas 17 072501.Google Scholar
Waltz, R. E. and Waelbroeck, F. L. 2012 Phys. Plasmas 19, 032508.Google Scholar
Watanabe, T.-H. and Sugama, H. 2004 Phys. Plasmas 11, 1476.CrossRefGoogle Scholar
Watanabe, T.-H. and Sugama, H. 2006 Nuclear Fusion 46, 24.Google Scholar
Watanabe, T.-H., Sugama, H. and Margalet, S. F. 2008 Phys. Rev. Lett. 100, 195002.Google Scholar
Wesson, J. 2004 Tokamaks. Oxford: Oxford University Press.Google Scholar