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Electromagnetic gyrokinetic simulation of turbulence in torus plasmas

  • A. Ishizawa (a1), S. Maeyama (a2), T.-H. Watanabe (a3), H. Sugama (a1) and N. Nakajima (a1)...


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.


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

  • A. Ishizawa (a1), S. Maeyama (a2), T.-H. Watanabe (a3), H. Sugama (a1) and N. Nakajima (a1)...


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