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Stellarator microinstabilities and turbulence at low magnetic shear

  • B. J. Faber (a1), M. J. Pueschel (a2), P. W. Terry (a1), C. C. Hegna (a3) and J. E. Roman (a4)...

Abstract

Gyrokinetic simulations of drift waves in low-magnetic-shear stellarators reveal that simulation domains comprised of multiple turns can be required to properly resolve critical mode structures important in saturation dynamics. Marginally stable eigenmodes important in saturation of ion temperature gradient modes and trapped electron modes in the Helically Symmetric Experiment (HSX) stellarator are observed to have two scales, with the envelope scale determined by the properties of the local magnetic shear and an inner scale determined by the interplay between the local shear and magnetic field-line curvature. Properly resolving these modes removes spurious growth rates that arise for extended modes in zero-magnetic-shear approximations, enabling use of a zero-magnetic-shear technique with smaller simulation domains and attendant cost savings. Analysis of subdominant modes in trapped electron mode (TEM)-driven turbulence reveals that the extended marginally stable modes play an important role in the nonlinear dynamics, and suggests that the properties induced by low magnetic shear may be exploited to provide another route for turbulence saturation.

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Copyright

Corresponding author

Email address for correspondence: bfaber@wisc.edu

References

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Al-Mohy, A. H. & Higham, N. J. 2010 A new scaling and squaring algorithm for the matrix exponential. SIAM J. Matrix Anal. Applics. 31 (3), 970989.
Anderson, F., Almagri, A. F., Anderson, D. T., Peter, G., Talmadge, J. N. & Shohet, J. L. 1995 The helically symmetric experiment, (HSX), goals, design and status. Fusion Technol. 27 (3T), 273277.
Bañón Navarro, A., Morel, P., Albrecht-Marc, M., Carati, D., Merz, F., Gorler, T. & Jenko, F. 2011 Free energy balance in gyrokinetic turbulence. Phys. Plasmas 18 (9), 092303.
Baumgaertel, J. A., Belli, E. A., Dorland, W., Guttenfelder, W., Hammett, G. W., Mikkelsen, D. R., Rewoldt, G., Tang, W. M. & Xanthopoulos, P. 2011 Simulating gyrokinetic microinstabilities in stellarator geometry with GS2. Phys. Plasmas 18, 122301.
Beer, M. A., Cowley, S. C. & Hammett, G. W. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 26872700.
Bhattacharjee, A., Sedlak, J. E., Similon, P. L., Rosenbluth, M. N. & Ross, D. W. 1983 Drift waves in a straight stellarator. Phys. Fluids 26 (1983), 880882.
Blackford, L. S., Choi, J., Cleary, A., D’Azeuedo, E., Demmel, J., Dhillon, I., Hammarling, S., Henry, G., Petitet, A., Stanley, K. et al. 1997 ScaLAPACK Users’ Guide. Society for Industrial and Applied Mathematics.
Boozer, A. H. 1981 Plasma equilibrium with rational magnetic surfaces. Phys. Fluids 24 (11), 19992003.
Boozer, A. H. 1998 What is a stellarator? Phys. Plasmas 5 (5), 16471655.
Candy, J. & Waltz, R. E. 2003 An Eulerian gyrokinetic-Maxwell solver. J. Comput. Phys. 186 (2), 545581.
Candy, J., Waltz, R. E. & Rosenbluth, M. N. 2004 Smoothness of turbulent transport across a minimum-q surface. Phys. Plasmas 11 (5), 18791890.
Canik, J. M., Anderson, D. T., Anderson, F. S. B., Likin, K. M., Talmadge, J. N. & Zhai, K. 2007 Experimental demonstration of improved neoclassical transport with quasihelical symmetry. Phys. Rev. Lett. 98, 085002.
Chen, H. & Chen, L. 2018 On drift wave instabilities excited by strong plasma gradients in toroidal plasmas. Phys. Plasmas 25, 014502.
Chen, Y., Parker, S. E., Wan, W. & Bravenec, R. 2013 Benchmarking gyrokinetic simulations in a toroidal flux-tube. Phys. Plasmas 20 (9), 18.
Connor, J. & Hastie, R. 2004 Microstability in tokamaks with low magnetic shear. Plasma Phys. Control. Fusion 46 (10), 15011535.
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1978 Shear, periodicity, and plasma ballooning modes. Phys. Rev. Lett. 40 (6), 396399.
Connor, J. W., Hastie, R. J. & Taylor, J. B. 1979 High mode number stability of an axisymmetric toroidal plasma. Proc. R. Soc. Lond. A 365 (1720), 117.
Cuthbert, P. & Dewar, R. L. 2000 Anderson-localized ballooning modes in general toroidal plasmas. Phys. Plasmas 7 (6), 23022305.
Dewar, R. & Glasser, A. 1983 Ballooning mode spectrum in general toroidal systems. Phys. Fluids 26 (10), 30383052.
Dimits, A. M., Williams, T. J., Byers, J. A. & Cohen, B. I. 1996 Scalings of ion-temperature-gradient-driven anomalous transport in tokamaks. Phys. Rev. Lett. 77 (1), 7174.
Dinklage, A., Beidler, C. D., Helander, P., Fuchert, G., Maaßberg, H., Rahbarnia, K., Sunn Pedersen, T., Turkin, Y., Wolf, R. C., Alonso, A. et al. & the W7-X Team 2018 Magnetic configuration effects on the Wendelstein 7-X stellarator. Nat. Phys 14 (8), 855860.
Dorland, W., Jenko, F., Kotschenreuther, M. & Rogers, B. N. 2000 Electron temperature gradient turbulence. Phys. Rev. Lett. 85 (26), 55795582.
Eiermann, M. & Ernst, O. G. 2006 A restarted Krylov subspace method for the evaluation of matrix functions. SIAM J. Numer. Anal. 44 (6), 24812504.
Faber, B. J., Pueschel, M. J., Proll, J. H. E., Xanthopoulos, P., Terry, P. W., Hegna, C. C., Weir, G. M., Likin, K. M. & Talmadge, J. N. 2015 Gyrokinetic studies of trapped electron mode turbulence in the helically symmetric experiment stellarator. Phys. Plasmas 22 (7), 072305.
Friedman, B. & Carter, T. A. 2014 Linear technique to understand non-normal turbulence applied to a magnetized plasma. Phys. Rev. Lett. 113, 025003.
Friedman, B., Carter, T. A., Umansky, M. V., Schaffner, D. & Joseph, I. 2013 Nonlinear instability in simulations of large plasma device turbulence. Phys. Plasmas 20, 055704.
Fulton, D. P., Lin, Z., Holod, I. & Xiao, Y. 2014 Microturbulence in DIII-D tokamak pedestal. I. Electrostatic instabilities. Phys. Plasmas 21, 042110.
Gates, D. A., Anderson, D., Anderson, S., Zarnstorff, M., Spong, D. A., Weitzner, H., Neilson, G. H., Ruzic, D., Andruczyk, D., Harris, J. H. et al. 2018 Stellarator research opportunities: a report of the national stellarator coordinating committee. J. Fusion Energy 37 (1), 5194.
Goldhirsch, I., Orszag, S. A. & Maulik, B. K. 1987 An efficient method for computing leading eigenvalues and eigenvectors of large asymmetric matrices. J. Sci. Comput. 2 (1), 3358.
Hatch, D. R., Jenko, F., Bañón Navarro, A., Bratanov, V., Terry, P. W. & Pueschel, M. J. 2016a Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra. New J. Phys. 18, 075018.
Hatch, D. R., Kotschenreuther, M., Mahajan, S., Valanju, P., Jenko, F., Told, D., Gorler, T. & Saarelma, S. 2016b Microtearing turbulence limiting the JET-ILW pedestal. Nucl. Fusion 56, 104003.
Hatch, D. R., Terry, P. W., Jenko, F., Merz, F. & Nevins, W. M. 2011a Saturation of gyrokinetic turbulence through damped eigenmodes. Phys. Rev. Lett. 106, 115003.
Hatch, D. R., Terry, P. W., Jenko, F., Merz, F., Pueschel, M. J., Nevins, W. M. & Wang, E. 2011b Role of subdominant stable modes in plasma microturbulence. Phys. Plasmas 18, 055706.
Hegna, C. C. & Hudson, S. R. 2001 Loss of second-ballooning stability in three-dimensional equilibria. Phys. Rev. Lett. 87 (3), 36.
Hegna, C. C., Terry, P. W. & Faber, B. J. 2018 Theory of ITG turbulent saturation in stellarators: identifying mechanisms to reduce turbulent transport. Phys. Plasmas 25, 022511.
Helander, P. 2014 Theory of plasma confinement in non-axisymmetric magnetic fields. Rep. Prog. Phys. 77, 087001.
Hernandez, V., Roman, J. E. & Vidal, V. 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans. Math. Softw. 31 (3), 351362.
Higham, N. J. 2008 Functions of Matrices: Theory and Computation. Society for Industrial and Applied Mathematics.
Jenko, F., Dorland, W., Kotschenreuther, M. & Rogers, B. N. 2000 Electron temperature gradient driven turbulence. Phys. Plasmas 7 (5), 19041910.
Martin, M. F., Landremann, M., Xanthopoulos, P., Mandell, N. R. & Dorland, W. 2018 The parallel boundary condition for turbulence simulations in low magnetic shear devices. Plasma Phys. Control. Fusion 60, 095008.
Meerbergen, K. & Sadkane, M. 1999 Using Krylov approximations to the matrix exponential operator in Davidson’s method. Appl. Numer. Maths 31 (3), 331351.
Merz, F.2008 Gyrokinetic simulation of multimode plasma turbulence. PhD thesis.
Nadeem, M., Rafiq, T. & Persson, M. 2001 Local magnetic shear and drift waves in stellarators. Phys. Plasmas 8 (10), 43754385.
Nagaoka, K., Takahashi, H., Murakami, S., Nakano, H., Takeiri, Y., Tsuchiya, H., Osakabe, M., Ida, K., Yokoyama, M., Yoshinuma, M. et al. & LHD Experimental Group 2015 Integrated discharge scenario for high-temperature helical plasma in LHD. Nucl. Fusion 55, 113020.
Pearlstein, L. D. & Berk, H. L. 1969 Universal eigenmode in a strongly sheared magnetic field. Phys. Rev. Lett. 23 (5), 220222.
Peeters, A. G., Camenen, Y., Casson, F. J., Hornsby, W. A., Snodin, A. P., Strintzi, D. & Szepesi, G. 2009 The nonlinear gyro-kinetic flux tube code GKW. Comput. Phys. Commun. 180 (12), 26502672.
Plunk, G. G., Helander, P., Xanthopoulos, P. & Connor, J. W. 2014 Collisionless microinstabilities in stellarators. III. The ion-temperature-gradient mode. Phys. Plasmas 21, 032112.
Plunk, G. G., Xanthopoulos, P. & Helander, P. 2017 Distinct turbulence saturation regimes in stellarators. Phys. Rev. Lett. 118, 105002.
Proll, J. H. E., Xanthopoulos, P. & Helander, P. 2013 Collisionless microinstabilities in stellarators. II. Numerical simulations. Phys. Plasmas 20, 122506.
Pueschel, M. J., Faber, B. J., Citrin, J., Hegna, C. C., Terry, P. W. & Hatch, D. R. 2016 Stellarator turbulence: subdominant eigenmodes and quasilinear modeling. Phys. Rev. Lett. 116, 085001.
Sugama, H. & Watanabe, T. H. 2006 Collisionless damping of zonal flows in helical systems. Phys. Plasmas 13, 012501.
Terry, P. W., Baver, D. A. & Gupta, S. 2006 Role of stable eigenmodes in saturated local plasma turbulence. Phys. Plasmas 13, 022307.
Terry, P. W., Faber, B. J., Hegna, C. C., Mirnov, V. V., Pueschel, M. J. & Whelan, G. G. 2018 Saturation scalings of toroidal ion temperature gradient turbulence. Phys. Plasmas 25, 012308.
Waltz, R. E. & Boozer, A. H. 1993 Local shear in general magnetic stellarator geometry. Phys. Fluids B 5 (7), 22012205.
Whelan, G. G., Pueschel, M. J. & Terry, P. W. 2018 Nonlinear electromagnetic stabilization of plasma microturbulence. Phys. Rev. Lett. 120, 175002.
Xanthopoulos, P., Cooper, W., Jenko, F., Turkin, Y., Runov, A. & Geiger, J. 2009 A geometry interface for gyrokinetic microturbulence investigations in toroidal configurations. Phys. Plasmas 16, 082303.
Xanthopoulos, P. & Jenko, F. 2007 Gyrokinetic analysis of linear microinstabilities for the stellarator Wendelstein 7-X. Phys. Plasmas 14, 042501.
Xanthopoulos, P., Merz, F., Görler, T. & Jenko, F. 2007 Nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence for the optimized Wendelstein 7-X stellarator. Phys. Rev. Lett. 99, 035002.
Xanthopoulos, P., Plunk, G. G., Zocco, A. & Helander, P. 2016 Intrinsic turbulence stabilization in a stellarator. Phys. Rev. X 6, 021033.
Yoshimura, Y., Kubo, S., Shimozuma, T., Igami, H., Mutoh, T., Nakamura, Y., Ohkubo, K., Notake, T., Takita, Y., Kobayashi, S. et al. & the LHD Experimental Group 2005 Achievement of one hour discharge with ECH on LHD. J. Phys.: Conf. Ser. 25, 189197.
Zocco, A., Xanthopoulos, P., Doerk, H., Connor, J. W. & Helander, P. 2018 Threshold for the destabilisation of the ion-temperature-gradient mode in magnetically confined toroidal plasmas. J. Plasma Phys. 84, 715840101.
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