Hostname: page-component-546b4f848f-fhndm Total loading time: 0 Render date: 2023-05-31T17:52:13.678Z Has data issue: false Feature Flags: { "useRatesEcommerce": true } hasContentIssue false
  • English

Turbulent impurity transport simulations in Wendelstein 7-X plasmas

Part of: Invited Contributions from the 18th European Fusion Theory Conference Focus on Fusion

Published online by Cambridge University Press:  02 February 2021

J. M. García-Regaña Open the ORCID record for J. M. García-Regaña[Opens in a new window] ,
M. Barnes Open the ORCID record for M. Barnes[Opens in a new window] ,
I. Calvo Open the ORCID record for I. Calvo[Opens in a new window] ,
F. I. Parra Open the ORCID record for F. I. Parra[Opens in a new window] ,
J. A. Alcusón Open the ORCID record for J. A. Alcusón[Opens in a new window] ,
R. Davies Open the ORCID record for R. Davies[Opens in a new window] ,
A. González-Jerez Open the ORCID record for A. González-Jerez[Opens in a new window] ,
A. Mollén Open the ORCID record for A. Mollén[Opens in a new window] ,
E. Sánchez Open the ORCID record for E. Sánchez[Opens in a new window]  and
J. L. Velasco Open the ORCID record for J. L. Velasco[Opens in a new window]
...Show all authors
J. M. García-Regaña*
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, Av. Complutense, 28040, Spain
M. Barnes
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OxfordOX1 3PU, UK
I. Calvo
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, Av. Complutense, 28040, Spain
F. I. Parra
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, OxfordOX1 3PU, UK
J. A. Alcusón
Affiliation:
Max-Planck Institut für Plasmaphysik, Wendelsteinstrasse 1, 17491, Germany
R. Davies
Affiliation:
York Plasma Institute, Department of Physics, University of York, Heslington, YorkYO10 5DD, UK
A. González-Jerez
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, Av. Complutense, 28040, Spain
A. Mollén
Affiliation:
Princeton Plasma Physics Laboratory, Princeton, NJ08543-0451, USA
E. Sánchez
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, Av. Complutense, 28040, Spain
J. L. Velasco
Affiliation:
Laboratorio Nacional de Fusión, CIEMAT, Av. Complutense, 28040, Spain
A. Zocco
Affiliation:
Max-Planck Institut für Plasmaphysik, Wendelsteinstrasse 1, 17491, Germany
*
†Email address for correspondence: jose.regana@ciemat.es
Get access Rights & Permissions[Opens in a new window]

Abstract

A study of turbulent impurity transport by means of quasilinear and nonlinear gyrokinetic simulations is presented for Wendelstein 7-X (W7-X). The calculations have been carried out with the recently developed gyrokinetic code stella. Different impurity species are considered in the presence of various types of background instabilities: ion temperature gradient (ITG), trapped electron mode (TEM) and electron temperature gradient (ETG) modes for the quasilinear part of the work; ITG and TEM for the nonlinear results. While the quasilinear approach allows one to draw qualitative conclusions about the sign or relative importance of the various contributions to the flux, the nonlinear simulations quantitatively determine the size of the turbulent flux and check the extent to which the quasilinear conclusions hold. Although the bulk of the nonlinear simulations are performed at trace impurity concentration, nonlinear simulations are also carried out at realistic effective charge values, in order to know to what degree the conclusions based on the simulations performed for trace impurities can be extrapolated to realistic impurity concentrations. The presented results conclude that the turbulent radial impurity transport in W7-X is mainly dominated by ordinary diffusion, which is close to that measured during the recent W7-X experimental campaigns. It is also confirmed that thermodiffusion adds a weak inward flux contribution and that, in the absence of impurity temperature and density gradients, ITG- and TEM-driven turbulence push the impurities inwards and outwards, respectively.

Keywords

plasma simulationfusion plasmaplasma confinement
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 1 , February 2021 , 855870103
Check for updates
Copyright
Copyright © The Author(s), 2021. 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

REFERENCES

Alcusón, J. A., Xanthopoulos, P., Plunk, G. G., Helander, P., Wilms, F., Turkin, Y., von Stechow, A. & Grulke, O. 2020 Suppression of electrostatic micro-instabilities in maximum-j stellarators. Plasma Phys. Control. Fusion 62 (3), 035005.CrossRefGoogle Scholar
Baldzuhn, J., Damm, H., Beidler, C. D., McCarthy, K., Panadero, N., Biedermann, C., Bozhenkov, S. A., Brunner, K. J., Fuchert, G., Kazakov, Y., et al. 2019 Pellet fueling experiments in Wendelstein 7-x. Plasma Phys. Control. Fusion 61 (9), 095012.CrossRefGoogle Scholar
Barnes, M., Parra, F. & Landreman, M. 2019 stella: an operator-split, implicit–explicit $\delta f$-gyrokinetic code for general magnetic field configurations. J. Comput. Phys. 391, 365–380.CrossRefGoogle Scholar
Barnes, M., Parra, F. I. & Dorland, W. 2012 Turbulent transport and heating of trace heavy ions in hot magnetized plasmas. Phys. Rev. Lett. 109, 185003.CrossRefGoogle ScholarPubMed
Barnes, M., Parra, F. I. & Schekochihin, A. A. 2011 Critically balanced ion temperature gradient turbulence in fusion plasmas. Phys. Rev. Lett. 107 (11).CrossRefGoogle ScholarPubMed
Beer, M. A., Cowley, S. C. & Hammett, G. W. 1995 Field-aligned coordinates for nonlinear simulations of tokamak turbulence. Phys. Plasmas 2 (7), 2687–2700.CrossRefGoogle Scholar
Bozhenkov, S., Kazakov, Y., Ford, O., Beurskens, M., Alcusón, J., Alonso, J., Baldzuhn, J., Brandt, C., Brunner, K., Damm, H., et al. 2020 High-performance plasmas after pellet injections in Wendelstein 7-x. Nucl. Fusion 60 (6), 066011.CrossRefGoogle Scholar
Buller, S. & Helander, P. 2020 Effects of collisions on impurity transport driven by electrostatic modes. J. Plasma Phys. 86 (3).CrossRefGoogle Scholar
Buller, S., Mollén, A., Newton, S. L., Smith, H. M. & Pusztai, I. 2019 The importance of the classical channel in the impurity transport of optimized stellarators. J. Plasma Phys. 85 (4).CrossRefGoogle Scholar
Buller, S., Smith, H. M., Helander, P., Mollén, A., Newton, S. L. & Pusztai, I. 2018 Collisional transport of impurities with flux-surface varying density in stellarators. J. Plasma Phys. 84 (4), 905840409.CrossRefGoogle Scholar
Burhenn, R., Feng, Y., Ida, K., Maassberg, H., McCarthy, K., Kalinina, D., Kobayashi, M., Morita, S., Nakamura, Y., Nozato, H., et al. 2009 On impurity handling in high performance stellarator/heliotron plasmas. Nucl. Fusion 49 (6), 065005.CrossRefGoogle Scholar
Calvo, I., Parra, F. I., Velasco, J. L. & Alonso, J. A. 2017 The effect of tangential drifts on neoclassical transport in stellarators close to omnigeneity. Plasma Phys. Control. Fusion 59 (5), 055014.CrossRefGoogle Scholar
Calvo, I., Parra, F. I., Velasco, J. L., Alonso, J. A. & García-Regaña, J. 2018 a Stellarator impurity flux driven by electric fields tangent to magnetic surfaces. Nucl. Fusion 58 (12), 124005.CrossRefGoogle Scholar
Calvo, I., Velasco, J. L., Parra, F. I., Alonso, J. A. & García-Regaña, J. M. 2018 b Electrostatic potential variations on stellarator magnetic surfaces in low collisionality regimes. J. Plasma Phys. 84 (4), 905840407.CrossRefGoogle Scholar
Fujita, K., Satake, S., Kanno, R., Nunami, M., Nakata, M., García-Regaña, J. M., Velasco, J. L. & Calvo, I. 2020 Global calculation of neoclassical impurity transport including the variation of electrostatic potential. J. Plasma Phys. 86 (3).CrossRefGoogle Scholar
García-Regaña, J. M., Beidler, C. D., Kleiber, R., Helander, P., Mollén, A., Alonso, J. A., Landreman, M., Maassberg, H., Smith, H. M., Turkin, Y., et al. 2017 Electrostatic potential variation on the flux surface and its impact on impurity transport. Nucl. Fusion 57 (5), 056004.CrossRefGoogle Scholar
García-Regaña, J. M., Kleiber, R., Beidler, C. D., Turkin, Y., Maaßberg, H. & Helander, P. 2013 On neoclassical impurity transport in stellarator geometry. Plasma Phys. Control. Fusion 55 (7), 074008.CrossRefGoogle Scholar
Geiger, B., Wegner, T., Beidler, C., Burhenn, R., Buttenschön, B., Dux, R., Langenberg, A., Pablant, N., Pütterich, T. & Turkin, Y., et al. 2019 Observation of anomalous impurity transport during low-density experiments in w7-x with laser blow-off injections of iron. Nucl. Fusion 59 (4), 046009.CrossRefGoogle Scholar
Geiger, J., Beidler, C. D., Feng, Y., Maassberg, H., Marushchenko, N. B. & Turkin, Y. 2015 Physics in the magnetic configuration space of W7–X. Plasma Phys. Control. Fusion 57 (1), 014004.CrossRefGoogle Scholar
Grimm, R. C., Dewar, R. L. & Manickam, J. 1983 Ideal MHD stability calculations in axisymmetric toroidal coordinate systems. J. Comput. Phys. 49, 94.CrossRefGoogle Scholar
Helander, P., Beidler, C. D., Bird, T. M., Drevlak, M., Feng, Y., Hatzky, R., Jenko, F., Kleiber, R., Proll, J. H. E., Turkin, Y., et al. 2012 Stellarator and tokamak plasmas: a comparison. Plasma Phys. Control. Fusion 54 (12), 124009.CrossRefGoogle Scholar
Helander, P., Newton, S. L., Mollén, A. & Smith, H. M. 2017 Impurity transport in a mixed-collisionality stellarator plasma. Phys. Rev. Lett. 118, 155002.CrossRefGoogle Scholar
Helander, P. & Zocco, A. 2018 Quasilinear particle transport from gyrokinetic instabilities in general magnetic geometry. Plasma Phys. Control. Fusion 60 (8), 084006.CrossRefGoogle Scholar
Hirsch, M., Baldzuhn, J., Beidler, C., Brakel, R., Burhenn, R., Dinklage, A., Ehmler, H., Endler, M., Erckmann, V., Feng, Y., et al. 2008 Major results from the stellarator wendelstein 7-AS. Plasma Phys. Control. Fusion 50 (5), 053001.CrossRefGoogle Scholar
Hirshman, S. P., Shaing, K. C., van Rij, W. I., Beasley, C. O. Jr. & Crume, E. C. Jr. 1986 Plasma transport coefficients for nonsymmetric toroidal confinement systems. Phys. Fluids 29, 2951.CrossRefGoogle Scholar
Ida, K., Yoshinuma, M., Osakabe, M., Nagaoka, K., Yokoyama, M., Funaba, H., Suzuki, C., Ido, T., Shimizu, A., Murakami, I., et al. 2009 Observation of an impurity hole in a plasma with an ion internal transport barrier in the large helical device. Phys. Plasmas 16, 056111.CrossRefGoogle Scholar
Klinger, T., Andreeva, T., Bozhenkov, S., Brandt, C., Burhenn, R., Buttenschön, B., Fuchert, G., Geiger, B., Grulke, O. & Laqua, H., et al. 2019 Overview of first wendelstein 7-x high-performance operation. Nucl. Fusion 59 (11), 112004.CrossRefGoogle Scholar
Langenberg, A., Wegner, T., Pablant, N. A., Marchuk, O., Geiger, B., Tamura, N., Bussiahn, R., Kubkowska, M., Mollén, A. & Traverso, P., et al. 2020 Charge-state independent anomalous transport for a wide range of different impurity species observed at wendelstein 7-x. Phys. Plasmas 27 (5), 052510.CrossRefGoogle Scholar
McCormick, K., Grigull, P., Burhenn, R., Brakel, R., Ehmler, H., Feng, Y., Gadelmeier, F., Giannone, L., Hildebrandt, D., Hirsch, M., et al. 2002 New advanced operational regime on the W7–AS stellarator. Phys. Rev. Lett. 89, 015001.CrossRefGoogle ScholarPubMed
Mikkelsen, D. R., Tanaka, K., Nunami, M., Watanabe, T.-H., Sugama, H., Yoshinuma, M., Ida, K., Suzuki, Y., Goto, M., Morita, S., et al. 2014 Quasilinear carbon transport in an impurity hole plasma in LHD. Phys. Plasmas 21, 082302.CrossRefGoogle Scholar
Mollén, A., Landreman, M., Smith, H. M., García-Regaña, J. M. & Nunami, M. 2018 Flux-surface variations of the electrostatic potential in stellarators: impact on the radial electric field and neoclassical impurity transport. Plasma Phys. Control. Fusion 60, 084001.CrossRefGoogle Scholar
Nunami, M., Nakata, M., Toda, S. & Sugama, H. 2020 Gyrokinetic simulations for turbulent transport of multi-ion-species plasmas in helical systems. Phys. Plasmas 27 (5), 052501.CrossRefGoogle Scholar
Proll, J. H. E., Xanthopoulos, P. & Helander, P. 2013 Collisionless microinstabilities in stellarators. II. Numerical simulations. Phys. Plasmas 20 (12), 122506.CrossRefGoogle Scholar
Velasco, J., Calvo, I., Parra, F. & García-Regaña, J. 2020 KNOSOS: a fast orbit-averaging neoclassical code for stellarator geometry. J. Comput. Phys. 418, 109512.CrossRefGoogle Scholar
Velasco, J. L., Calvo, I., García-Regaña, J. M., Parra, F. I., Satake, S. & Alonso, J. A. 2018 Large tangential electric fields in plasmas close to temperature screening. Plasma Phys. Control. Fusion 60 (7), 074004.CrossRefGoogle Scholar
Xanthopoulos, P., Bozhenkov, S., Beurskens, M., Smith, H., Plunk, G., Helander, P., Beidler, C., Alcusón, J., Alonso, A., Dinklage, A., et al. 2020 Turbulence mechanisms of enhanced performance stellarator plasmas. Phys. Rev. Lett. 125 (7).CrossRefGoogle ScholarPubMed