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Nonlinear gyrokinetic PIC simulations in stellarators with the code EUTERPE

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

Published online by Cambridge University Press:  17 September 2020

E. Sánchez Open the ORCID record for E. Sánchez [Opens in a new window] ,
A. Mishchenko Open the ORCID record for A. Mishchenko [Opens in a new window] ,
J. M. García-Regaña Open the ORCID record for J. M. García-Regaña [Opens in a new window] ,
R. Kleiber Open the ORCID record for R. Kleiber [Opens in a new window] ,
A. Bottino Open the ORCID record for A. Bottino [Opens in a new window] ,
L. Villard Open the ORCID record for L. Villard [Opens in a new window]  and
the W7-X team
E. Sánchez*
Affiliation:
Laboratorio Nacional de Fusión-CIEMAT, Avda. Complutense 40, 28040Madrid, Spain
A. Mishchenko
Affiliation:
Max-Planck Insitut für Plasmaphysik, D-17491Greifswald, Germany
J. M. García-Regaña
Affiliation:
Laboratorio Nacional de Fusión-CIEMAT, Avda. Complutense 40, 28040Madrid, Spain
R. Kleiber
Affiliation:
Max-Planck Insitut für Plasmaphysik, D-17491Greifswald, Germany
A. Bottino
Affiliation:
Max-Planck Insitut für Plasmaphysik, D-85748Garching, Germany
L. Villard
Affiliation:
Ecole Polytechnique Fédérale de Lausanne, Swiss Plasma Center, CH-1015Lausanne, Switzerland
*
†Email address for correspondence: edi.sanchez@ciemat.es
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Abstract

In this work, the first nonlinear particle-in-cell simulations carried out in a stellarator with the global gyrokinetic code EUTERPE using adiabatic electrons and realistic plasma parameters are reported. Several studies are conducted with the aim of enabling reliable nonlinear simulations in stellarators with this code. First, EUTERPE is benchmarked against ORB5 in both linear and nonlinear settings in a tokamak configuration. Next, the use of noise control and stabilization tools, a Krook-type collision operator, markers’ weight smoothing and heating sources is investigated. It is studied in detail how these tools influence the linear growth rate of instabilities in both tokamak and stellarator geometries, and their influence on the linear zonal flow evolution in a stellarator. Then, it is studied how these tools allow improvement of the quality of the results in a set of nonlinear simulations of electrostatic turbulence in a stellarator configuration. Finally, these tools are applied to a W7-X magnetic configuration using experimental plasma parameters.

Keywords

fusion plasmaplasma instabilitiesplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 86 , Issue 5 , October 2020 , 855860501
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

Allfrey, S. & Hatzky, R. 2003 A revised $\delta f$ algorithm for nonlinear PIC simulation. Comput. Phys. Commun. 154 (98), 98–104.CrossRefGoogle Scholar
Angelino, P., Bottino, A., Hatzky, R., Jolliet, S., Sauter, O., Tran, T. M. & Villard, L. 2006 On the definition of a kinetic equilibrium in global gyrokinetic simulations. Phys. Plasmas 13, 052304.CrossRefGoogle Scholar
Aydemir, A. Y. 1994 A unified Monte Carlo interpretation of particle simulations and applications to non-neutral plasmas. Phys. Plasmas 1 (4), 822.CrossRefGoogle Scholar
Bozhenkov, S. A., Kazakov, Y., Ford, O., Beurskens, M. N. A., Alcuson, J. A., Alonso, J. A., Baldzuhn, J., Brandt, C., Brunner, K. J., Damm, H., et al. 2020 High-performance plasmas after pellet injections in wendelstein 7–X.CrossRefGoogle Scholar
Brunner, S., Valeo, E. & Krommes, J. A. 1999 Collisional delta-f scheme with evolving background for transport time scale simulations. Phys. Plasmas 6 (12), 4504–4521.CrossRefGoogle Scholar
Cole, M. D. J., Hager, R., Moritaka, T., Lazerson, S., Kleiber, R., Ku, S. & Chang, C. S. 2019 Comparative collisionless alpha particle confinement in stellarator reactors with the XGC gyrokinetic code. Phys. Plasmas 26 (3), 032506.CrossRefGoogle Scholar
Dimits, A. M., Bateman, G., Beer, M. A., Cohen, B. I., Dorland, W., Hammett, G. W., Kim, C., Kinsey, J. E., Kotschenreuther, M., Kritz, A. H., et al. 2000 Comparisons and physics basis of tokamak transport models and turbulence simulations. Phys. Plasmas 7 (3), 969.CrossRefGoogle Scholar
Donnel, P., Brunner, S., Gheller, C., Lanti, E., Ohana, N. & Villard, L. 2019 Multi-species collision operator for particle-in-cell gyrokinetic codes. In European Fusion Theory Conference 2019, Ghent, Belgium.Google 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, 074008.CrossRefGoogle Scholar
Grimm, R. C., Greene, J. M. & Johnson, J. L. 1976 Methods in Computational Physics. Academic, vol. 16.Google Scholar
Görler, T., Tronko, N., Hornsby, W. A., Bottino, A., Kleiber, R., Norscini, C., Grandgirard, V., Jenko, F. & Sonnendrücker, E. 2016 Intercode comparison of gyrokinetic global electromagnetic modes. Phys. Plasmas 23 (7), 072503.CrossRefGoogle Scholar
Hahm, T. S. 1988 Nonlinear gyrokinetic equations for tokamak microturbulence. Phys. Fluids 31 (9), 2673.CrossRefGoogle Scholar
Helander, P., Bird, T., Jenko, F., Kleiber, R., Plunk, G., Proll, J., Riemann, J. & Xanthopoulos, P. 2015 Advances in stellarator gyrokinetics. Nucl. Fusion 55 (5), 053030.CrossRefGoogle Scholar
Jolliet, S., Bottino, A., Angelino, P., Hatzky, R., Tran, T. M., Mcmillan, B. F., Sauter, O., Appert, K., Idomura, Y. & Villard, L. 2007 A global collisionless PIC code in magnetic coordinates. Comput. Phys. Commun. 177 (5), 409–425.CrossRefGoogle Scholar
Jost, G., Tran, T., Appert, K., Cooper, W. A. & Villard, L. 2000 Global linear gyrokinetic PIC simulations in 3D magnetic configurations. In Joint Varenna-Lausanne International Workshop Theory of Fusion Plasmas.Google Scholar
Jost, G., Tran, T. M., Cooper, W. A., Villard, L. & Appert, K. 2001 Global linear gyrokinetic simulations in quasi-symmetric configurations. Phys. Plasmas 8 (7), 3321.CrossRefGoogle Scholar
Kauffmann, K., Kleiber, R., Hatzky, R. & Borchardt, M. 2010 Global linear gyrokinetic simulations for LHD including collisions. J. Phys.: Conf. Ser. 260, 012014.Google Scholar
Kornilov, V., Kleiber, R., Hatzky, R., Villard, L. & Jost, G. 2004 Gyrokinetic global three-dimensional simulations of linear ion-temperature-gradient modes in wendelstein 7–X. Phys. Plasmas 11 (6), 3196.CrossRefGoogle Scholar
Krommes, J. A. 1999 Thermostatted delta f. Phys. Plasmas 6 (5), 1477–1494.CrossRefGoogle Scholar
Lanti, E., Ohana, N., Tronko, N., Hayward-Schneider, T., Bottino, A., McMillan, B. F., Mishchenko, A., Scheinberg, A., Biancalani, A., Angelino, P., Brunner, S., et al. 2019 ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry. arXiv:1905.01906 [physics].CrossRefGoogle Scholar
McMillan, B. F., Jolliet, S., Tran, T. M., Villard, L., Bottino, A. & Angelino, P. 2008 Long global gyrokinetic simulations: source terms and particle noise control. Phys. Plasmas 15 (5), 52308–52310.CrossRefGoogle Scholar
Mishchenko, A., Helander, P. & Könies, A. 2008 Collisionless dynamics of zonal flows in stellarator geometry. Phys. Plasmas 15 (7), 072309.CrossRefGoogle Scholar
Mishchenko, A. & Kleiber, R. 2012 Zonal flows in stellarators in an ambient radial electric field. Phys. Plasmas 19 (7), 072316.CrossRefGoogle Scholar
Monreal, P., Calvo, I., Bustos, A. & Kleiber, R. 2016 Residual zonal flow level in stellarators for arbitrary wavelengths. Plasma Phys. Control. Fusion 58 (1), 2–5.CrossRefGoogle Scholar
Monreal, P., Sánchez, E., Calvo, I., Bustos, A., Parra, F. I., Mishchenko, A., Könies, A. & Kleiber, R. 2017 Semianalytical calculation of the zonal-flow oscillation frequency in stellarators. Plasma Phys. Control. Fusion 59 (6), 065005.CrossRefGoogle Scholar
Sánchez, E., Calvo, I., Velasco, J. L., Medina, F., Alonso, A., Monreal, P., Kleiber, R., the TJ-II team 2018 Oscillatory relaxation of zonal flows in a multi-species stellarator plasma. Plasma Phys. Control. Fusion 60 (9), 094003.CrossRefGoogle Scholar
Sánchez, E. K., Kleiber, R., Hatzky, R., Soba, A., Sáez, X., Castejon, F. & Cela, J. M. 2010 Linear and nonlinear simulations using the EUTERPE gyrokinetic code. IEEE Trans. Plasma Sci. 38 (9 PART 1), 2119–2128.CrossRefGoogle Scholar
Slaby, C., Könies, A., Kleiber, R. & García-Regaña, J. M. 2018 Effects of collisions on the saturation dynamics of TAEs in tokamaks and stellarators. Nucl. Fusion 58, 082018.CrossRefGoogle Scholar
Sonnendrücker, E., Wacher, A., Hatzky, R. & Kleiber, R. 2015 A split control variate scheme for PIC simulations with collisions. J. Comput. Phys. 295, 402–419.CrossRefGoogle Scholar
Stechow, A. V., Grulke, O., Wegner, T., Proll, J. H., Alcuson, J., Smith, H., Xanthopoulos, P., Beidler, C., Beurskens, M., Bozhenkov, S., et al. 2020 Suppression of core turbulence by profile shaping in wendelstein 7–X. Submitted.Google Scholar
Sugama, H. & Watanabe, T. 2009 Turbulence-driven zonal flows in helical systems with radial electric fields. Phys. Plasmas 16 (5), 1–10.CrossRefGoogle Scholar
Tran, T. M., Appert, K., Fivaz, M., Jost, G., Vaclavik, J. & Villard, L. 1999 Global gyrokinetic simulation of ion-temperature-gradient-driven instabilities using particles. In Theory of Fusion Plasmas, Societa Italiana di Fisica.Google Scholar
Tronko, N., Bottino, A. & Sonnendrucker, E. 2016 Second order gyrokinetic theory for particle-in-cell codes. Phys. Plasmas 23, 082505.CrossRefGoogle Scholar
Vernay, T., Brunner, S., Villard, L., McMillan, B., Jolliet, S., Tran, T. M., Bottino, A. & Graves, J. P. 2010 Global collisional gyrokinetic simulations of ITG microturbulence starting from a neoclassical equilibrium. Phys. Plasmas 17, 122301.CrossRefGoogle Scholar
Villard, L., Allfrey, S. J., Bottino, A., Brunetti, M., Falchetto, G. L., Grandgirard, V., Hatzky, R., Nührenberg, J., Peeters, A. G.Sauter, O., et al. 2004 Full radius linear and nonlinear gyrokinetic simulations for tokamaks and stellarators: zonal flows, applied $\boldsymbol {E}\times \boldsymbol {b}$ flows, trapped electrons and finite beta. Nucl. Fusion 44, 172.CrossRefGoogle Scholar
Villard, L., McMillan, B. F., Lanti, E., Ohana, N., Bottino, A., Biancalani, A., Novikau, I., Brunner, S., Sauter, O., Tronko, N., et al. 2019 Global turbulence features across marginality and non-local pedestal-core interactions. Plasma Phys. Control. Fusion 61 (3), 034003.CrossRefGoogle Scholar
Xanthopoulos, P., Bozhenkov, S. A., Smith, H. M., Plunk, G. G., Helander, P., Beidler, C. D., Alcuison, J. A., Grulke, O., Stechov, A., Alonso, A., et al. 2020 Turbulence suppression in enhanced performance stellarator plasmas. Submitted.CrossRefGoogle Scholar