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A fast tool for ICRH + NBI modelling within the EU-IM framework

Published online by Cambridge University Press:  12 April 2021

Dirk Van Eester*
Affiliation:
LPP-ERM/KMS, EUROfusion Consortium Member - Trilateral Euregio Cluster, Brussels, Belgium
E.A. Lerche
Affiliation:
LPP-ERM/KMS, EUROfusion Consortium Member - Trilateral Euregio Cluster, Brussels, Belgium
Ph. Huynh
Affiliation:
CEA, IRFM, F-13108Saint-Paul-lez-Durance, France
T. Johnson
Affiliation:
Dept. of Fusion Plasma Physics, School of Electrical Engineering and Computer Science, KTH, Stockholm, Sweden
JET contributors
Affiliation:
See the author list of E. Joffrin et al., Nucl. Fusion59 (2019) 112021
EUROfusion-IM team
Affiliation:
See http://www.euro-fusionscipub.org/eu-im
*
Email address for correspondence: d.van.eester@fz-juelich.de

Abstract

Most if not all tokamak heating scenarios involve multiple ion populations being heated simultaneously. To allow the simulation of various aspects of physics dynamics determining the characteristics of operational scenarios in a flexible way, speedy yet sufficiently accurate models are needed, and they should be connected to each other via a ‘backbone’. Under the umbrella of EUROfusion's Integrated Modelling efforts, such a structure is provided. The present paper focuses on one physics aspect: auxiliary heating. After solving the wave equation or beam source equation, this requires solving a set of coupled Fokker–Planck equations for the various populations involved. The adopted modules – enabling accounting for the Coulomb collisional interaction of several non-Maxwellian (minority, majority and beam) populations – are discussed and a practical example of their use is provided: the JET ‘baseline’ scenario heating a minority of ${}^3\textrm {He}$ ions in a balanced D$+$T mix heated by D and T neutral beams.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Bilato, R., Brambilla, M., Maj, O., Horton, L. D., Maggi, C. F. & Stober, J. 2011 Simulations of combined neutral beam injection and ion cyclotron heating with the TORIC-SSFPQL package. Nucl. Fusion 51, 103034.CrossRefGoogle Scholar
Bosch, H.S. & Hale, G.M. 1992 Improved formulas for fusion cross-sections and thermal reactivities. Nucl. Fusion 32, 611.CrossRefGoogle Scholar
Brambilla, M. 1994 Quasi-linear ion distribution function during ion cyclotron heating in tokamaks. Nucl. Fusion 34, 1121.CrossRefGoogle Scholar
Brezinsek, S., et al. 2013 Fuel retention studies with the ITER-Like Wall in JET. Nucl. Fusion 53, 083023.CrossRefGoogle Scholar
Coster, D., Basiuk, V., Pereverzev, G., Kalupin, D., Zagorski, R., Stankiewicz, R., Huynh, P. & Imbeaux, F. 2010 The European transport solver. IEEE Trans. Plasma Sci. 38 (9), 2085.CrossRefGoogle Scholar
Falchetto, G. L., Coster, D., Coelho, R., Scott, B. D., Figini, L., Kalupin, D., Nardon, E., Nowak, S., Alves, L. L., Artaud, J.-F., et al. 2014 The European Integrated Tokamak Modelling (ITM) effort: achievements and first physics results. Nucl. Fusion 54, 043018.CrossRefGoogle Scholar
Falchetto, G. L., Airila, M. I., Alberto, M. A., Andersson, S. E., Aniel, T., Artaud, J.-F., Asunta, O., Atanasiu, C. V., Baelmans, M., Basiuk, V., et al. 2016 EUROfusion Integrated Modelling (EU-IM) capabilities and selected physics applications. In 26th IAEA Fusion Energy Conference.Google Scholar
Falchetto, G.L., et al. 2019 Multi-machine analysis of EU experiments using the EUROfusion Integrated Modelling (EU-IM) framework. In Proceedings of the 46th Conference on Plasma Physics.Google Scholar
Gaffey, J.D. 1976 Energetic ion distribution resulting from neutral beam injection in tokamaks. J. Plasma Phys. 16, 149.CrossRefGoogle Scholar
Garzotti, L., Challis, C., Dumont, R., Frigione, D., Graves, J., Lerche, E., Mailloux, J., Mantsinen, M., Rimini, F., Casson, F., et al. 2019 Scenario development for D-T operation at JET. Nucl. Fusion 59, 076037.CrossRefGoogle Scholar
Goniche, M., Lerche, E., Jacquet, P., Van Eester, D., Bobkov, V., Brezinsek, S., Colas, L., Czarnecka, A., Drewelow, P., Dumont, R., et al. 2014 Optimization of ICRH for tungsten control in JET H-mode plasmas. In Proceedings of the 41th EPS on Conference on Controlled Fusion and Plasma Physics, vol. 45.Google Scholar
Harvey, R. W., McCoy, M. G., Kerbel, G. D. & Chiu, S. C. 1986 ICRF fusion reactivity enhancement in tokamaks. Nucl. Fusion 26, 43.CrossRefGoogle Scholar
Harvey, R. W. & McCoy, M. G. 1992 The CQL3D code. In Proceedings of the IAEA TCM on Advances in Simulation and Modeling of Thermonuclear Plasmas, vol. 489.Google Scholar
Hawryluk, R. J. 1980 An empirical approach to tokamak transport. In Physics of Plasmas Close to Thermonuclear Conditions (ed. B. Coppi et al.), vol. 1, p. 19.Google Scholar
Hedin, J., Hellsten, T., Eriksson, L.-G. & Johnson, T. 2002 The influence of finite drift orbit width on ICRF heating in toroidal plasmas. Nucl. Fusion 42 (5), 527.CrossRefGoogle Scholar
Hirvijoki, E., Asunta, O., Koskela, T., Kurki-suonio, T., Miettunen, J., Sipilä, S., Snicker, A. & Äkäslompolo, A. 2014 ASCOT: solving the kinetic equation of minority particle species in tokamak plasmas. Comput. Phys. Commun. 185 (4), 1310.CrossRefGoogle Scholar
Huynh, P., Lerche, E. A., Van Eester, D., Bilato, R., Varje, J., Johnson, T., Sauter, O., Villard, L., Ferreira, J. & JET contributors and the EUROfusion-IM team 2019 Modeling ICRH and ICRH-NBI synergy in high power JET scenarios using European Transport Simulator (ETS). In Proceedings of the 23rd Topical Conference on RF Power in Plasmas.Google Scholar
Huynh, P., Lerche, E., Van Eester, D., Garcia, J., Johnson, T., Ferreira, J., Kirov, K., Yadykin, D., & Strand, P. 2020 European transport simulator modelling: the role of ICRH/NBI synergy in the extrapolation of high power JET D scenarios to D-T, submitted to Nuclear Fusion.Google Scholar
Imbeaux, F., Lister, J. B., Huysmans, G. T. A., Zwingmann, W., Airaj, M., Appel, L., Basiuk, V., Coster, D., Eriksson, L. G., Guillerminet, B., et al. 2010 A generic data structure for integrated modelling of tokamak physics and subsystems. Comput. Phys. Commun. 181, 987.CrossRefGoogle Scholar
Imbeaux, F., Pinches, S. D., Lister, J. B., Buravand, Y., Casper, T., Duval, B., Guillerminet, B., Hosokawa, M., Houlberg, W., Huynh, P., et al. 2015 Design and first applications of the ITER integrated modelling & analysis suite. Nucl. Fusion 55 (12), 123006.CrossRefGoogle Scholar
Jacquinot, J., Bhatnagar, V. P., Cordey, J. G., Horton, L. D., Start, D. F. H., Barnsley, R., Breger, P., Christiansen, J. P., Clement, S., Davies, S. J., et al. 1999 Overview of ITER physics deuterium-tritium experiments in JET. Nucl. Fusion 39, 235.CrossRefGoogle Scholar
Jaeger, E. F., Berry, L. A., Ahern, S. D., Barrett, R. F., Batchelor, D. B., Carter, M. D., D'azevedo, E. F., Moore, R. D., Harvey, R. W., Myra, J. R., et al. 2006 Self-consistent full-wave and Fokker-Planck calculations for ion cyclotron heating in non-Maxwellian plasmas. Phys. Plasmas 13, 056101.CrossRefGoogle Scholar
Joffrin, E., Sips, A. C. C., Artaud, J. F., Becoulet, A., Bertalot, L., Budny, R., Buratti, P., Belo, P., Challis, C. D., Crisanti, F., et al. 2005 The ‘hybrid’ scenario in JET: towards its validation for ITER. Nucl. Fusion 45, 626.CrossRefGoogle Scholar
Joffrin, E., Baruzzo, M., Beurskens, M., Bourdelle, C., Brezinsek, S., Bucalossi, J., Buratti, P., Calabro, G., Challis, C. D., Clever, M., et al. 2014 First scenario development with the JET new ITER-like wall. Nucl. Fusion 54, 013011.CrossRefGoogle Scholar
Joffrin, E., Abduallev, S., Abhangi, M., Abreu, P., Afanasev, V., Afzal, M., Aggarwal, K. M., Ahlgren, T., Aho-mantila, L., Aiba, N., et al. 2019 Overview of the JET preparation for deuterium-tritium operation with the ITER like-wall. Nucl. Fusion 59, 112021.CrossRefGoogle Scholar
Joly, J., Garcia, J., Imbeaux, F., Dumont, R., Schneider, M., Johnson, T. & Artaud, J.-F. 2019 Self-consistent modelling of heating synergy between NBI and ICRH in JET deuterium plasmas. Plasma Phys. Control. Fusion 61, 075017.CrossRefGoogle Scholar
Jucker, M. 2010 Self-consistent ICRH distribution functions and equilibria in magnetically confined plasmas. PhD thesis, CRPP/EPFL, Lausanne, Switzerland.Google Scholar
Kalupin, D., Basiuk, V., Coster, D., Huynh, P. H., Alves, L. L., Aniel, T. H., Artaud, J.-F., Bizarro, J. P. S., Boulbe, C., Coelho, R., et al. 2012 The European transport solver: an integrated approach for transport simulations in the plasma core. In 24th IAEA Fusion Energy Conference.Google Scholar
Karney, C.F. F 1986 Fokker-Planck and quasilinear codes. Comput. Phys. Rep. 4, 183.CrossRefGoogle Scholar
Keilhacker, M., Gibson, A., Gormezano, C., Lomas, P. J., Thomas, P. R., Watkins, M. L., Andrew, P., Balet, D., Borba, D., Challis, C. D., et al. 1999 High fusion performance from deuterium-tritium plasmas in JET. Nucl. Fusion 39, 209.CrossRefGoogle Scholar
Kim, H.-T., Sips, A. C. C., Romanelli, M., Challis, C. D., Rimini, F., Garzotti, L., Lerche, E., Buchanan, J., Yuan, X., Kaye, S. & JET contributors 2018 High fusion performance at high $T_i/T_e$ in JET-ILW baseline plasmas with high NBI heating power and low gas puffing. Nucl. Fusion 58, 036020.CrossRefGoogle Scholar
Lamalle, P.U. 1994 Nonlocal theoretical generalization and tridimensional study of the coupling of an ICRH antenna to a tokamak plasma. PhD Thesis, LPP-ERM/KMS Rep. 101, Université de Mons, Mons, Belgium.Google Scholar
Lee, J., Wright, J., Bertelli, N., Smithe, D., Valeo, E., Petrov, Y., Jaeger, E. F., Berry, L., Harvey, R. & Bonoli, P. 2017 A new quasilinear formulation for ICRF plasmas in a toroidal geometry. Eur. Phys. J. 157, 03028.Google Scholar
Lerche, E., Van Eester, D., Krasilnikov, A., Ongena, J., Lamalle, P. & JET-EFDA contributors 2009 Modelling of D majority ICRH at JET: impact of absorption at the Doppler-shifted resonance. Plasma Phys. Control. Fusion 51, 044006.CrossRefGoogle Scholar
Lerche, E., Goniche, M., Jacquet, P., Van Eester, D., Bobkov, V., Colas, L., Monakhov, I., Rimini, F., Czarnecka, A., Crombé, K., et al. 2015 ICRH for core impurity mitigation in JET-ILW. AIP. Conf. Proc. 1689, 030002.Google Scholar
Lerche, E., Lennholm, M., Carvalho, I. S., Dumortier, P., Durodie, F., Van Eester, D., Graves, J., Jacquet, P. H., Murari, A. & JET contributors 2017 Sawtooth pacing with on-axis ICRH modulation in JET-ILW. Nucl. Fusion 57, 036027.CrossRefGoogle Scholar
Litaudon, X., Abduallev, S., Abhangi, M., Abreu, P., Afzal, M., Aggarwal, K. M., Ahlgren, T., Ahn, J. H., Aho-mantila, L., Aiba, N., et al. 2017 Overview of the JET results in support to ITER. Nucl. Fusion 57, 102001.CrossRefGoogle Scholar
Petrov, Y.V. & Harvey, R.W. 2016 A fully-neoclassical finite-orbit-width version of the CQL3D Fokker-Planck code. Plasma Phys. Control. Fusion 58, 115001.CrossRefGoogle Scholar
Philipps, V., Mertens, P. H., Matthews, G. F., Maier, H. & JET-EFDA contributors 2010 Overview of the JET ITER-like Wall Project. Fusion Engng Des. 85, 1581.CrossRefGoogle Scholar
Pinches, S. D., Artaud, J. F., Casson, F. J., Corrigan, G., De Bock, M., Dubrov, M., Harying, D., Hollocombe, J., Hosokawa, M., Imbeaux, F., et al. 2018 Progress in the ITER integrated modelling programme and the ITER scenario database. In 27th IAEA Fusion Energy Conference - IAEA CN-258.Google Scholar
Pinches, S. D., Akers, R., Andre, R., Aniel, T., Bandyopadhyay, I., Basiuk, V., Belli, E. A., Bonnin, X., Candy, J., Chattopadhyay, A. K., et al. 2016 Progress in the ITER integrated modelling programme and the use and validation of IMAS within the ITER Members. In Proceedings of the 26th IAEA Fusion Energy Conference.Google Scholar
Romanelli, M. & EUROfusion WPCD team 2019 Status of code integration, verification and validation in EUROfusion. In 3rd IAEA Technical Meeting on Fusion Data Processing, Validation and Analysis.Google Scholar
Romanelli, M., et al. 2020 Predictive multi-physics integrated modelling of tokamaks scenarios using the ITER Integrated Modelling and Analysis System (IMAS) in support of ITER Exploitation. In 28th IAEA Fusion Energy Conference, postponed to 2021 (Covid).Google Scholar
Ronquist, E.M. & Patera, A.T. 1987 Spectral element multigrid. I. Formulation and numerical results. J. Sci. Comput. 2, 389.CrossRefGoogle Scholar
Schneider, M., Johnson, T., Dumont, R., Eriksson, J., Eriksson, L.-G., Giacomelli, L., Girardo, J. B., Hellsten, T., Khilkevitch, E., Kiptily, V. G., et al. 2016 Modelling third harmonic ion cyclotron acceleration of deuterium beams for JET fusion product studies experiments. Nucl. Fusion 56, 112022.CrossRefGoogle Scholar
Schneider, M., Artaud, J.-F., Bonoli, P., Kazakov, Y., Lamalle, P. H., Lerche, E., Van Eester, D. & Wright, J. 2017 ICRF heating schemes for the ITER non-active phase. Eur. Phys. J. 157, 03046.Google Scholar
Schneider, M., Polevoi, A. R., Kim, S. H., Loarte, A., Pinches, S. D., Artaud, J.-F., Militello-ASP, E., Beaumont, B., Bilato, R., Boilson, D., et al. 2019 Modelling one-third field operation in the ITER pre-fusion power operation phase. Nucl. Fusion 59, 126014.CrossRefGoogle Scholar
Schneider, M., Mitterauer, V., Pinches, S., Johnson, T., Arbina, I., Artaud, J.-F., Van Eester, D., Figini, L., Kojima, S., Lerche, E., et al. 2020 Simulation of heating and current drive sources for various scenarios of the ITER research plan. In 62nd Annual Meeting on the APS Division of Plasma Physics.Google Scholar
Start, D. F. H., Jacquinot, J., Bergeaud, V., Bhatnagar, V. P., Conroy, S. W., Cottrell, G. A., Clement, S., Ericsson, G., Eriksson, L.-G., Fasoli, A., et al. 1999 Bulk ion heating with ICRH in JET DT plasmas. Nucl. Fusion 39, 321.CrossRefGoogle Scholar
Stix, T. H. 1992 Waves in Plasmas. AIP.Google Scholar
Strand, P., Coelho, R., Coster, D., Eriksson, L.-G., Imbeaux, F., Guillerminet, B., Contributors to the EFDA ITM-TF Work Programme & the EUFORIA Project 2010 Simulation and high performance computing - building a predictive capability for fusion. Fusion Engng Des. 85, 383.CrossRefGoogle Scholar
Strand, P., See, Y., Ferreira, J., Figueiredo, A., Coelho, R., Lerche, E.,Van Eester, D., Moradi, S., JoHnson, T., Tholerus, E., et al. 2018 Towards a predictive modelling capacity for DT plasmas: European Transport Simulator (ETS) verification and validation. IAEA CN-258, Gandhinagar, India, TH/P6-14.Google Scholar
Van Eester, D. 2001 Evaluating the efficiency of radiofrequency heating in tokamaks: the impact of orbital topology and poloidal inhomogeneity. J. Plasma Phys. 65, 407.CrossRefGoogle Scholar
Van Eester, D. & Lerche, E.A. 2011 Simple 1D Fokker-Planck modelling of ion cyclotron resonance frequency heating at arbitrary cyclotron harmonics accounting for Coulomb relaxation on non-Maxwellian populations. Plasma Phys. Control. Fusion 53, 092001.CrossRefGoogle Scholar
Van Eester, D., Crombé, K., Lauwens, B., Kazakov, Y., Vergote, M. & van Schoor, M. 2016 a A new tool for modelling ion cyclotron resonance heating wave propagation and damping in non-axisymmetrical magnetic confinement fusion machines. In Proceedings of the 43rd EPS Conference on Plasma Physics.Google Scholar
Van Eester, D., Lerche, E., Kazakov, Y., Jacquet, P., Bobkov, V., Crombé, K., Czarnecka, A., Dumont, R., Eriksson, J., Giacomelli, L., et al. 2016 b Recent ion cyclotron resonance heating experiments in JET in preparation of a DT campaign. In 26th IAEA Fusion Energy Conference.Google Scholar
Voitsekhovitch, I., Hatzky, R., Coster, D., Imbeaux, F., Mc Donald, D. C., Fehér, T. B., Kang, K. S., Leggate, H., Martone, M., Mochalskyy, S., et al. 2018 Recent EUROfusion achievements in support of computationally demanding multiscale fusion physics simulations and integrated modeling. Fusion Sci. Technol. 74, 186.CrossRefGoogle Scholar