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Dynamics of Runaway Electrons in Tokamak Plasmas Emelie Nilsson

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Dynamics of Runaway Electrons in Tokamak Plasmas Emelie Nilsson Dynamics of runaway electrons in tokamak plasmas Emelie Nilsson To cite this version: Emelie Nilsson. Dynamics of runaway electrons in tokamak plasmas. Physics [physics]. CEA, 2015. English. tel-01212017 HAL Id: tel-01212017 https://pastel.archives-ouvertes.fr/tel-01212017 Submitted on 5 Oct 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Association Euratom-CEA Ecole´ Polytechnique Institut de Recherche sur la Fusion par confinement Magn´etique Graduate School CEA/DSM/IRFM/SCCP/GSEM 91128 Palaiseau F-13118 Saint-Paul-lez-Durance France France Dynamics of runaway electrons in tokamak plasmas Th`esede doctorat pr´esent´eedevant la Graduate School de l’Ecole´ Polytechnique par Emelie Nilsson pour obtenir le grade de Docteur de l’Ecole´ Polytechnique Sp´ecialit´e:Physique des plasmas soutenue le 9 September 2015 devant le jury compos´ede Prof. Nathaniel Fisch Princeton Plasma Physics Laboratory Pr´esident du Jury Prof. Yves Peysson CEA, IRFM Directeur de Th`ese Prof. Lars-G¨oranEriksson European Commission Rapporteur Dr. Gergo Pokol Budapest University of Technology Rapporteur Prof. Jean-Marcel Rax Ecole´ Polytechnique de Paris Examinater Dr. Joan Decker Ecole´ Polytechnique de Lausanne Examinateur Ann´ee2015 Graduate School de l’Ecole Polytechnique Abstract Une des propri´et´escl´esdes plasma est la d´ecroissancede la force de friction resultant des interactions Coulombiennes avec la vitesse des ´electrons.Ainsi, en pr´esenced’un champ ´electrique d´epassant un certain seuil critique, les ´electronsayant une vitesse suffisamment ´elev´eesont susceptibles d’ˆetre acc´el´er´escontinuement. Ces ´electrons d´enomm´es“d´ecoupl´es” peuvent atteindre des ´energiesconsid´erables,de l’orde de plusieurs MeV, et de ce fait sont susceptibles de causer des d´egˆatsimportants dans ITER, le prochain tokamak de grande taille. La population d’´electronsd´ecoupl´esest susceptible d’ˆetremultipli´eepar les collisions `alarge angle de d´eflection,processus au cours duquel un ´electrond´ecoupl´ede grande ´energie peut transf`erer une fraction significative de son ´energiecin´etique`aun ´electronpresque `a l’arrˆet,tout en restant d´ecoupl´e.La compr´ehension du processus de formation des ´electrons d´ecoupl´es est essentielle `ala r´eductionde cette population de particules. Dans ce contexte, la mod´elisationde la dynamique des ´electronsd´ecoupl´esis ´etudi´ee avec le code cin´etiqueLUKE r´esolvant l’´equation3-D relativiste et lin´earis´eede Fokker- Planck, moyenn´eesur les orbites, avecun effort particulier concernant les collisions `alarge angle de d´eflectionde la part des ´electronsrapides sur les ´electronsthermiques, ce qui peut conduire `aune avalanche d’´electrons relativistes. La th´eoriede ce m´ecanismeest d’abord d´ecritedans la cadre d’un d´eveloppement original, et l’op´erateurassoci´eest implant´edans le code ci´entique LUKE. Les d´ependances param´etriquesdu taux de croissance des ´el´ectrons d´ecoupl´es sont ´etudi´ees, en fonction de l’intensit´edu champ ´electrique, de la densit´e, de la temp´eraturedu plasma ainsi que de sa configuration. L’importance relative entre la g´en´erationprimaire et secondaire des ´electronsd´ecoupl´es,cette derni`erer´esultant du ph´enom`ened”avalanche est ´egalement analys´ee.On montre que les avalanches d’´electrons d´ecoupl´es peuvent ˆetreimportantes mˆemepour des r´egimesnon-disprutifs, et que cet effet peut devenir dominant dans la mise en place du faisceau d’´electronsrelativistes. En raison de leur forte magn´etisation,les ´electronsacqu´erant de l’´energie grˆaceau processus de diffusion `alarge angle restent en g´en´eralpi´eg´es. Leur population est donc r´eduitehors de l’axe m´egntique. Cet effet entraine une accumulation ´electronsd´ecoupl´es dans la r´egioncentrale du plasma. La dynamique de ces ´electronspieg´esdans le cadre de la formation d’une population d’´electronsd´ecoupl´esest ´etudi´ee. Enfin, la formation des ´electronsd´ecoupl´esdans des d´echarges en r´egime Ohmique r´ealis´eesdans les tokamaks Tore Supra et COMPASS est mod´elis´eavec le code LUKE, `a partir des param`etresglobaux du plasma comme le champ ´electrique ou l’´equilibreMHD toro¨ıdald´etermin´epar le code METIS. Les caract´eristiquesde la fonction de distribution en vitesse sont donn´ees,de mˆemeque la comparaison quantitative avec le rayonnement de freinage non thermique pour le tokamak Tore Supra. i Abstract One of the key features of a plasma is that the collisional friction resulting from Coulomb interactions decreases with the electron velocity. Therefore, in the presence of a parallel electric field larger than a critical value, electrons with sufficient velocity will be continuously accelerated. These so-called runaway electrons may reach energies on the order of several MeVs and cause serious damage to plasma facing components in ITER - the next large-scale tokamak. The runaway population may be multiplied through knock- on collisions, where an existing runaway electron can transfer a significant fraction of its energy to a secondary electron nearly at rest, while remaining in the runaway region. Un- derstanding of the runaway electron formation processes is crucial in order to develop ways to mitigate them. In this context, modelling of runaway electron dynamics is performed using the 3-D linearized relativistic bounce-averaged electron Fokker-Planck solver LUKE, with a partic- ular emphasis on knock-on collisions of fast electrons on thermal ones, which can lead to an avalanche of relativistic electrons. The theory of bounce-averaged knock-on collisions is derived, and the corresponding operator is implemented in the kinetic solver LUKE. The dependencies of the runaway electron growth rate on the electric field strength, density, temperature and magnetic configuration, is investigated, in order to identify the relative importance between primary and secondary runaway generation, the latter resulting from the avalanche process. It is shown that avalanches of runaway electrons can be important even in non-disruptive regimes and this effect may become dominant in the build-up of the highly relativistic electron tail. Owing to their high magnetization, most of the knock-on electrons are born into the magnetic trapping domain in momentum space, which leads to a reduction of the runaway population off the magnetic axis. This accumulates the runaway electrons near the mag- netic axis. The dynamics of the trapped electrons in the framework of runaway electron generation is investigated. Finally, the runaway electron formation in Ohmic discharges performed in the Tore Supra and COMPASS tokamaks is modelled with the LUKE code, using global plasma parameters such as parallel electric field and the toroidal MHD equilibrium calculated with the fast integrated modelling code, METIS. Details of the fast electron velocity distribution function are provided as well as quantitative comparison with non-thermal bremsstrahlung for the Tore Supra tokamak. iii Acknowledgements I would like to thank my supervisor Yves Peysson for his invaluable guidance and encouragement through my thesis work. Thank you for your inspiring creative mind and skills in plasma physics as well as on the glacier. I am also grateful for helping me tune my slightly ancient laptop into a powerful machine worthy of heavy calculations. I am very thankful for the support of Joan Decker, who supervised both during my master thesis and in the first half of my thesis work, before he left CEA to work in Switzerland. Thank you for your creativity. It is thanks to you that I started this thesis. My deepest gratitude to the IRFM (Institut de Recherche sur la Fusion par confinement Magnetique) institute for the unique opportunity to work with world leading scientists on cutting edge nuclear fusion research. I thank the Tore Supra team for the fruitful work and making me feel at home in France. A special thank you to Annika Ekedahl who initiated the collaboration between Chalmers and CEA and supervised me through my master’s and licentiate thesis. I also want to thank Frederic Imbeaux, Xavier Litaudon, Jean-Francois Artaud, Francois Saint-Laurent, Marc Goniche, Julien Hillairet, Tuong Hoang, Gerardo Giruzzi and Didier Mazon. Thanks for all the interesting discussions and for making research such a pleasure. I would like to thank T¨undeF¨ul¨op,who introduced me to fusion physics and with her passion and hard work is a great inspiration. Thank you for keeping my motivation up and for always believing in me. My ’second family’ at Chalmers has been a great support and inspiration to me from the start of the master’s thesis throughout the PhD thesis. I thank CEA for letting me broaden my horizons through various missions abroad. I am very grateful to our collaborators around the world; Nathaniel Fisch, Robert Granetz, Eric Hollmann, Lars-G¨oranEriksson, Gergo Pokol, Vasily Kiptily and Rudi Koslowski. Thanks to Jan ’Honsa’ Mlynar, Jakub ’Kuba’ Urban, Richard Paprok, Milos Vlainic, Vladimir Wainzetti, Ondrej Ficker, Martin Imr´ısekand Nikita Varavin at IPP Prague for your warm welcome to the COMPASS experimental campaign on runaway electrons. My participation in experiments in this creative environment has been one of the most memorable experiences during my thesis. Thanks to colleagues and friends who inspire me in work as well as in life: Claudia Norscini, Farah Hariri, Albert Moll´en,Adam Stahl, Geri Papp, Istvan Pusztai, Jakob Ryd´en,Ola Em- breus, Robert Nyqvist, Sarah Newton, Jonathan Citrin, Billal Chouli, Maxim Irishkin, Hugo Arnichand, Alberto Gallo, Alexandre Fil and Jorge Morales. For the fun times, summer schools, conferences and trips we shared.
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