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Nonlinear Features of Instabilities, Turbulence and Transport in Hot Plasmas Maxime Lesur

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Nonlinear Features of Instabilities, Turbulence and Transport in Hot Plasmas Maxime Lesur Nonlinear features of instabilities, turbulence and transport in hot plasmas Maxime Lesur To cite this version: Maxime Lesur. Nonlinear features of instabilities, turbulence and transport in hot plasmas. Plasma Physics [physics.plasm-ph]. Université de Lorraine, 2020. tel-02882428v2 HAL Id: tel-02882428 https://hal.archives-ouvertes.fr/tel-02882428v2 Submitted on 5 Jul 2020 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. Th`esed'Habilitation `aDiriger des Recherches de l'Universit´ede Lorraine Sp´ecialit´e: Physique des Plasmas Nonlinear features of instabilities, turbulence and transport in hot plasmas par Maxime Lesur Soutenue le 25 mai 2020 devant un jury compos´ede L. Vermare Charg´ee de Recherche HDR, Rapportrice Laboratoire de Physique des Plasmas, Palaiseau P. Lauber Privatdozent HDR, Rapporteur Max-Planck-Institut f¨urPlasmaphysik, Garching bei M¨unchen L. Villard Professeur Rapporteur Ecole Polytechnique F´ed´eralede Lausanne, Lausanne X. Garbet Directeur de Recherche, Examinateur Commissariat `al'Energie Atomique, Cadarache H. Wilson Professeur, Examinateur University of York, Heslington York E. Gravier Professeur, Examinateur Universit´ede Lorraine, Nancy Acknowledgements I am sincerely grateful to the three referees, Laure Velmare, Philipp Lauber, and Laurent Villard, who took the time to read this manuscript carefully and write detailed reports. I thank also the other members of the jury, Xavier Garbet, Etienne Gravier, and Howard Wilson. The jury provided insightful questions and comments, which will help me adjust the directions of future research. During these 10 years of research since obtaining my PhD, I have been given constant freedom in pursuing the fundamental topics I was most interested in, but also many oppor- tunities to connect them with recent experimental observations. I am extremely grateful for the trust and support of my mentors, in chronological order, doctor Yasuhiro Idomura, doc- tor Xavier Garbet, professor Patrick H. Diamond, the late professor Sanae-I. Itoh, professor Kimitaka Itoh, and professor Etienne Gravier, who also sponsored my HDR candidacy. I also thank the institutions, hierarchies and funding bodies of the Japan Atomic Energy Agency (JAEA) in Tokyo, the Institute for Magnetic Fusion Research (IRFM) in Cadarache, the World-Class-Institute (WCI) Center for Fusion Theory in Daejeon, the Research Institute for Applied Mechanics (RIAM - Kyushu U.) in Fukuoka, and the Institut Jean Lamour (IJL) in Nancy. Parts of the work presented in this manuscript were performed by master and PhD students. Let me thank my two PhD students : Julien M´edinaand Kyungtak Lim ; the students whose M2 internship I supervised : Sebastian Hendricks, Djerroud Chabha, and Nicolas Berkenheier ; and the students whose M1 internship I supervised : Chen Xiang, Soni Kunal, Francis Devasagayam, Hanne Thienpondt, and Alejandro Guillevic. I am also grateful to my co-authors, colleagues, and people I met in conferences or semi- nars, who contributed to the present work. Special thanks to the organizers and participants of the Festival de Th´eorie,where I learn so much every two years. Warmest thoughts to my family, Ula, Neo, Tamaki, and my friends, for their unfaltering support. The various parts of this work were supported throughout the years by the JAEA Fo- reign Researcher Inviting Program and the MEXT under Grant No. 22866086 ; by the Eu- ropean Communities under the contract of Association between EURATOM and CEA ; by the WCI Program of the NRF of Korea funded by the Ministry of Education, Science and Technology of Korea (WCI 2009-001) ; by CMTFO via U.S. DoE Grant No. DE-FG02- 04ER54738 ; by the JSPS, Japan (16K18335, 16H02442, 15K18305, 15H02155, 21224014, 23244113, 25887041, and 15H02335), by the collaboration programs of the RIAM of Kyushu University and of NIFS (NIFS14KNST072, NIFS15KNST089) and Asada Science Founda- tion ; by the the EUROfusion Consortium via the French Research Federation for Magnetic Fusion Studies (FR-FCM) ; by the Euratom research and training programme 2014-2018 under Grant Agreement No. 633053 for the project WP17-ENRCEA-02 ; and by the Agence Nationale de la Recherche under project GRANUL (ANR-19-CE30-0005). The views and opinions expressed herein do not necessarily reflect those of the European Commission. Computations were performed on Altix3700 and BX900 systems at JAEA ; on Norma system at CEA ; on the Kraken system at NFRI ; on the Plasma Simulator at NIFS ; on the XT and SX systems at Kyushu University ; on the HPC resources of IDRIS (ADA and Jean-Zay) under Allocation No. 2017-27862 made by GENCI ; on Asterix and EXPLOR sys- tems at Lorraine University under Project No. 2017M4XXX0251 ; and on CINECA Marconi supercomputer within the framework of the GSNTIT and GSNTITS projects. Abstract Resonant interactions between waves and particles often play major roles in collisionless, or high-temperature plasmas. In this manuscript, I focus on a kinetic nonlinear effect, due to these resonances : the self-trapping of charged particles by their own electrostatic potential. This self-trapping leads to a formation of structures resembling vortices, in the phase-space of the particle distribution function (real space + velocity space). Based on the dynamics in phase-space, we clarify the mechanisms of phenomenon that can seem counter-intuitive from the point-of-view of an observer in real-space. This manuscript focuses on three types of waves : waves driven by supra-thermal particles in fusion plasmas, ion-acoustic waves in space plasmas, and drift-waves driven by trapped particles in tokamaks. I describe the impact of phase-space structures on stability and the nonlinear evolution of waves, as well as turbulence properties, particle transport, anomalous resistivity, and turbulent heating associated with these waves. I propose several experimental applications of phase-space structures as diagnostic and mean of control. Finally, I describe the outline of a long-term research project, which aims at developing a turbulence theory in a regime dominated by phase-space structures. R´esum´e Les plasmas chauds sont souvent le lieu d'importantes interactions r´esonantes entre ondes et particules. Dans ce manuscrit, je me focalise sur un effet cin´etiquenon-lin´eaire,li´e`a ces r´esonances: l'auto-pi´egeagede particules charg´eespar leur propre potentiel ´electrique. Cet auto-pi´egeageconduit `ala formation de structures semblables `ades vortex, mais dans l'espace des phases de la fonction de distribution des particules (espace r´eel+ espace des vitesses). En ´etudiant la dynamique des particules dans l'espace des phases, je propose de clarifier les m´ecanismesde ph´enom`enesqui semblent contre-intuitifs du point de vue d'un observateur de l'espace r´eel.Je me concentre sur trois types d'ondes : les ondes engendr´ees par des particules supra-thermiques dans les plasmas de fusion, les ondes acoustiques ioniques dans les plasmas astrophysiques, et les ondes de d´erives dues aux particules pi´eg´eesdans les tokamaks. Je d´ecriel'impact des structures de l'espace des phases sur la stabilit´eet l'´evolution non-lin´eairedes ondes, ainsi que sur les propri´et´esde la turbulence, le transport de particules, la r´esistivit´eanormale, et le chauffage turbulent associ´es`aces ondes. Je propose ´egalement quelques applications exp´erimentales des structures de l'espace des phases comme diagnostic et moyen de contr^ole. Enfin, je d´ecrisles grandes lignes d'un projet de recherche sur le plus long terme qui vise `ad´evelopper une th´eoriede la turbulence dans un r´egime domin´epar les structures de l'espace des phases. Table des mati`eres 1 Introduction 1 1.1 Hot plasmas . .1 1.1.1 Plasmas : ubiquitous, electromagnetic fluids . .1 1.1.2 Hot plasmas, and the Vlasov equation . .1 1.2 Turbulence . .2 1.2.1 Turbulence in hot plasmas . .2 1.2.2 Socio-economic impacts of a successful theory of hot plasma turbulence3 1.2.3 Conventional turbulence theories . .3 1.3 Phase-space structures . .4 1.3.1 Phase-space holes . .4 1.3.2 Kubo number and granulation theory . .5 1.4 Magnetic confinement nuclear fusion . .5 1.4.1 Towards a clean, safe, and efficient energy source . .5 1.4.2 Energetic particles in MCF . .6 1.4.3 Turbulence in MCF . .6 1.5 Outline of this manuscript . .7 2 Vlasov plasmas 8 2.1 Foundations of the Vlasov equation . .8 2.2 From linear to nonlinear theories . .9 2.2.1 Equilibrium . .9 2.2.2 Linear theory . 10 2.2.3 Nonlinear flux . 10 2.2.4 Quasi-linear theory . 11 2.2.5 Nonlinear theories . 13 2.3 Invariants . 15 2.3.1 Entropy . 15 2.3.2 Phasestrophy . 16 2.3.3 The Energy-Phasestrophy relation . 16 3 Subcritical instabilities 18 3.1 Introduction . 18 3.2 Concepts of subcritical instability . 19 3.3 Subcritical instabilities in neutral fluids . 22 3.3.1 Experimental measurement of subcritical bifurcation . 23 3.3.2 Physical mechanism of subcritical growth in neutral fluids . 24 3.4 Subcritical instabilities in plasmas . 25 3.4.1 Fluid-like subcritical instabilities in plasmas . 26 3.4.2 Kinetic subcritical instabilities . 26 3.4.3 Hybrid Fluid-Kinetic subcritical instabilities . 30 3.5 Conclusions . 30 ii 4 Energetic-particle-driven modes in 1D 31 4.1 From 3D to 1D . 33 4.1.1 Reduction of the perturbed Hamiltonian . 33 4.1.2 Reduction of the collision operator . 34 4.1.3 Reduction of the background damping mechanisms .
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