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Phd Thesis) Highlights the Crucial Contribution of J.D ÉCOLE DOCTORALE DE SCIENCES FONDAMENTALES ET APPLIQUÉES LABORATOIRE JEAN-ALEXANDRE DIEUDONNÉ THÈSE DE DOCTORAT Présentée en vue de l’obtention du grade de Docteur en Physique d’Université Côte d’Azur par David Métivier MODÈLES CINÉTIQUES, DE KURAMOTO À VLASOV : BIFURCATIONS ET ANALYSE EXPÉRIMENTALE D’UN PIÈGE MAGNÉTO-OPTIQUE KINETIC MODELS, FROM KURAMOTO TO VLASOV: BIFURCATIONS AND EXPERIMENTAL ANALYSIS OF A MAGNETO-OPTICAL TRAP Dirigée par Julien Barré Soutenue le 22 Septembre 2017 Devant le jury composé de : Bastien Fernandez DR CNRS, Laboratoire de Probabilités et Modèles Rapporteur Philip J. Morrison Professeur, The University of Texas at Austin Rapporteur Médéric Argentina Professeur, Université Côte d’Azur Examinateur Caroline Champenois CR CNRS, Laboratoire PIIM Examinatrice Alessandro Torcini Professeur, Université de Cergy-Pontoise Examinateur Pascal Viot Professeur, Université Pierre et Marie Curie Examinateur Julien Barré Maitre de Conférence HDR, Université d’Orléans Directeur Pour mon Papa REMERCIEMENTS Ici commence la déferlante de mercis, néanmoins tout est authentique, sans ces gens ou moments les choses auraient été différentes. C’est avec plein de joie et de sincérité que je remercie Julien qui depuis le début de mon stage de M2 n’a eu de cesse de montrer patience et enthousiasme et ce jusqu’à l’heure où j’écris ces lignes. Ses conseils avisés et francs m’ont permis d’en arriver là où je suis (c’est-à-dire en fin de thèse). Son encadrement a été super, sa réactivité à toute heure a permis d’effacer la distance. Je crois pouvoir dire qu’il m’a transmis sa passion pour le sujet. Je pense qu’il aurait été difficile d’en trouver un qui me convienne mieux. Je dois au passage remercier Thierry Dauxois qui m’a conseillé d’aller à Nice (c’est aussi lui qui m’avait conseillé mon inoubliable stage de M1) après que je lui ai simplement dit « système autogravitant » (parce que je trouvais que ça sonnait bien). Donc Julien, merci et encore merci ! Je dois évidement saluer tout le personnel administratif du laboratoire Dieudonné en particu- lier Jean-Marc et Roland qui m’ont sorti de toutes mes galères numériques ; ainsi que Jean-Louis et les secrétaires qui m’ont aidé à tout moments Angélique, Clara, Julia. J’ai eu la chance de collaborer avec Guillaume et Robin de l’INLN, je les remercie pour leur patience et pour avoir accepté cette collaboration. Thanks to Yoshi for his comments and ideas always relevant ! Many thanks to Michael always ready to help and for organizing the amazing Trieste conference. I am thankful to T. Rocha for providing his excellent GPU Vlasov-HMF solver. I would like to thank sincerely every member of my Jury for taking the time to read my work and for their precious advices and suggestions. Merci aussi à Bruno pour m’avoir initié à CUDA sans qui tout aurait été plus long ! Merci à Shamik pour m’avoir accueilli à Dresde et ensuite m’avoir suggéré de regarder Kuramoto avec retard ! Bien sûr je remercie tous les occupants du bureau 809 : un merci à Bienvenu et Jacques pour leurs nombreuses histoires ; merci à Samira et Ludovick pour m’avoir raconté la saison 3 de Watatatow et d’avoir su travailler la carotte. Merci à Luis pour avoir été toujours jovial et prêt à aider, pour son manoir et tous ses précieux tricks. Merci aussi à Simon qui m’a initié à Python et qui m’a aidé à faire les jolies vidéos ! Merci à Marouane pour sa disponibilité. Merci à Jason, Alyson, Seann, Tara pour avoir été derrière moi tout au long de ces trois ans. Merci à Pavel pour m’avoir bien facilité la tâche d’enseignement. Merci à Alain Olivetti qui v m’avait judicieusement conseillé Julien et à qui j’ai pris ce modèle de thèse ma foi fort bien fait. Merci à David C. d’avoir pris le temps de réfléchir à mes petits problèmes de maths ! Je remercie aussi André pour son éternelle curiosité et son enthousiasme. Merci à tous les autres doctorants du laboratoire qui ont vraiment contribué à une ambiance géniale ; Charles pour les discussions et m’avoir aidé à trouver mon homonyme ! Merci à Rinel pour les discussions à pas d’heure. Merci aussi à Marcella (pour ton aide), Julie, Arthur, Victor, Bjorn, Giula et tous les autres, partis ou présents, au GDR goûter ! Merci aussi à Zhiyan. Merci à Reine de m’avoir aidé à répéter MT180s. Je salue aussi les doctorants de l’INLN. Merci à Fernando et tous les Patitos d’avoir toujours été au laboratoire et de m’avoir écouté et fait répéter. Merci à Fernanda pour les bons moments des conférences et pour m’avoir aidé à coder en CUDA ! Merci à tous les Ziggles pour tous ces samedi matin à Vence! Merci à tous les PhDisc et autres Lyonnais ainsi qu’à la Horde, Grimaud, Paul, Clément, Fred, Timéloan, Guilhem, Hugo, Félix, Victor, Bertrand, La machine, Loïc, Madi, Carpi, Gilles. Le tournoi c’est vraiment une pratique très « marrante » ! Merci aux Counta et bons amis niçois qui m’ont bien fait rigoler : Leslie, Karim, Aude, Mariannick, David R., Jo, Emma, Céline, Steven, Mathilde, Yogi Sarah, LdP,...! Merci à Loïc (le meilleur colocorrecteur) et Grimaud de m’avoir spammé. Merci à Félix d’avoir fait voyager le Ter-Ter et Ludo pour m’avoir dit un jour : « mille » et merci à tous les autres parisiens pour les brèves retrouvailles. Merci à Michael et George de m’avoir inspiré. Je remercie ma maman, parce que quand même ! Mon Frère, mon Papi, ma Mami (de m’avoir poussé à finir le plus vite possible) et toute ma famille pour leur « énergie » inspirante ! Leslie, ma fiancée d’aujourd’hui et ma femme de demain, je te dis un grand merci de me supporter depuis le début et vu comme c’est parti jusqu’à la fin. Université Côte d’Azur vi CONTENTS CONTENTS .................................................................. VII FOREWORD .................................................................. 15 INTRODUCTION .............................................................. 17 PART ONE EXPERIMENTAL COLLABORATION:DEBYE LENGTH IN MAGNETO-OPTICAL-TRAPS? CHAPTER IF ROM MAGNETO-OPTICAL-TRAPS TO PLASMA 1S TANDARD MODEL FOR MOT................................................. 28 1.1 The trapping .......................................................... 28 1.1.a Doppler effect ................................................ 30 1.1.b Zeeman effect ................................................. 30 1.1.c Radiation pressure ............................................. 31 1.2 Diffusion.............................................................34 1.3 Shadow effect: an effective attractive force between atoms .................... 35 1.4 Multiple scattering: an effective Coulomb force between atoms ................ 36 1.5 Other quantum effects .................................................. 37 2S UM UP AND QUESTIONS ..................................................... 38 2.1 Sum-Up of the model .................................................. 38 2.2 Experimental confirmation? ............................................. 38 vii CONTENTS 3N ON NEUTRAL PLASMA ...................................................... 39 3.1 Presentation of NNP model .............................................. 39 3.1.a Standard NNP model ........................................... 39 3.1.b NNP model for the MOT.........................................40 3.1.c Debye length ................................................. 42 3.1.d Plasma parameter ............................................. 43 3.2 Some numerical values for experimental MOT .............................. 44 CHAPTER IIT HEORETICAL AND EXPERIMENTAL OBSERVABLES 1D ENSITY ..................................................................... 47 2P AIR DISTRIBUTION FUNCTION ................................................ 48 3N UMERICAL EXAMPLES ...................................................... 49 3.1 Numerical details ...................................................... 49 3.2 Numerics ............................................................ 50 4S TRUCTURE FACTOR .......................................................... 52 5C OMPARISON WITHOUT CORRELATIONS ....................................... 53 5.1 Random arrangement...................................................54 5.2 Turning off the trap and interactions.......................................54 6D IFFRACTION AND STRUCTURE FACTOR: LINK WITH EXPERIMENTS ............ 55 CHAPTER IIIL OOKING FOR DEBYE LENGTH AND OTHER PLASMA PHYSICS EFFECTS 1D IRECT PROBING ............................................................. 57 1.1 With a Gaussian probing beam ........................................... 57 1.2 Comparison with experiments............................................58 2R ESPONSE TO AN EXTERNAL POTENTIAL ...................................... 59 2.1 Experiment principle ................................................... 59 2.2 Fluorescence-like density profile ......................................... 60 2.2.a The Response function .......................................... 60 2.2.b Numerical Simulations .......................................... 60 2.2.c Experiments .................................................. 62 2.3 Diffraction ........................................................... 62 2.3.a Expression of the ~k vector ....................................... 62 2.3.b A simple example: existence of two diffraction regimes Raman-Nath/Bragg...64 2.3.c Diffraction discs ............................................... 65 2.3.d Comparison theory simulations ................................... 66 Université Côte d’Azur viii CONTENTS 2.3.e Comparison theory/experiments ..................................
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