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Fluid Modeling of Transport and Instabilities in Magnetized Low-Temperature Plasma Sources Sarah Sadouni

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Fluid Modeling of Transport and Instabilities in Magnetized Low-Temperature Plasma Sources Sarah Sadouni Fluid modeling of transport and instabilities in magnetized low-temperature plasma sources Sarah Sadouni To cite this version: Sarah Sadouni. Fluid modeling of transport and instabilities in magnetized low-temperature plasma sources. Physics [physics]. Université Paul Sabatier - Toulouse III, 2020. English. NNT : 2020TOU30014. tel-02978476 HAL Id: tel-02978476 https://tel.archives-ouvertes.fr/tel-02978476 Submitted on 26 Oct 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. THÈSE En vue de l’obtention du DOCTORAT DE L’UNIVERSITÉ DE TOULOUSE Délivré par l'Université Toulouse 3 - Paul Sabatier Présentée et soutenue par Sarah SADOUNI Le 27 février 2020 Modélisation fluide du transport et des instabilités dans une source plasma froid magnétisé Ecole doctorale : GEET - Génie Electrique Electronique et Télécommunications : du système au nanosystème Spécialité : Ingénierie des Plasmas Unité de recherche : LAPLACE - Laboratoire PLAsma et Conversion d'Énergie - CNRS-UPS-INPT Thèse dirigée par Gerjan HAGELAAR et Andrei SMOLYAKOV Jury Mme Anne BOURDON, Rapporteure Mme Sedina TSIKATA, Rapporteure M. Pierre FRETON, Examinateur M. Jan VAN DIJK, Examinateur M. Gerjan HAGELAAR, Directeur de thèse M. Andrei SMOLYAKOV, Co-directeur de thèse Contents R´esum´e 4 Abstract 5 Introduction 6 Plasma devices and applications . 6 Plasma confinement, instabilities and transport . 8 The scope of the thesis . 10 1 Plasma basics and modeling 14 1.1 General introduction . 14 1.2 Elementary plasma processes . 16 1.2.1 Motion of particles in uniform static fields . 16 1.2.2 Collisions . 20 1.2.3 Quasi-neutrality and plasma sheath . 21 1.3 Kinetic models . 25 1.4 Fluid models . 27 1.4.1 Fluid quantities and equations . 27 1.4.2 Closures in fluid models . 33 1.4.3 Simplified fluid models . 36 2 The fluid code MAGNIS 39 2.1 Introduction . 39 2.2 Physical model . 40 2.2.1 Main equations . 40 2.2.2 Boundary conditions . 43 1 2.2.3 Transport losses along the magnetic field lines: 2 2 D approach . 44 2.3 Numerical aspects and procedure . 46 1 2.3.1 Time integration cycle . 47 2.3.2 Momentum equation . 47 2.3.3 Current conservation equation . 49 2.3.4 Continuity equation for ions . 49 2.3.5 Electron heat flux and energy . 50 2.4 Examples of MAGNIS results . 50 2.4.1 Magnetic filter . 50 2.4.2 Periodic magnetic filter with closed drift . 53 3 Waves and instabilities in partially magnetized plasma 55 3.1 Preliminaries and basic eigen-modes . 55 3.2 Mechanisms for instabilities . 61 3.3 Linear instabilities in partially magnetized plasmas . 63 3.3.1 Farley-Buneman instability . 63 3.3.2 Simon-Hoh, or gradient-drift instability. 65 3.3.3 General case: transition to the lower-hybrid and ion sound instabilities . 68 3.4 Conclusion . 70 4 Linear analysis in MAGNIS 71 4.1 Linear dispersion relation modified with the account of inhomogeneous equilibrium profiles 72 4.1.1 Geometry . 72 4.1.2 Plasma equilibrium . 73 4.1.3 Perturbed equations and final general dispersion equation . 76 4.2 Linear instabilities from the generalized dispersion equation . 79 4.2.1 Case 1 : a gradient type instability, the classical Simon-Hoh . 80 4.2.2 Case 2 : a drift type instability, Farley-Bunemann . 86 4.2.3 Case 3 : a gradient-drift type instability, a combination of the first two cases . 92 4.3 Comparisons with MAGNIS . 97 4.3.1 Setting up MAGNIS for the simple model conditions . 97 4.3.2 Implementation of the diagnostics tools . 99 4.3.3 Comparisons : results . 100 4.4 Conclusion . 109 5 Non-linear regime : Analysis of non-linear effects and anomalous transport 110 5.1 Introduction . 110 5.2 Evolution of instabilities in a non-linear regime : qualitative description . 111 5.2.1 Definition of test cases . 112 2 5.2.2 Diagnostics . 114 5.2.3 Analysis of non-linear modes and anomalous transport . 115 5.3 Magnetized plasma column . 135 5.4 Magnetic barrier : Hall thruster alike case . 140 5.5 Conclusion . 144 6 Exploratory developments and extensions of fluid models 146 6.1 Discussion on approximations in fluid models . 146 6.2 Modeling of kinetic ion effects via an ion viscosity . 148 6.2.1 Definition . 148 6.2.2 Dispersion relation and linear analysis . 148 6.2.3 Effects of the ion viscosity in non-linear regime : implementation in MAGNIS . 151 6.3 Deviation from quasi-neutrality : Poisson equation and effective potential . 153 6.3.1 Poisson equation . 153 6.3.2 Dispersion relation and linear analysis . 153 6.3.3 Effective potential . 158 Conclusion and prospects 162 3 R´esum´e Il est bien connu que les plasmas froids magn´etis´esdans des dispositifs tels que les propulseurs Hall et les sources d'ions montrent souvent l'´emergenced'instabilit´esqui peuvent provoquer des ph´enom`enes de transport anormaux et affecter fortement le fonctionnement du dispositif. Dans cette th`ese,nous ´etudionsles possibilit´esde simuler ces instabilit´esde mani`ereauto-coh´erente par la mod´elisationfluide. Cela n'a jamais ´et´efait auparavant pour ces conditions de plasma froid, mais cela pr´esente un grand int´er^etpotentiel pour l'ing´enierie.Nous avons utilis´eun code fluide quasi-neutre d´evelopp´eau laboratoire LAPLACE, appel´eMAGNIS (MAGnetized Ion Source), qui r´esoutun ensemble d'´equations fluides pour les ´electrons et les ions dans un domaine 2D perpendiculaire au champ magn´etique.On a constat´eque dans de nombreux cas d'int´er^etpratique, les simulations MAGNIS produisent des instabilit´eset des fluctuations du plasma. Un premier objectif de cette th`eseest de comprendre l'origine de ces instabilit´es observ´eesdans MAGNIS et de s'assurer qu'elles sont un r´esultatphysique et non un artefact num´erique. Pour ce faire, nous avons effectu´eune analyse de stabilit´elin´eairebas´eesur des relations de dispersion, dont les taux de croissance et les fr´equencesqui en sont issus analyse ont ´et´ecompar´esavec succ`es`aceux mesur´esdans les simulations de MAGNIS pour des configurations simples et forc´es`arester dans un r´egime lin´eaire. Nous avons ensuite identifi´eles principaux modes et m´ecanismesde ces instabilit´es(induits par les champs ´electrique et magn´etique,le gradient de densit´eet l'inertie), connus de la litt´erature, susceptibles de se produire dans ces simulations de fluides. Par la suite, nous avons simul´el'´evolution non-lin´eaireet la saturation des instabilit´eset quantifi´ele transport anormal g´en´er´edans diff´erents cas relatifs aux sources d'ions en fonction de divers param`etrescl´esdu syst`eme(champs ´electriqueset magn´etiqueset temp´eraturedes ´electrons). Enfin, nous avons mis en ´evidenceplusieurs limitations de MAGNIS, et plus g´en´eralement de mod`elesfluides, dues aux approximations physiques (quasi-neutralit´e, absence d’effets cin´etiques).Nous avons montr´eque les modes fluides sont parfois les plus instables `ades ´echelles infiniment petites o`ula th´eorien'est plus valable et ne peuvent donc ^etrer´esoluesnum´eriquement. Nous avons propos´ediff´erentes mani`eresde rem´edier`ace probl`emepar l'introduction de termes diffusifs inspir´esde la physique `apetite ´echelle (non-neutralit´e,rayon de Larmor), que nous avons ensuite test´es dans MAGNIS. mots cl´es: mod´elisationfluide, plasma, instabilit´es,d´erive ExB, transport anormal, propulseur de Hall 4 Abstract It is well known from experiments that magnetized low-temperature plasmas in devices such as Hall thrusters and ion sources often show the emergence of instabilities that can cause anomalous transport phenomena and strongly affect the device operation. In this thesis we investigate the possibilities to simulate these instabilities self-consistently by fluid modeling. This is of great potential interest for en- gineering. We used a quasineutral fluid code developed at the LAPLACE laboratory, called MAGNIS (MAGnetized Ion Source), solving a set of fluid equations for electrons and ions in a 2D domain per- pendicular to the magnetic field lines. It was found that in many cases of practical interest, MAGNIS simulations show plasma instabilities and fluctuations. A first goal of this thesis is to understand the origin of the instabilities observed in MAGNIS and make sure that they are a physical result and not numerical artifacts. For this purpose, we carried out a detailed linear stability analysis based on disper- sion relations, from which analytical growth rates and frequencies were successfully compared with those measured in MAGNIS simulations for simple configurations forced to remain in a linear regime. We then identified these linear unstable modes and their responsible mechanisms (involving parameters such as the density gradient, electric and magnetic fields and inertia), known from the literature, that are likely to occur in these fluid simulations. Subsequently, we simulated the nonlinear evolution and saturation of the instabilities and quantified the anomalous transport generated in different cases relevant to ion sources, depending on various key parameters of the system (electric and magnetic fields and electron temperature). Finally, we highlighted several limitations of MAGNIS, and more generally of fluid models, due to the physical approximations made (quasineutrality, absence of kinetic effects). We showed that the fluid modes are sometimes most unstable at infinitely small scales for which the theory is no longer valid and which cannot be resolved numerically.
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