京都大学 / 0048 / 新制・課程博士 / 博士(エネルギー科学) / 甲第21888号 / エネ博第389号 / 新制||エネ||75(附属図書館) / 京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻 / (主査)教授 岸本 泰明, 教授 中村 祐司, 教授 田中 仁 / 学位規則第4条第1項該当 / Doctor of Energy Science / Kyoto University / DFAM

Vlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models. The ‘inverse problem' is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation of the plasma, and make conjectures for all classes. The inverse problem is considered for nonlinear ‘force-free Harris sheets'. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging' process. We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets', and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations. We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle' model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.

I present an overview of the tools and methods of gravitational dynamics motivated by a variety of dynamics problems. Particular focus will be given to the development of dynamic phase-space configurations as well as the distribution functions of collisionless systems. Chapter 1 is a short review of the descriptions of a gravitational system examining Poisson's equations, the probability distribution of particles, and some of the most popular model groups before working through the challenges of introducing anisotropy into a model. Chapter 2 covers the work of Barber2014b which looks at the relations between quantities in collisionless systems. Analytical methods are employed to describe a model that can violate the GDSAI, a well-known result connecting the density slope to the velocity anisotropy. We prove that this inequality cannot hold for non-separable systems and discuss the result in the context of stability theorems. Chapter 3 discusses the background for theories of gravity beyond Newton and Einstein. It covers the `dark sector' of modern astrophysics, motivates the development of MOND, and looks at some small examples of these MONDian theories in practice. Chapter 4 discusses how to perform detailed numerical simulations covering code methods for generating initial conditions and simulating them accurately in both Newtonian and MONDian approaches. The chapter ends with a quick look at the future of N-body codes. Chapters 5 and 6 contain work from Barber 2012 and Barber 2014a which look at the recent discovery of an attractor in the phase-space of collisionless systems and present a variety of results to demonstrate the robustness of the feature. Attempts are then made to narrow down the necessary and sufficient conditions for the effect while possible mechanisms are discussed. Finally, the epilogue is a short discussion on how best to communicate scientific ideas to others in a lecturing or small group setting. Particular focus is given to ideas of presentation and the relative importance of formality versus personality.

Turbulent magnetic fields are ubiquitous in space physics and astrophysics. The influence of magnetic turbulence on the motions of charged particles contains the essential physics of the transport and acceleration of energetic charged particles in the heliosphere, which is to be explored in this thesis. After a brief introduction on the energetic charged particles and magnetic fields in the heliosphere, the rest of this dissertation focuses on three specific topics: 1. the transport of energetic charged particles in the inner heliosphere, 2. the acceleration of ions at collisionless shocks, and 3. the acceleration of electrons at collisionless shocks. We utilize various numerical techniques to study these topics. In Chapter 2 we study the propagation of charged particles in turbulent magnetic fields similar to the propagation of solar energetic particles in the inner heliosphere. The trajectories of energetic charged particles in the turbulent magnetic field are numerically integrated. The turbulence model includes a Kolmogorov-like magnetic field power spectrum containing a broad range of scales from those that lead to large-scale field-line random walk to small scales leading to resonant pitch-angle scattering of energetic particles. We show that small-scale variations in particle intensities (the so-called "dropouts") and velocity dispersions observed by spacecraft can be reproduced using this method. Our study gives a new constraint on the error of "onset analysis", which is a technique commonly used to infer information about the initial release of energetic particles. We also find that the dropouts are rarely produced in the simulations using the so-called "two-component" magnetic turbulence model (Matthaeus et al., 1990). The result questions the validity of this model in studying particle transport. In the first part of Chapter 3 we study the acceleration of ions in the existence of turbulent magnetic fields. We use 3-D self-consistent hybrid simulations (kinetic ions and fluid electrons) to investigate the acceleration of low-energy particles (often termed as "injection problem") at parallel shocks. We find that the accelerated particles always gain the first amount of energy by reflection and acceleration at the shock layer. The protons can move off their original field lines in the 3-D electric and magnetic fields. The results are consistent with the acceleration mechanism found in previous 1-D and 2-D simulations. In the second part of Chapter 3, we use a stochastic integration method to study diffusive shock acceleration in the existence of large-scale magnetic variations. We show that the 1-D steady state solution of diffusive shock acceleration can be significantly modified in this situation. The results suggest that the observations of anomalous cosmic rays by Voyager spacecraft can be explained by a 2-D shock that includes the large-scale magnetic field variations. In Chapter 4 we study electron acceleration at a shock passing into a turbulent magnetic field by using a combination of hybrid simulations and test-particle electron simulations. We find that the acceleration of electrons is greatly enhanced by including the effect of large-scale magnetic turbulence. Since the electrons mainly follow along the magnetic lines of force, the large-scale braiding of field lines in space allows the fast-moving electrons interacting with the shock front multiple times. Ripples in the shock front occurring at various scales also contribute to the acceleration by mirroring the electrons. Our calculation shows that this process favors electron acceleration at perpendicular shocks. We discuss the application of this process in interplanetary shocks and flare termination shocks. We also discuss the implication of this study to solar energetic particles (SEPs) by comparing the acceleration of electrons with that of protons. The intensity correlation of electrons and ions in SEP events indicates that perpendicular or quasi-perpendicular shocks play an important role in accelerating charged particles. In Chapter 5 we summarize the results of this thesis and discuss possible future work.

Les chocs sans collision sont omniprésents dans l'Univers, notamment dans les restes de supernova, et sont formés via diverses instabilités plasmas dépendant essentiellement de la vitesse et de la magnétisation des flux de plasmas. La description de tels chocs nécessite une approche cinétique, tant analytique que numérique.Dans cette thèse, nous avons étudié, au travers de simulations Particle-In-Cell (PIC), les processus sous-jacents par lesquels les instabilités rentrent en compétition les unes avec les autres. Nous avons montré que la diminution du rapport des masses entre ions et électrons, souvent utilisée en simulations numériques pour accélérer la dynamique des chocs, peut avoir de fortes conséquences sur le transfert d'énergie entre particules durant la phase non-linéaire des instabilités.Ces dernières, comme l'instabilité acoustique ionique (IAI) amènent sous certaines conditions à la formation de chocs électrostatiques, pouvant donner naissance à la formation de trous dans l'espace des phases, se propageant dans la région aval du choc, et accélérant ce dernier. L'ajout d'un champ magnétique externe conduit à un changement de médiation du choc, pouvant varier entre l'IAI et les ondes magnéto-soniques lente ou rapide en fonction de l'obliquité entre le champ magnétique et la normale au choc. De plus, nous avons montré que l'orientation du champ magnétique permet de choisir entre une dispersion convexe ou concave des ondes plasma conduisant à la création d'ondes précurseurs dans les régions amont ou aval du choc.Ces chocs magnétisés se trouvent être correctement représentés par le modèle magnétohydrodynamique (MHD) tant qu'ils restent laminaire et que leur potentiel dans la région aval n'est pas suffisamment grand pour réfléchir les particules du milieu amont.Nous avons montré que même pour des chocs sous critiques, une fraction d'ions réfléchis, ne pouvant pas être représentés par la MHD, est suffisante à la croissance d'ondes solitaires en amont du choc, conduisant à l’accélération de ce dernier, mais pas à un processus d'auto-reformation comme pour les chocs super critiques.Bien que les échelles spatio-temporelles soient très différentes, les lois d'échelle rendent possible l'étude de tels phénomènes en laboratoire. Nos études numériques ont été faites dans un cadre de type tube à choc pouvant être testé expérimentalement.A ce titre, nous proposons dans cette thèse une expérience sur la création d'îlots magnétiques, formés par l’interaction de plasmas générés par l'irradiation de cibles par laser baignant dans un champ magnétique externe, et conduisant à la formation de tels chocs.Enfin, nous avons démontré expérimentalement et numériquement la formation de chocs électromagnétiques sans collisions par le biais de l'instabilité de Weibel stimulée par l'instabilité de batterie Biermann, conduisant à l'accélération de particules par le mécanisme de Fermi. Ce nouveau type d'expérience pourrait expliquer l'origine du rayonnement cosmique provenant des restes de supernova. / Collisionless shocks are ubiquitous in the Universe, especially in the supernova remnants, and are formed via various plasma instabilities mainly depending on the speed and magnetization of plasma flows. The description of such shocks requires a kinetic approach, both analytical and numerical.In this thesis, we have studied, through Particle-In-Cell (PIC) simulations, the underlying processes by which instabilities compete with each other.We have shown that the reduction of the ion-to-electron mass ratio, often used in numerical simulations to accelerate the dynamics of shocks, can have strong consequences on the energy transfer between particles during the non-linear phase of instabilities.These instabilities, like the ionic acoustic instability (IAI) lead under certain conditions to the formation of electrostatic shocks, which can give rise to phase space holes formation, propagating in the downstream shock region, and accelerating the shock.The addition of an external magnetic field leads to different shock mediation, which can vary between the IAI to the slow or fast magneto-sonic waves as a function of the obliquity between the magnetic field and the shock normal.Furthermore, we have shown that the orientation of the magnetic field makes it possible to choose between a convex or concave dispersion of the plasma waves leading to the creation of precursor waves in the upstream or downstream shock regions.These magnetized shocks are correctly represented by the magnetohydrodynamic (MHD) model as long as they remain laminar and their potential in the downstream region is not large enough to reflect the particles of the upstream medium.We have shown that even for sub-critical shocks, a fraction of reflected ions, which cannot be modeled by the MHD, is sufficient for the growth of solitary waves upstream of the shock, leading to the acceleration of the latter, but not to a process of 'self-reformation' as for super-critical shocks.Although spatio-temporal scales are very different, scaling laws make possible the study of such phenomena in the laboratory. Our numerical studies have been done in the context of shock tubes that can be experimentally tested.As such, we propose in this thesis an experiment on the creation of magnetic islands, formed by the interaction of plasmas generated by the irradiation of laser targets bathed in an external magnetic field, leading to the formation of such shocks.Finally, we experimentally and numerically demonstrated the formation of collisionless electromagnetic shocks through the Weibel instability stimulated by theBiermann Battery instability, and leading to particle acceleration by the Fermi mechanism.This new type of experiment could explain the origin of cosmic radiation from supernova remnants.

Cette thèse est consacrée à l’étude des processus d’ondes au voisinage des chocs dans les plasmas spatiaux. La propagation des ondes de Langmuir dans un plasma présentant des inhomogénéités aléatoires de densité a été modélisée numériquement; les résultats obtenus ont été comparés aux données des instruments WHISPER et WBD à bord des satellites CLUSTER. Les résultats de modélisation et l’étude statistique portant sur l’intensité des ondes de Langmuir observées dans le préchoc terrestre et le vent solaire ont montré que le théorème central limite n’est pas applicable aux statistiques sur l’intensité, du fait du nombre insuffisant d’inhomogénéités. Il en résulte que la fonction de distribution de probabilité pour le logarithme des énergies d’ondes n’atteint pas la distribution normale. D’autre part la détection à distance de la zone quasi-perpendiculaire du front de choc terrestre a pu être effectuée en analysant la modulation des ondes de Langmuir et celle des ondes électrostatiques avec fréquence décalée à proximité de la limite du pré-choc. Il a été montré que la probabilité d’observation de la non-stationnarité du front de choc augmente avec le nombre de Mach du choc. Enfin le rayonnement de transition des électrons relativistes au front de choc quasi-perpendiculaire a été calculé pour expliquer le mécanisme de l’émission électromagnétique observée par les satellites près du front de choc interplanétaire le 22 janvier 2004. Les paramètres du calcul correspondent aux véritables paramètres de l’évènement. Le spectre du rayonnement de transition établi théoriquement a son maximum dans le même domaine de fréquence que pour les mesures. / The doctoral thesis is devoted to the investigation of wave processes in the vicinity of space plasma shocks. The numerical modelling of the Langmuir wave propagation in a plasma with random density inhomogeneities was performed and its results were compared with experimental data obtained by WHISPER and WBD instruments of the CLUSTER spacecraft project. The analysis results showed that the Central Limit Theorem is not applicable to the Langmuir wave intensity statistics in the Earth’s foreshock and the solar wind, because of insufficient number of inhomogeneities affecting the amplitude of the waves. Consequently the normal distribution of the probability distribution function for logarithm of wave energies is not achieved. The remote sensing of quasi-perpendicular part of the Earth’s bow shock front was performed using the analysis of the modulation of Langmuir, upshifted and downshifted wave intensities close to the foreshock boundary. The probability of the shock front nonstationarity observation was found to grow with shock Mach number. The transition radiation of the relativistic electrons at the interplanetary quasi-perpendicular shock front was calculated to explain the mechanism of electromagnetic emission observed by satellites near the shock front on January, 22, 2004. The parameters of the calculation corresponded to the actual parameters of the event. The theoretically predicted spectrum of transition radiation has its maximum in the same frequency region as in the measurements.

Neste trabalho um modelo é apresentado que permite-nos prever quantitativamente o estado estacionário atingido por um plasma não-neutro durante um processo de relaxação nãocolisional. Como uma aplicação específica, a teoria é usada para estudar a relaxação de feixes de partículas carregadas na qual, mostra-se que, um feixe inicialmente casado relaxa para a distribuição de Lynden-Bell. No entanto, quando existe um descasamento inicial, o mesmo oscila e ressonâncias paramétricas conduzem-no a uma separação de fases: caroço e halo. A abordagem desenvolvida vale tanto para a densidade como para a distribuição de velocidade no estado final estacionário. / In this work a theoretical framework is presented which allows us to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particle beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a corehalo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.

Neste trabalho um modelo é apresentado que permite-nos prever quantitativamente o estado estacionário atingido por um plasma não-neutro durante um processo de relaxação nãocolisional. Como uma aplicação específica, a teoria é usada para estudar a relaxação de feixes de partículas carregadas na qual, mostra-se que, um feixe inicialmente casado relaxa para a distribuição de Lynden-Bell. No entanto, quando existe um descasamento inicial, o mesmo oscila e ressonâncias paramétricas conduzem-no a uma separação de fases: caroço e halo. A abordagem desenvolvida vale tanto para a densidade como para a distribuição de velocidade no estado final estacionário. / In this work a theoretical framework is presented which allows us to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particle beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a corehalo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.

Neste trabalho um modelo é apresentado que permite-nos prever quantitativamente o estado estacionário atingido por um plasma não-neutro durante um processo de relaxação nãocolisional. Como uma aplicação específica, a teoria é usada para estudar a relaxação de feixes de partículas carregadas na qual, mostra-se que, um feixe inicialmente casado relaxa para a distribuição de Lynden-Bell. No entanto, quando existe um descasamento inicial, o mesmo oscila e ressonâncias paramétricas conduzem-no a uma separação de fases: caroço e halo. A abordagem desenvolvida vale tanto para a densidade como para a distribuição de velocidade no estado final estacionário. / In this work a theoretical framework is presented which allows us to quantitatively predict the final stationary state achieved by a non-neutral plasma during a process of collisionless relaxation. As a specific application, the theory is used to study relaxation of charged-particle beams. It is shown that a fully matched beam relaxes to the Lynden-Bell distribution. However, when a mismatch is present and the beam oscillates, parametric resonances lead to a corehalo phase separation. The approach developed accounts for both the density and the velocity distributions in the final stationary state.

<p>The Earth's bow shock is a boundary where the solar wind becomes decelerated from supersonic to subsonic speed before being deflected around the Earth. This thesis presents measurements by the Cluster spacecraft upstream and at the Earth's quasi-parallel bow shock where the angle between the upstream magnetic field and the bow shock normal is less than 45 degrees. An intrinsic feature of quasi-parallel shocks is the ability of ions, that are reflected off the shock in a specular manner, to propagate far upstream and to interact with the incident solar wind. This leads to the generation of a variety of plasma waves, e.g., Ultra-Low Frequency (ULF) waves, which in their turn interact with the different ion populations. Some of the ULF waves are thought to steepen into so-called Short Large-Amplitude Magnetic Structures (SLAMS). </p><p>This thesis studies the impact of SLAMS on the incident solar wind. SLAMS are thought to play an important role in terms of 1) returning shock-reflected ions back to the shock where they can eventually contribute to downstream thermalisation and 2) local pre-dissipation of the solar wind. </p><p>The first electric field measurements of SLAMS showed a strong electric field rotation over SLAMS in association with the rotation of the magnetic field. This often leads to a local change from quasi-parallel to quasi-perpendicular conditions. In addition, short-scale electric field features were observed, e.g., spiky electric field structures associated with the leading edge of SLAMS and solitary electric field structures on Debye length scales, which are suggested to represent ion phase space holes. </p><p>Using the abilitiy of the four Cluster satellites to obtain propagation vectors of SLAMS and the high-resolution electric field measurements, the electric potential over SLAMS was studied. These structures are associated with a significant potential on the order of a few hundred to thousand Volt. Comparing these findings with data from the ion spectrometer, it was found that the bulk flow is locally significantly decelerated and moderately deflected and heated. In addition, SLAMS reflect incident ions on both the leading and trailing edge. The flux of so-called gyrating ions show a clear maximum in association with SLAMS. This indicates that SLAMS indeed play an important role for pre-dissipation of the solar wind upstream of the shock.</p>