Rozprawy doktorskie na temat „Plasma turbulence; Nonlinear theories”

Frequency domain analysis tools have been developed to analyse simultaneous multi-point measurements of developed space plasma turbulence. The Coherence Length technique enables the scale length for plasma wave structures to be measured from magnetic field measurements. The coherence length defines a length scale for the measurement of wave phenomena. Single satellite measurements can be used, the technique becoming more reliable with higher numbers of satellites. The technique is used to identify coherence lengths for waves observed in the magnetic field near the bow shock by the dual AMPTE-UKSIAMPTE-IRM satellites, and for mirror wave structures observed in the magnetic field in the magnetosheath by the dual ISEE-lIISEE-2 satellites. The Transfer Function Estimation technique enables the transfer of energy between plasma waves to be measured, from simultaneous dual-point measurements, resulting in linear growth / damping rates and second-order wave coupling. The technique is improved by replacing the Least Squares method for inversion with Regularisation. The technique is applied to simultaneous magnetic field measurements near the bow shock by the AMPTE-UKSIAMPTE-IRM satellites, where a linear instability in the wave field is identified, which is attributed to an ion anisotropy instability, and accompanying sequence of second-order three-wave coupling processes is also identified, which dissipates the energy from the linear instability. The Wave vector Determination technique enables the identification of wave vectors from simultaneous four-point measurements. The availability of four-point measurements means that the reliance on Minimum Variance Analysis, and that of only being able to use magnetic field measurements, is removed, the wave vector can be determined unambiguously directly from the magnetic field measurements. The technique can identify between waves of different frequency, and waves at the same frequency but propagating in different directions. The technique is applied to simultaneous observations of the electric field by the four-point ii Cluster II satellites, enabling the determination of the wave vector and the identification of a mirror mode structure, solely from the electric field measurements. Chapter 1 introduces the solar-terrestrial environment, briefly describing exploration of this environment by man-made satellites and listing some aims of the analysis of data collected by the satellites. Chapter 2 elaborates on what is meant by data analysis; Spectral Transforms are introduced and described, with a comparison made between Fourier Transforms and Wavelet Transforms, before a review is made of current data analysis techniques for satellite data. Chapter 3 defines and focuses attention on the objectives of this thesis, which are addressed in the following three chapters. Chapter 4 investigates the coherence length of plasma waves through use of the Wavelet Transform and the Fourier Shift Theorem. Chapter 5 makes estimates of wave Transfer Functions, replacing an established Least Squares inversion technique with a Regularisation inversion. Chapter 6 uses a method to determine wave propagation directions, from multi-satellite data, that has not been applied before due to the lack of availability of suitable data sets. Chapter 7 summarises the preceding chapters. The Appendices contain reprints of papers resulting from, and relating to, this research.

Le contrôle du transport turbulent est l'une des clés pour l'amélioration du temps de confinement nécessaire à la réalisation de la fusion thermonucléaire contrôlée. La description de la turbulence cinétique du plasma est un problème à 3 coordonnées spatiales et 3 coordonnées en vitesse. La théorie comme la simulation pour un problème de si haute dimensionnalité sont très difficiles, et des modèles réduits sont nécessaires pour comprendre la turbulence dans les Tokamaks. La technique largement utilisée est de faire moyenner le mouvement cyclotron, qui est beaucoup plus rapide que le phénomène de turbulence. Une telle réduction permet de simplifier le problème à trois coordonnées spatiales des centres-guides des particules, une vitesse parallèle ou énergie et une vitesse perpendiculaire apparaissant comme l'invariant adiabatique. La description gyrocinétique non linéaire requiert des simulations numériques de haute performance massivement parallèles. Toute la difficulté est due aux termes non linéaires (crochets de Poisson) qui décrivent les interactions multi-échelles, ce qui constitue un défi tant pour la théorie que pour la simulation. Toute approche réduite, basée sur des hypothèses bien contrôlées, est donc intéressante à développer.Sur la base de cette ambition, cette thèse concerne la turbulence des particules piégées dans le plasma magnétisé. C'est un système 4D, obtenu après avoir fait la moyenne de la fonction de distribution des particules sur les mouvements cyclotron et de rebond, ce qui peut être considéré comme une forme réduite de la théorie gyrocinétique standard. Nous l'avons appelé "bounce averaged gyrokinetics" pendant ce travail. Même si cette description est grandement réduite par rapport à la théorie gyrocinétique, la simulation directe non-linéaire reste un challenge.Une description des termes non linéaires en coordonnées polaires est choisie, avec une grille logarithmique en norme du vecteur d'onde, tandis que les angles sont discrétisés sur une grille régulière. L'utilisation d'une grille logarithmique permet de prendre en compte une large gamme de vecteurs d'ondes, donc la physique à très petite échelle. De manière analogue aux modèles en couches en turbulence fluide et afin de simplifier le système, seules les interactions entre couches voisines sont considérées.Dans un premier temps, l'étude du système linéaire est présentée, en particulier les seuils des paramètres et l'instabilité linéaire permettant de retrouver la forte anisotropie des taux de croissance des modes d'ions piégés (ou TIM) et des modes d'électrons piégés (ou TEM). Ces études permettent également de valider les codes numériques non-linéaires vis-à-vis d'un solveur aux valeurs propres développé indépendamment.Dans un second temps, l'hypothèse isotrope pour les termes non linéaires est utilisée. Ainsi il n'y a pas d'information de phase exacte pour de tels modèles en couches 1D, ce qui laisse un paramètre libre dans les coefficients d'interaction. Une loi de puissance originale est mise en évidence, qui n'est pas affectée par la valeur du paramètre libre, mesurant l'intensité des effets non-linéaires relativement aux termes linéaires.À partir de la simulation du modèle isotrope, l'information de phase apparaît très importante. Puisque l'instabilité linéaire est anisotrope pour la fusion, la simulation du modèle anisotrope est donc réalisée dans un troisième temps. Le système résolu numériquement est réduit à une espèce cinétique, en supposant que les autres espèces sont adiabatiques. Deux systèmes différents peuvent ainsi être étudiés: ions cinétiques + électrons adiabatiques et électrons cinétiques + ions adiabatiques. Des spectres différents sont observés dans chacun de ces deux cas, et la validité de l'hypothèse adiabatique est discutée pour chaque espèce, avec pour base de comparaison une simulation cinétique à deux espèces
Turbulent transport is one of the keys to improve the energy confinement time required for thermonuclear fusion reactors. The description of the kinetic turbulence of the plasma is a problem with 3 spatial coordinates and 3 velocity coordinates. Both theory and simulation of a problem of such high dimensionality are very difficult, and reduced models are helpfull to understand turbulence in Tokamaks. A widely used technique consists into averaging the cyclotron motion, which is much faster than the turbulence time scale. Such a reduction makes it possible to simplify the problem to three spatial coordinates of the particle guide centers, a parallel velocity or energy, and a perpendicular velocity appearing as the adiabatic invariant. Nonlinear gyrokinetic description requires massively parallel high performance numerical simulations. The difficulty lies in the non-linear terms (Poisson hooks) that describe multi-scale interactions, which is a challenge for both theory and simulation. Any reduced approach, based on well-controlled hypotheses, is therefore interesting to develop.On the basis of this ambition, this thesis concerns the turbulence of particles trapped in magnetized plasma. It is a 4D system, obtained after averaging the particle distribution function on cyclotron and bounce motions, which can be considered as a reduced form of standard gyrokinetic theory. We called it "bounce averaged gyrokinetics" during this work. Even if this description is greatly reduced compared to the gyrokinetic theory, nonlinear direct simulation remains a challenge.A description of the nonlinear polar coordinate terms is chosen, with a logarithmic grid along the norm of the wave vector, while the angles are discretized on a regular grid. The use of a logarithmic grid makes it possible to take into account a wide range of wave vectors, so physics on a very small scale. In a similar way to shell models for fluid turbulence, and in order to simplify the system, only the interactions between neighboring shells are considered.In a first step, the study of the linear system is presented, in particular the paraetric dependence of the instability thresholds and the linear growth rate, allowing to recover the strong anisotropy of the growth rates of the trapped ion modes (or TIM) and the modes of trapped electrons (or TEM). These studies also make it possible to validate the non-linear numerical codes with respect to an independently developer eigenvalue solver.In a second step, the isotropic hypothesis for nonlinear terms is used. Thus, there is no exact phase information for such 1D layer models, which leaves with a free parameter in the interaction coefficients. An original power law is evidenced, which is unaffected by the value of the free parameter, measuring the intensity of the nonlinear effects relative to the linear terms.From the simulation of the isotropic model, the phase information appears very important. Since the linear instability is anisotropic for the fusion, the simulation of the anisotropic model is thus carried out in a third time. The numerically resolved system is reduced to a kinetic species, assuming that the other species are adiabatic. Two different systems can thus be studied: kinetic ions + adiabatic electrons and kinetic electrons + adiabatic ions. Different spectra are observed in each of these two cases, and the validity of the adiabatic hypothesis is discussed for each species, based on a kinetic simulation with two species

This thesis presents an investigation into the behaviour of a laser beam of finite diameter in a plasma with respect to forces and optical properties, which lead to self-focusing of the beam. The transient setting of ponderomotive nonlinearity in a collisionless plasma has been studied, and consequently the self- focusing of the pulse, and the focusing of the plasma wave occurs. The description of a self-focusing mechanism of laser radiation in the plasma due to nonlinear forces acting on the plasma in the lateral direction, relative to the laser has been investigated in the non-relativistic regime. The behaviour of the laser beams in plasma, which is the domain of self-focusing at high or moderate intensity, is dominated by the nonlinear force. The investigation of self-focusing processes of laser beams in plasma result from the relativistic mass and energy dependency of the refractive index at high laser intensities. Here the relativistic effects are considered to evaluate the relativistic self-focusing lenghts for the neodymium glass radiation, at different plasma densities of various laser intensities. A sequence of code in C++ has been developed to explore in depth self-focusing over a wide range of parameters. The nonlinear plasma dielectric function to relativistic electron motion will be derived in the latter part of this thesis. From that, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing as compared to ponderomotive non-relativistic self-focusing, at very high laser intensities. When the laser intensity is very high, pondermotive self-focusing will be dominant. But at some point, when the oscillating velocity of the plasma electron becomes very large, relativistic effects will also play a role in self-focusing. A numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit of the nonlinear paraxial equation is presented in this thesis. In a general setting of both dimension and nonlinearity, the essential differences between the 'defocusing' and 'focusing' cases hence is identified. Presented in this thesis are the nonlinearity and dispersion effects involved in the propagation of solitions which can be understood by using a numerical routines were implemented through the use of the mathematica program, and results give a very clear idea of this interesting phenomena

Possibilities of generating plasma turbulence to provide control of space weather processes have been of particular interest in recent years. Such turbulence can be created by chemical released into a magnetized background plasma. The released plasma clouds are heavy ions which have ring velocity distribution and large free energy to drive the turbulence. An electromagnetic hybrid (fluid electrons and particle ions) model incorporating electron inertia is developed to study the generation and nonlinear evolution of this turbulence. Fourier pseudo-spectral methods are combined with finite difference methods to solve the electron momentum equations. Time integration is accomplished by a 4th-order Runge-Kutta scheme or predicator-corrector method. The numerical results show good agreement with theoretical prediction as well as provide further insights on the nonlinear turbulence evolution. Initially the turbulence lies near harmonics of the ring plasma ion cyclotron frequency and propagates nearly perpendicular to the background magnetic field as predicted by the linear theory. If the amplitude of the turbulence is sufficiently large, the quasi-electrostatic short wavelength ion cyclotron waves evolve nonlinearly into electromagnetic obliquely propagating shear Alfven waves with much longer wavelength. The results indicate that ring densities above a few percent of the background plasma density may produce wave amplitudes large enough for such an evolution to occur. The extraction of energy from the ring plasma may be in the range of 10-15% with a generally slight decrease in the magnitude as the ring density is increased from a few percent to several 10's of percent of the background plasma density. Possibilities to model the effects of nonlinear processes on energy extraction by introducing electron anomalous resistivity are also addressed. Suitability of the nonlinearly generated shear Alfven waves for applications to scattering radiation belt particles is discussed.
Master of Science

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. In the inertial range, the self-similar turbulent energy cascade to smaller spatial scales is driven by the nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions. For the more realistic case of the collision between two initially separated Alfvén wavepackets (rather than previous idealized, periodic cases), we use a nonlinear gyrokinetic simulation code, AstroGK, to demonstrate three key properties of strong Alfvén wave collisions: they (i) facilitate the perpendicular cascade of energy and (ii) generate current sheets self-consistently, and (iii) the modes mediating the nonlinear interaction are simply Alfvén waves. Once the turbulent cascade reaches the ion gyroradius scale, the Alfvén waves become dispersive and the turbulent energy starts to dissipate, energizing the particles via wave-particle interactions with eventual dissipation into plasma heat. The novel Field-Particle Correlation technique determines how turbulent energy dissipates into plasma heat by identifying which particles in velocity-space experience a net gain of energy. By utilizing knowledge of discrete particle arrival times, we devise a new algorithm called PATCH (Particle Arrival Time Correlation for Heliophysics) for implementing a field-particle correlator onboard spacecraft. Using AstroGK, we create synthetic spacecraft data mapped to realistic phase-space resolutions of modern spacecraft instruments. We then utilize Poisson statistics to determine the threshold number of particle counts needed to resolve the velocity-space signature of ion Landau damping using the PATCH algorithm.

Thesis (M. S.)--Physics, Georgia Institute of Technology, 2009.
Committee Chair: Cvitanovic, Predrag; Committee Member: Dieci, Luca; Committee Member: Grigoriev, Roman; Committee Member: Schatz, Michael; Committee Member: Wiesenfeld, Kurt

Orientadores: Jose Manoel Balthazar, Paulo R. G. Kurka
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica
Made available in DSpace on 2018-08-09T22:56:56Z (GMT). No. of bitstreams: 1 Pereira_DaniloCarlos_D.pdf: 3711639 bytes, checksum: 2413d33f619760c04be8cc5320c0a84b (MD5) Previous issue date: 2007
Resumo: Neste trabalho analisou-se a dinâmica não linear de uma aeronave em vôo longitudinal. Efetuou-se a análise do comportamento bifurcacional da aeronave F-8 ¿Cruzader¿. Na análise bifurcacional foi estudado o comportamento topológico desta aeronave tomando-se dois parâmetros de controle: a deflexão do profundor e a alteração da massa da referida aeronave. Ante a pesquisa desenvolvida, foi proposto um projeto de controle linear ótimo com o objetivo de estabilizar as oscilações do ângulo de ataque, considerando-se regiões criticas do comportamento não linear da aeronave. Adicionalmente, incluiu-se no modelo matemático a variação da velocidade longitudinal da aeronave, visto tratar-se de simulações numéricas em um túnel de vento virtual
Abstract: In this work it was analyzed the non linear dynamic of an aircraft taken onto longitudinal flight. It was done analysis of the bifurcacional behavior of the aircraft F-8 ¿Cruzader¿. In the bifurcational analysis was studied the topological behavior of this aircraft taken into account two parameters of control: the deflection of the elevator and the alteration of the mass of the related aircraft. In the face of the developed research, an optimum linear control project was proposed with the objective of stabilizing the oscillations of the angle-of-attack. Additionally, the variation of the longitudinal speed of the aircraft was included in the mathematic model in order to simulate the oscillatory movement of the aircraft considered, in a tunnel of virtual wind
Doutorado
Materiais e Processos de Fabricação
Mestre em Engenharia Mecânica

Several aspects of the thermalisation process in non-Abelian gauge theories are investigated. Both numerical simulations in the classical statistical approximation and analytical computations in the framework of the two-particle-irreducible effective action are carried out and their results are compared to each other. The physical quantities of central importance are the correlation functions of the gauge field in Coulomb and temporal axial gauge as well as the gauge invariant energy-momentum tensor. Following a general introduction, the theoretical framework of the ensuing investigations is outlined. In doing so, the range of validity of the employed approximation schemes is discussed as well. The first main part of the thesis is concerned with the early stage of the thermalisation process where particular emphasis is on the role of plasma instabilities. These investigations are relevant to the phenomenological understanding of present heavy ion collision experiments. First, an ensemble of initial conditions motivated by the "colour glass condensate" is developed which captures characteristic properties of the plasma created in heavy ion collisions. Here, the strong anisotropy and the large occupation numbers of low-momentum degrees of freedom are to be highlighted. Numerical calculations demonstrate the occurrence of two kinds of instabilities. Primary instabilities result from the specific initial conditions. Secondary instabilities are caused by nonlinear fluctuation effects of the preceding primary instabilities. The time scale associated with the instabilities is of order 1 fm/c. It is shown that the plasma instabilities isotropize the initially strongly anisotropic ensemble in the domain of low momenta (less than approximately 1 GeV). Essential results can be translated from the gauge group SU(2) to SU(3) by a simple rescaling procedure. Finally, the role of Nielsen-Olesen instabilities in an idealised setup is investigated. In the second part, the quasi-stationary phase following the saturation of instabilities is studied. Numerical as well as analytical calculations show that the classical time evolution drives the system towards a nonthermal fixed point which exhibits properties of turbulence. The fixed point is characterised by power-law correlation functions of the gauge field. The determined exponents 4/3 and 5/3 are identical to those found in scalar field theories, which provides indication for universality out of thermal equilibrium. Taking into account the quantum contributions in the analytical approach it is demonstrated that the full quantum theory does not possess a nonthermal fixed point at large momenta.