This thesis presents a complete theoretical framework for turbulence and transport in tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio of the gyroradius to the equilibrium scale length. Proceeding order-by- order in this expansion, a framework for plasma turbulence is developed. It comprises an instantaneous equilibrium, the fluctuations driven by gra- dients in the equilibrium quantities, and the transport-timescale evolu- tion of mean profiles of these quantities driven by the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the high-flow gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local cascade of free energy. Transport equations for the evolution of the mean density, temperature and flow ve- locity profiles are derived. These transport equations show how the neo- classical corrections and the fluctuations act back upon the mean profiles through fluxes and heating. This framework is further developed by exploiting the scale separation between ions and the electrons. The gyrokinetic equation is expanded in powers of the electron to ion mass ratio, which provides a rigorous method for deriving the electron response to ion-scale turbulence. We prove that such turbulence cannot change the magnetic topology, and ar- gue that, therefore, the magnetic field lies on fluctuating flux surfaces. These flux surfaces are used to construct magnetic coordinates, and in these coordinates a closed system of equations for the electron response is derived. All fast electron timescales have been eliminated from these equations. Simplified transport equations for electrons in this limit are also derived.

O trabalho apresentado aqui visou estudar a implantação de elementos em superfícies metálicas (particularmente cobre) de maneira controlada, investigando-se as alterações que tal implante causou na estrutura da superfície, objetivando uma possível melhoria no comportamento desses metais a serem utilizados como catodos em tochas de plasma ou para várias outras aplicações, tais como em catálise, micro eletrônica, oxidação e corrosão de metais e outros. Filmes finos de cobre policristalino foram implantados com íond (energia de 20KeV até 50KeV; doses da ordem de 10 15íons/cm2) de metais alcalinos (Li, Na, K, Rb e Cs) bem como de O e Cl. Foram realizadas diversas análises de superfície visando determinar as alterações ocorridas no cobre quando da implantação dos íons, tais como: composição de superfície (Auger Electron Spectroscopy, X-ray Photoelectron Spectroscopy), estrutura de superfícies em termos de topografia e do potencial de superfície (Kelvin Probe Force Microscopy), composição volumétrica X-ray Fluorescence, Rutherford Backscattering Spectroscopy e Energy Dispersive X-ray Spectroscopy), concentração de oxigênio (Elastic non-Rutherford Backscattering Spectroscopy) e estrutura cristalina (X-ray Diffraction). Modelos teóricos foram utilizados para se obter uma compreensão melhor das alterações estruturais que ocorrem durante a implantação iônica em uma superfície metálica (Stopping and Range of Ions in Matter e Tight-Binding Linear Muffin-Tin Orbital Atomic Sphere Approximation (Coherent Potential Approximation)). As análises de composição superficial mostraram que as concentrações dos elementos C, N, Cl e S dos substratos de cobre não implantados e implantados foram similares e que a única alteração na composição superficial, causada pelo processo da implantação iônica, foi a introdução dos íons desejados nos filmes de cobre. Observou-se que mesmo as pequenas doses de íons podem causar uma grande diminuição da função de trabalho (2-30%) em relação ao cubro puro; já a implantação de O e Cl gerou um aumento na função de trabalho de 300mV e 900MV, respectivamente. As concentrações detectadas de íons implantados de metais alcalinos podem ser consideradas altas (tendo em vista as doses de implantação relativamente pequenas, da ordem de 10.15ions/cm2) diminuindo rápido na direção do bulk das amostras; esta distribuição se deve provavelmente a um processo de migração de íons na direção da superfície. Os resultados de EBS e KPFM indicam que uma maior dose não necessariamente gera uma concentração maior de íons implantados na primeira camada superficial. Observou-se também que somente uma parte da dose total dos íons é efetivamente implantada, devido ao processo de sputtering, que ocorre durante a implantação iônica. A implantação iônica de diferentes íons alcalinos influencia diferentemente os processos de oxidação das amostras. A principal influência no aumento da oxidação é a estrutura topográfica das amostras; porém, a presença de íons implantados nas superfícies das amostras parece influenciar as etapas iniciais de oxidação, aumentando ou diminuindo a absorção de oxigênio. Para o caso da implantação dos íons de O e Cl, a concentração desses íons parece aumentar com a profundidade até um certo nível, o que, por sua vez, indica que não houve um processo de migração durante a implantação. Isto se deve provavelmente ao fato de que estes íons criam ligações com os elementos de substrato. As alterações da função de trabalho de dois casos distintos de deposição de metais (Ag e Cs) sobre Cu (111), foi estudada com o programa TB-LMTO-ASA (CPA), utilizando-se, nas simulações, valores diferentes para o raio de Wigner-Seitz para esferas vazias (WSES); os resultados das alterações da função de trabalho durante a deposição foram aproximadamente 20% menores em comparação com os valores experimentais da literatura. O efeito de WSES, que é, em princípio, um artefato computacional, sobre o valor da função de trabalho do sistema é normalmente interpretado como uma não confiabilidade dos modelos baseados nos conceitos de ASA. Porém, os resultados obtidos durante este trabalho indicam a existência de uma relação entre WSES e a rigorosidade da superfície; portanto, o sentido físico de esferas vazias pode ser visto como uma medida da rugosidade superficial. / In this work, the controlled implantation of the different elements in the metallic surfaces (particularly copper) was performed, in order to study the changes that the implantation causes on the surface structure, aiming to improve the behaviour of those metals for their use as cathodes in plasma torches or other applications, such as: catalysis, microelectronics, oxidation and corrosion of metals and others. Thin polycrystalline copper films were implanted with ions (energy 20-50keV; doses of order of \'10 POT. 15\' ions/\'cm POT. 2\') of alkaline metals (\'LI\', \'NA\', \'K\', \'RB\', and \'CS\') as well as of \'O\' and \'CL\'. Different surface analyses were performed in order to determine the changes on copper due to the ion implantation, in terms of: surface composition (Auger Electron Spectroscopy, X-ray Photoelectron Spectroscopy), topographic and surface potential structure (Kelvin Probe Force Microscopy), bulk composition (X-ray Fluorescence, Rutherford Backscattering Spectroscopy e Energy Dispersive X-ray Spectroscopy), oxygen concentration (Elastic non-Rutherford Backscattering Spectroscopy) and crystalline structure (X-ray Diffraction). Theoretical models were used to understand better the structural changes which occur on the metallic surface during the ion implantation process (Stopping and Range of Ions in Matter e Tight-Binding Linear Muffin-Tin Orbital Atomic Sphere Approximation (Coherent Potential Approximation)). The surface composition analyses of implanted and non-implanted copper substrates showed similar concentration of \'C\', \'N\', \'CL\' and \'S\' and that the only change in surface concentration, due to the ion implantation process, was the introduction of the desired ions in the surface of copper films. It was observed that even small ion doses can cause relatively large decrease of work function (2-30%) in relation to the pure copper value; the implantation of O and CL caused an increase in work function of 300m V and 900mV, respectively. The detected concentration of implanted alkali metal ions was relatively high (taking into consideration relatively small implantation doses, of the order of \'10 POT. 15\' ions/\'cm POT. 2\'), decreasing fast towards bulk of the samples; this distribution were probably caused by a migration process of implanted ions towards the surface. The EBS and KPFM results indicate that not always the largest dose produces the largest implanted ion concentration in the surface layer. It was also observed that only a part of the total ion dose is effectively implanted, due to the sputtering during the ion implantation process. Implantation of different alkali ions influences the sample oxidation process in a different way. The principal influence in the increase of oxidation is the topographic structure of the samples; however, the presence of the implanted ions on the samples surface seems to influence the initial stages of the oxidation, increasing or decreasing the oxygen adsorption. Of the cases of the O and CL implantation, the concentration of these ions seems to increase with depth, which indicates that there were no migration process involved. This is probably due to the fact that these ions create bonds with the substrate elements. The changes in the work function for two distinct cases of metal (AG and CS) deposition on CU (111) was studied with the computational programme TB-LMTO-ASA (CPA), using, in the simulations, different values for the Wigner-Seitz radius for Empty Spheres (\'WS IND. ES\'); the results on the work function changes during the deposition were approximately 20% lower in comparison with the experimental data from the literature. The effect of \'WS IND. ES\', which is, in principle, a computation artefact, on the work function value of the studied systems is normally interpreted as the non-reliability of the models based on the ASA concepts. However, the results obtained during this work indicate that there is a relation between the \'WS IND. ES\' and the surface roughness; therefore, physical meaning of the empty spheres can be understood as a \"measure\" of surface roughness.

The destabilization of plasma waves upon their interaction with fast ions is studied using a kinetic framework. The work consists of two parts: (I) a study of the applicability of quasilinear theory using a pertubative, early-time nonlinear evolution of a mode and its prediction with respect to chirping oscillations, and (II) the resonance-broadened quasilinear formulation of the evolution of unstable modes. In part I, we have developed predictive capabilities for the type of fast-ion-induced transport by means of a criterion for the likelihood of a mode to oscillate at a constant frequency or to evolve to a bifurcation consisting of nonlinear chirping oscillations. The proposed criterion is derived and evaluated using the linear codes NOVA and NOVA-K. The criterion was shown to be in agreement with experimentally observed modes in the tokamaks DIII-D and NSTX. The analysis reveals that micro-turbulence is a key mediator for suppressing chirping and therefore allowing quasilinear theory to be applicable. In part II, a system of resonance-broadened quasilinear equations (RBQ) was derived using action and angle variables, which takes advantage of system symmetries by using the invariants of the unperturbed motion as variables when accounting for the effects of perturbations due to modes. The equations capture information on mode structures and on resonances that are spread over phase space. We then expressed them in terms of NOVA code notation. The RBQ model is presented, along with the finite-difference scheme used for numerical integration. Numerical results and future developments are also described. / A desestabilização de ondas em plasmas quando de sua interação com íons rápidos é estudada utilizando a abordagem cinética. Este trabalho consiste em duas partes: (I) um estudo sobre a aplicabilidade da teoria quase-linear, utilizando a evolução não linear perturbada em seu estágio inicial de um modo e sua previsão com respeito às oscilações do tipo gorjeio (chirping), e (II) a formulação quase-linear de ressonâncias alargadas da evolução de modos instáveis. Na parte I, desenvolvemos capacidades preditivas em relação ao tipo de transporte in- duzido por íons rápidos por meio de um critério a respeito da probabilidade de um modo oscilar com uma frequência constante ou evoluir para uma bifurcação que consista de os- cilações de gorjeio não lineares. O critério proposto é derivado e calculado utilizando os códigos lineares NOVA e NOVA-K. Mostramos que o critério obtido concorda com modos observados experimentalmente nos tokamaks DIII-D e NSTX. A análise revela que a mi- croturbulência é um mediador-chave na supressão dos gorjeios e que, portanto, permite que a teoria quase-linear seja aplicável. Na parte II, um sistema de equações quase-lineares com ressonâncias alargadas (RBQ) foi derivado utilizando variáveis de ângulo e ação, tirando-se proveito das simetrias do sistema ao se tomar como variáveis os invariantes do movimento não perturbado quando consideramos os efeitos das perturbações aos modos. As equações capturam as informações sobre a estrutura dos modos e sobre as ressonâncias que se espalham sobre o espaço de fase. Expressamo-las, então, em termos da notação do código NOVA. O modelo RBQ é apresentado, juntamente com um esquema de diferenças finitas, utilizado para a integração numérica. Resultados numéricos e desenvolvimentos futuros também são descritos.

As means of investigating the various mechanisms which contribute to the persistence of magnetized turbulence in the solar wind, this dissertation details the development of tools through which turbulence theories can be directly compared to in situ observations. This comparison is achieved though the construction of synthetic spacecraft time series from spectra of randomly phased linear eigenmodes. A broad overview of the current understanding of plasma turbulence through analytic theory, spacecraft observation, and numerical simulation is presented with particular emphasis on previous uses of linear eigenmode characteristics in the literature. An analytic treatment of relevant fluid and kinetic linear waves follows, providing motivation for the choice of three eigenmode characteristics for studying solar wind turbulence in this dissertation. The novel synthetic spacecraft time series method is next detailed and its use in describing magnetized turbulence justified. The three metrics are then individually employed as a means of comparing the turbulence models used to generate synthetic time series with in situ observations. These comparisons provide useful constraints on various proposed mechanisms for sustaining the turbulence cascade and heating the solar wind plasma.

The theory of quantum electrodynamics (QED) was born out of an attempt to merge Einsteins theory of special relativity and quantum mechanics. Einsteins energy/mass equivalence together with Heisenberg's uncertainty principle allows for particle pairs to be spontaneously created and annihilated in vacuum. These spontaneous fluctuations gives the quantum vacuum properties analogous to that of a nonlinear medium. Although these fluctuations in general does not give note of themselves, effects due to their presence can be stimulated or enhanced through external means, such as boundary conditions or electromagnetic fields. Whereas QED has been very well tested in the high-energy, low-intensity regime using particle accelerators, the opposite regime where the photon energy is low but instead the intensity is high is still to a large degree not investigated. This is expected to change with the rapid progress of modern high-power laser-systems. In this thesis we begin by studying the QED effect of photon-photon scattering. This process has so far not been successfully verified experimentally, but we show that this may change already with present day laser powers. We also study QED effects due to strong magnetic fields. In particular, we obtain an analytical description for vacuum birefringence valid at arbitrary field strengths. Astrophysics already offer environments where QED processes may be influential, e.g. in neutron star and magnetar environments. For astrophysical purposes we investigate how effects of QED can be implemented in plasma models. In particular, we study QED dispersive effects due to weak rapidly oscillating fields, nonlinear effects due to slowly varying strong fields, as well as QED effects in strongly magnetized plasmas. Effects of quantum dispersion and the electron spin has also been included in an extended plasma description, of particular interest for dense and/or strongly magnetized systems.

An algorithm for modeling two species plasmas, which evolves the number density, flow velocity, and temperature equations coupled to Maxwell's electric and magnetic field equations, is discussed. Charge separation effects and the displacement current are retained. Mathematical derivations of normal modes in cold and hot plasmas, as represented by dispersion relations resulting from a linear analysis of the two fluid equations, are presented. In addition, numerical theory in relation to the ideas of geometry, temporal and spatial discretization, linearization of the fluid equations, and an expansion using finite elements is given. Numerical results generated by this algorithm compare favorably to analytical results and other published work. Specifically, we present numerical results, which agree with electrostatics, plasma oscillations at zero pressure, finite temperature acoustic waves, electromagnetic waves, whistler waves, and magnetohydrodynamics (MHD) waves, as well as a Fourier analysis showing fidelity to multiple dispersion relations in a single simulation. Final consideration is given to two species plasma stability calculations with a focus on the force balance of the initial conditions for a resistive MHD tearing mode benchmark and a static minimum energy plasma state.

<p>The work presented in this thesis involves experimental and theoretical studies related to plasma properties in high power impulse magnetron sputtering (HiPIMS), and more specifically plasma transport. HiPIMS is an ionized PVD method based on conventional direct current magnetron sputtering (dcMS). In dcMS very little of the sputtered material is ionized since the plasma power density is not high enough. This is not the case for HiPIMS, where a substantial part is ionized, and thus presents many new opportunities for thin film growth. Understanding the dynamics of the charged species in the HiPIMS discharge is therefore of essential value when producing high-quality thin film coatings.</p><p>In the first part of the work a new type of anomalous electron transport was found. Investigations of the transport resulted in the discovery that this phenomenon could quantitatively be described as being related and mediated by highly nonlinear waves, likely due to the modified two-stream instability (MTSI), resulting in electric field oscillations in the MHz-range (the so-called lower hybrid frequency). Measurements in the plasma confirmed these oscillations as well as trends predicted by the theory of these types of waves. The degree of anomalous transport in the plasma could also be determined by measuring the current density ratio between the azimuthal current density (of which the Hall current density is one contribution) and the discharge current density, <em>J</em><em>φ</em><em> / J</em><em>D</em>. The results provided important insights into understanding the mechanism behind the anomalous transport.</p><p>It was furthermore found that the current ratio <em>J</em><em>φ</em><em> / J</em><em>D</em> is inversely proportional to the transverse resistivity, eta_perpendicular , which governs how well momentum is transferred from the electrons to the ions in the plasma. By looking at the forces involved in the charged particle transport it was expected that the azimuthally rotating electrons would exert a volume force on the ions tangentially outwards from the circular race track region. The effect of having an anomalous transport would therefore be a large fraction of highly energetic ions being transported sideways and lost to the walls. In a series of experiments, deposition rates as well as incoming ion energy distributions were measured directly at the side of the magnetron. It was found that a substantial fraction of sputtered material is transported radially away from the cathode and lost to the walls in HiPIMS as well as dcMS, but more so for HiPIMS giving one possible explanation to why the deposition rate for substrates placed in front of the target is lower for HiPIMS compared to dcMS. Furthermore, the recorded, incoming ion energy distributions confirmed theoretical estimations on this type of transport regarding energy and direction.</p>

No description available.

<p>With a new generation of lepton colliders being conceived, muons have been proposed as an alternative particle to electrons. Muons lose less energy to synchrotron radiation and a Muon Collider can provide luminosity within a smaller energy range than a comparable electron collider. This allows a circular collider to be built. As part of the accelerator, it would also be possible to allow the muons to decay to study neutrinos. </p><p> Because the muon is an unstable particle, a muon beam must be cooled and accelerated within a short amount of time. Muons are generated with a huge phase space, so radio frequency cavities placed in strong magnetic fields are required to bunch, focus, and accelerate the muons. Unfortunately, traditional vacuum RF cavities have been shown to break down in the magnetic fields necessary. </p><p> To successfully operate RF cavities in strong magnetic fields, the cavity can be filled with a high pressure gas in order to mitigate breakdown. The gas has the added benefit of providing cooling for the beam. The electron-ion plasma created in the cavity by the beam absorbs energy and degrades the accelerating electric field of the cavity. As electrons account for the majority of the energy loss in the cavity, their removal in a short time is highly desirable. The addition of an electronegative dopant gas can greatly decrease the lifetime of an electron in the cavity. </p><p> Measurements in pure hydrogen of the energy consumption of electrons in the cavity range in 10^-18 and 10^-16 joules per RF cycle per electron. When hydrogen doped with dry air is used, measurements of the power consumption indicate an energy loss range of 10^-20 to 10^-18 joules per RF cycle per ion, two orders of magnitude improvement over non-doped measurements. The lifetime of electrons in a mixture of hydrogen gas and dry air has been measured from &lt; 1 ns, up to 200 ns. The results extrapolated to the parameters of a Neutrino Factory and Muon Collider indicate that a high pressure gas filled RF cavity will work in a cooling-channel for either machine. </p>

The complete set of Kubo conductivity tensors are computed for two- and three-dimensional linear magnetic null systems using collisionless single-particle simulations. Chaos regions are constructed for each case, along with the complete Lyapunov spectrum. It is found that stochastic frequency mixing of particle bounce motion, as well as gyromotion, contribute significantly to the conductivity. For many cases, the conductivity curve is well approximated by power-laws, resulting in a divergent value of the direct-current conductivity, while others can be described by a sum of Maxwellian curves. The energy dissipation of these systems is also briefly discussed.