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Conventional transport orderings employed in the core of a tokamak plasma allow large divergence‐free flows in flux surfaces, but only weak radial flows. However, alternate orderings are required in the edge region where radial diffusion must balance the rapid loss due to free streaming to divertor plates or limiters. Kinetic equations commonly used to study the plasma core do not allow such a balance and are, therefore, inapplicable in the plasma edge. Similarly, core transport formulas cannot be extended to the edge region without major, qualitative alteration. Here the necessary changes are addressed. By deriving and solving a novel kinetic equation, distinctive collisional transport laws for the plasma edge are constructed. It is found that the new edge ordering retains the radial diffusion and parallel flow of particles, momentum, and heat to lowest order in the conservation equations. To higher order a surprising form for parallel transport in the scrape‐off layer is found, in which the parallel flo...

From the BBGKY equations for a pure electron plasma a derivation is made of a collision integral that includes the combined effects of particle gyration in a strong magnetic field and non-uniformities of both the distribution function and the self-consistent electric field on the collisional scale. A series expansion of the collision integral through the distribution function and the electric field on the collisional scale is carried out to third order in derivatives of the distribution function and to second order in derivatives of the electric field. For the strong-magnetic-field case when collision-term contributions to only first order in 1/B are included, a particle flux transverse to the magnetic field proportional to l/B2 is derived. The importance of long-range collective collisions in this process is shown. The result is in contrast with the classical l/B4 proportionality, and is in accordance with earlier studies.

Tese de Doutoramento em Matemática Aplicada, O principal objetivo desta tese é o estudo de misturas gasosas multicomponentes – sistemas gasosos com três ou mais espécies misturadas ao nível molecular – e a dedução de modelos macroscópicos da mecânica de fluidos a partir de uma descrição cinética das partículas que constituem a mistura. Mais especificamente, consideram-se equações cinéticas de tipo Boltzmann que descrevem a evolução de misturas quimicamente reativas, com estrutura monatómica ou poliatómica, que participam numa reação química reversível de tipo bi-molecular e deduzem-se, no limite hidrodinâmico, modelos macroscópicos que descrevem como as espécies se propagam no espaço devido ao processo de difusão e como se transformam quimicamente devido ao processo de reação. Para obter estes modelos macroscópicos, diferentes regimes de adimensionamento das equações cinéticas são considerados, correspondendo a diferentes regimes químicos. O primeiro regime descreve um estado físico em que as colisões mecânicas são dominantes relativamente à reação química, enquanto o segundo regime corresponde a um estado em que as colisões mecânicas e reativas têm a mesma relevância na evolução. No primeiro regime, obtémse, como limite hidrodinâmico das equações cinéticas, um sistema de reação-difusão em que o processo de difusão é modelado pelas equações de Maxwell-Stefan. No segundo regime, obtêm-se as equações de Maxwell-Stefan reativas, com termos adicionais que descrevem a difusão das espécies reativas. As propriedades matemáticas dos modelos cinéticos considerados, relacionadas com as leis de conservação, o equilíbrio termodinâmico, o teorema H e as taxas de produção química, que são fundamentais para a análise desenvolvida nesta tese, são estabelecidas e estudadas rigorosamente., The purpose of this thesis is to study multicomponent gaseous mixtures – systems composed of three or more species mixed at a molecular level – and derive macroscopic models of fluid mechanics from a kinetic description of particles that constitute the mixture. Specifically, this thesis considers Boltzmann-type kinetic equations that model the evolution of reactive monatomic and polyatomic gaseous mixtures participating in a bi-molecular reversible chemical reaction and derive, in the hydrodynamic limit, macroscopic models that describe how the species spread in space due to diffusion and how the species are transformed into each other as a result of the chemical reaction. To obtain these macroscopic models, different scalings of the Boltzmann-type kinetic equations, which correspond to different chemical regimes, are considered. The first regime describes a physical situation in which mechanical collisions are dominant with respect to chemical reaction, whereas the other regime corresponds to a situation in which mechanical and reactive collisions are of the same relevance in the evolution. In the former regime, reaction-diffusion systems where the diffusion process is modelled by the Maxwell-Stefan equations are obtained as hydrodynamic limits of the scaled kinetic equations, while in the latter regime, the reactive Maxwell-Stefan equations, with additional terms describing the diffusion of the reactive species, are obtained. Moreover, the mathematical properties of the considered kinetic models related to the conservation laws, thermodynamic equilibrium, H-theorem, and chemical production rates, which are fundamental for the analysis developed in this thesis, are stated and studied in detail., This thesis was supported by Centro de Matemática, Universidade do Minho, Fundação para a Ciência e a Tecnologia (FCT) through the PhD grant PD/BD/128188/2016, and Program Pessoa of Cooperation between Portugal and France reference 406/4/4/2017/S.