The hot, magnetized, relativistic Vlasov Maxwell system




Preissl, Dayton

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This master thesis is devoted to the kinetic description in phase space of strongly magnetized plasmas. It addresses the problem of stability near equilibria for magnetically confined plasmas modeled by the relativistic Vlasov Maxwell system. A small physically pertinent parameter ε, with 0 < ε << 1, related to the inverse of a gyrofrequency, governs the strength of a spatially inhomogeneous applied magnetic field given by the function x→ε−1Be(x). Local C1-solutions do exist. But these solutions may blow up in finite time. This phenomenon can only happen at high velocities [14] and, since ε−1is large, standard results predict that this may occur at a time Tε shrinking to zero when ε goes to 0. It has been proved recently in [7] that, in the case of neutral, cold, and dilute plasmas (like in the Earth’s magnetosphere), smooth solutions corresponding to perturbations of equilibria exist on a uniform time interval [0,T], with 0< T independent of ε. We investigate here the hot situation, which is more suitable for the description of fusion devices. A condition is derived for which perturbed W1,∞-solutions with large initial momentum also exist on a uniform time interval, they remain bounded in the sup norm for well-prepared initial data, and moreover they inherit some kind of stability.



Vlasov-Maxwell, Kinetic Theory, Plasma Physics, Analysis of Partial Differential Equations