Termodynamická interpretace Landauova tlumení

Kužílek, Adam Oliver

This thesis studies the long-time hydrodynamic properties of collisionless plasmas in the context of Landau damping. In the first half of the work, an overview of the kinetic theory of gases, Landau damping, and the principle of entropy maximisation is given. In the second half, the hydrodynamic variables (the moments of the distribution function), their evolution, and the evolution of hydrodynamic entropy are studied using the Vlasov-Poisson equations linearised around a homogeneous solution. In the linearised regime, a theorem is formulated establishing sufficient conditions for the damping of the hydrodynamic variables (density, momentum, and energy), which is related to the growth of hydrodynamic entropy. The theorem is an adaptation of the 2011 theorem on linear Landau damping by C. Mouhot and C. Villani, under strengthened conditions on the initial condition and the homogeneous solution. Finally, the analytical estimates are verified by a numerical simulation using the Particle-in-Cell method.

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