Stationary plasmas in Vlasov theory

High temperature laboratory and rarefied space plasmas can be considered in many situations as collisionless and described by kinetic theory. The fundamental dynamics of the system is regulated by the Vlasov equation (collisionless Boltzmann equation) for the evolution of the distribution functions of the species present in the plasma, coupled to Maxwell's equations for the electromagnetic fields. This nonlinear system of equations relates self-consistently the fields to their source terms that are given by the moments of the distribution functions in velocity space. In this work stationary solutions of the coupled Vlasov-Maxwell system will be explored, in order to find interesting equilibrium configurations in plasmas. These stationary solutions of the Vlasov-Maxwell system are of interest because both for astrophysical and laboratory plasmas the nonlinear dynamics and the stability are strongly affected by the initial equilibrium conditions, in particular by density and temperature gradients as well as by pressure inhomogeneities and anisotropy of the distribution functions; the aim of this work is to provide a general overview on what conditions of pressure, temperature and density can be found inside a plasma at equilibrium. Both analytical and numerical solutions are found. Analytical solutions are obtained for various choices of the electronic distribution function, but only in the limit of small spatial inhomogeneities. Homogeneous configurations can be found in this limit; soliton-like solutions are obtained as limiting cases of periodic solutions. Equilibria where the same magnetic field configuration is produced by different temperature and density profiles are found as well. The solutions obtained numerically clearly show that it is possible to create a very wide variety of configurations, from periodic to isothermal.