  The mesoscopic properties of a plasma in a cylindrical magnetic field are
investigated from the view point of test-particle dynamics. When the system has
enough time and spatial symmetries, a Hamiltonian of a test particle is
completely integrable and can be reduced to a single degree of freedom
Hamiltonian for each initial state. The reduced Hamiltonian sometimes has
unstable fixed points (saddle points) and associated separatrices. To choose
among available dynamically compatible equilibrium states of the one particle
density function of these systems we use a maximum entropy principle and
discuss how the unstable fixed points affect the density profile or a local
pressure gradient, and are able to create a steep profile that improves plasma
confinement.
