Creating steep density profile with a separatrix

Themesoscopic 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 freedomHamiltonian for each initial state. The reduced Hamiltonian sometimes has an unstable fixed point (saddle point) and a separatrix. Using a maximum entropy principle we compute dynamically compatible equilibrium states of the one particle density functionof these systems and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a so called internal transport barrier.