  Full self-consistent stationary Vlasov-Maxwell solutions of magnetically
confined plasmas are built for systems with cylindrical symmetries. The
stationary solutions are thermodynamic equilibrium solutions. These are
obtained by computing the equilibrium distribution function resulting from
maximizing the entropy and closing the equations with source terms that are
then computed by using the obtained distribution. This leads to a
self-consistent problem corresponding to solving a set of two coupled second
order non-linear differential equations. Relevant plasma parameters are
introduced and a bifurcation leading to an improvement of plasma confinement is
shown. Conversely in the improved confinement setting, we exhibit the emergence
of a separatrix in the integrable motion of a charged particles.
