  Starting from the given passive particle equilibrium particle cylindrical
profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov
equation at thermodynamic equilibrium with non-flat density profiles. The
solutions to the obtained equations are then discussed. It appears that the
presence of an azimuthal (poloidal) flow in the plasma can insure radial
confinement, while the presence of a longitudinal (toroidal) flow can enhance
greatly the confinement. Moreover in the global physically reasonable
situation, we find that no unstable point can emerge in the effective
integrable Hamiltonian of the individual particles, hinting at some stability
of the confinement when considering a toroidal geometry in the large aspect
ratio limit.
