Dissipative stationary plasmas: Kinetic modeling, Bennett's pinch and generalizations

The structure of the self-consistent electromagnetic fields, E, B, and one-particle distribution functions, f_s, of a stationary dissipative unbounded S-species plasma, which satisfy a system of Maxwell-Vlasov-Fokker- Planck-Boltzmann equations with velocity-independent (effective) dissipation coefficients and applied constant electric field ℰ, is studied. It is proven that when the plasma is invariant along the direction of ℰ, then (a) the f_s are given by S drifting Maxwell-Boltzmann distributions, with densities satisfying self-consistent Poisson-Boltzmann equations of the type first considered by Bennett for S=2; (b) all smooth radial current profiles with normalized particle densities satisfy a generalized Bennett relation; (c) Bennett's current profile is the only fully conformally invariant one; (d) there exist other radial solutions with profiles different from Bennett's.