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.