Equilibrium of a plasma in the fluid- and Vlasov–Maxwell systems

It is shown that a recently constructed exact solution of the Vlasov equation describing a plasma with density and temperature gradients can be expressed in terms of the constants of motion. The distribution function is then used to illustrate the differences between a Vlasov and a one-fluid description. In fluid theory, only the pressure profile is determined (unless one postulates an equation of state), while the Vlasov description leads to a separate determination of density (g) and temperature (ψ2) profiles; the equation of state, g=ψ3−2/β, comes out naturally in the latter case.