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A fluid-kinetic model of the collisionless plasma row in a convergent-divergent magnetic nozzle is presented. The model combines the leading-order Vlasov equation and the fluid continuity and perpendicular momentum equation for magnetized electrons, and the fluid equations for cold ions, which must be solved iteratively to determine the self-consistent plasma response in a three-dimensional magnetic field. The kinetic electron solution identifies three electron populations and provides the plasma density and pressure tensor. The far downstream asymptotic behavior shows the anisotropic cooling of the electron populations. The fluid equations determine the electric potential and the fluid velocities. In the small ion-sound gyroradius case the solution is constructed one magnetic line at a time. In the large ion-sound gyroradius case, ion detachment from magnetic lines makes the problem fully three-dimensional.