The transient and steady-state expansion of a weakly-collisional plasma beam in a paraxial magnetic nozzle is studied with a kinetic Boltzmann-Poisson model. Only intraspecies collisions involving electrons are considered and these are modeled with a Bhatnagar-Gross-Krook operator. Simulations show that occasional collisions progressively populate the phase-space region of isolated trapped electrons until a steady state is reached, which is independent of transient history. The steady state is characterized by a partial occupancy of that region increasing with the collisionality rate but far away from the full occupancy postulated by an alternative steady-state kinetic model. The changes on the amount of trapped electrons with the collisionality rate explain, in turn, the changes on the spatial profiles of main plasma magnitudes. Conclusions on the momentum and energy balances of ions and electrons agree, in terms of general trends, with those of the steady-state kinetic model. In the downstream region of the expansion, ions and electrons lose all their perpendicular energy but they still keep part of their parallel thermal energy. Electron heat fluxes of parallel energy are not negligible and are approximately proportional to enthalpy fluxes.
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