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A model is developed to describe the plasma jet generated in a vacuum arc, which enters and flows inside a straight magnetic filter with a realistic magnetic field configuration. Considering a low-density collisionless plasma projection of the electron momentum equation along the magnetic field lines and the assumption of quasi-neutrality allows one to relate the plasma density to the electrostatic potential. The system of equations is closed using the ion mass conservation and ion momentum equations. The model is compared to measurements on the plasma jet generated in a pulsed copper vacuum arc with an annular anode, moving along a straight magnetic filter. Probe measurements of the ion saturation current and of the floating potential at different axial and radial positions along the filter, and for different magnetic field values, are used in the comparison with the model results. It is found that anomalous diffusion is needed to fit the experimental measurements. Moreover, a novel anomalous friction effect for ion motion across magnetic lines has to be invoked in order to prevent strong radial oscillations triggered by the fast magnetic focusing of the plasma at the filter entrance and obtain realistic results. A simple model is presented to account for both of these effects, based on the assumption of a high level of fluctuations in the plasma.