The spatial structure of remote plasma regions in rf discharges is analyzed based on a 2D model of free-fall regime discharge maintenance. Since the study is directed towards description of the magnetic filter region in the tandem plasma sources of negative hydrogen ions, hydrogen discharges are considered, with a weak magnetic field located outside the region of the rf power deposition. With the formation of different regions in the discharge—the rf power deposition region, the region with electron magnetization, the transition between them and the region behind the filter—the results display superimposed effects of nonlocal discharge maintenance without and with a magnetic field. Slight decrease of the electron temperature accompanied with strong drop of the electron density is the “pure” effect of the plasma expansion in regions without external magnetic field. Strong drop of the electron temperature accompanied with formation of a maximum of the electron density in the filter region is the “pure” effect of the plasma expansion through a magnetic field. Based on the results for the spatial distribution of the electron density and temperature obtained with shifting the position of the magnetic filter, optimization of the source regarding high yield of volume-produced negative ions is discussed.