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Magnetic fields can be used to enhance the performance and operational envelope of rf capacitive discharges for semiconductor processing. Antennas in magnetized experimental fusion devices can experience similar rf processes that lead to surface erosion and degraded antenna performance. Two-dimensional modeling is needed to understand the combined effects of production and transport in these plasmas; however, magnetized plasma is a complicated medium because of tensor rf conductivity, anisotropic transport, and the fact that rf power alone sustains the plasma. In this paper, we give results from a model originally derived for studies of magnetized fusion and helicon discharges that has been adapted to capacitive discharges and compare the results with experimental data. The two-dimensional model combines the effects of the magnetic field on the plasma’s rf properties and the bulk transport of plasma, including a sheath layer with finite thickness at the boundaries. A collisionless sheath model uses the rf fields in the sheath region, along with the density at the interface between the bulk plasma and the sheath, to determine the sheath thickness and to estimate the rectified dc potential. The driven rf fields are resolved inside the sheath region by including resistive dissipation caused by ion acceleration. These results are iterated with a model for transport of the bulk plasma to produce a global model of the sheath voltages and bulk rf plasma heating. The results at various iterative steps help isolate magnetic field effects that are caused by modification of the plasma’s rf response from transport effects that are caused by the reduced electron mobility perpendicular to the magnetic field. The magnetic field can enhance confinement for some pressure regimes and magnetic configurations. More importantly, the magnetic field can restrict the motion of electrons that are heated by the rf, localizing the nonequilibrium distribution of electron energy- and reducing the electron transport across magnetic field lines. Changes in the plasma rf response can also play a role in the behavior of the discharge by further localizing the rf power deposition in the plasma.