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Modeling of a crossed pulser-sustainer discharge in the presence of a transverse magnetic field is used to obtain insight into the kinetics of a low-temperature magnetohydrodynamics (MHD) nitrogen plasma. Ionization in the discharge is produced by repetitive high-voltage nanosecond-duration pulses, while the low-voltage DC sustainer discharge couples power to the plasma between pulses. Model predictions are compared with the experimental sustainer discharge current, both without and with magnetic field, showing a satisfactory agreement. At low DC voltages (below the cathode voltage fall UC), the calculations show that the entire sustainer discharge, including the cathode layer, remains nonself-sustained and that the electric field does not penetrate into the plasma, which results in a very low sustainer current. This demonstrates that MHD power generation in low-temperature plasmas with MHD open voltages that are below the cathode fall is not feasible. At higher voltages (UDC > UC), when the cathode layer becomes self-sustained, the sustainer current grows approximately linear with the DC voltage. This occurs because the applied DC field does not produce any additional ionization in the plasma that is outside the cathode layer. In the presence of a magnetic field, the sustainer current is significantly lower than the current without a magnetic field, which is due to the Hall effect. At UDC > UC, the model predicts a significant electron and ion drift in the EtimesB direction due to the Lorentz force. Charge separation that is induced by the disparity in electron and ion mobilities also causes the entire plasma to shift in the EtimesB direction, which is approximately at the ion slip velocity. The estimated neutral flow velocity change due to a collisional momentum transfer from the charged to the neutral species in the plasma is consistent with the prediction of quasi-1-D phenomenological MHD equations, - as well as with the previous experimental results in a low-temperature MHD wind tunnel.