Electromagnetic modeling of the beam position monitors (BPMs) for the Spallation Neutron Source (SNS) linac has been performed with MAFIA. The signal amplitudes and phases on the BPM electrodes are computed as functions of the beam transverse position using timedomain 3-D simulations with an ultra-relativistic beam. An analytical model is then applied to extrapolate the results to lower beam velocities. It is shown that while the signal phases on the individual electrodes for an off-axis beam

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... n differ from those for a centered beam by a few degrees, the phase of the summed signal from all electrodes is insensitive to the beam transverse position inside the device. Based on the analysis results, an optimal BPM design with 4 one-endshorted 60-degree electrodes has been chosen. It provides a very good linearity and sufficient signal power for both position and phase measurements, while satisfying the linac geometrical constrains and mechanical requirements.