We employ the 2D (r-z) code Hall2De to conduct numerical simulations of the SPT-140, a Hall thruster that operates with an external hollow cathode. The simulations are informed by direct measurements of the plasma conditions in the acceleration channel that were obtained using the laser-induced fluorescence technique. We validate our simulation results with additional plasma measurements, wear test erosion rates, and performance data as a function of background pressure. The comparisons of the simulation results with thrust measurements provide insight into the longstanding question of how background pressure affects Hall thruster performance. We find that in thrusters with an external cathode changes in the thrust with varying backpressure can be partially explained by changes in the plasma density near the cathode. We argue that such changes in the density affect the voltage coupling and, eventually, the thrust. However, accounting for this mechanism alone in the simulations over-predicts the thrust measured during ground tests for backpressures less than 10 μTorr. Also, at these backpressures, the measurements showed a higher rate of change of the thrust compared to the simulations. We propose that one explanation for this discrepancy is that the acceleration region may be axially shifting downstream with decreasing backpressure. Though possible, we also recognize that such shifts are not observed in LIF measurements at the lowest pressures for which such diagnostics are possible. We discuss alternative explanations in Part II of this article.