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Penetrating radiation in the Earth's space environment can induce substantial backgrounds in electron multiplier detectors used on space instruments. Background count rates from the Magnetospheric Plasma Analyzer (MPA) on LANL satellites in geosynchronous orbit are calculated and compared to the ambient penetrating particle radiation environment to develop a basis for estimating and predicting detector background count rates throughout the magnetosphere. For several solar energetic proton events and, separately, relativistic electron events, it is shown that background counts in the largely unshielded channel electron multiplier (CEM) detectors on MPA are highly correlated with fluxes of greater than 50 MeV protons or greater than 1.1 MeV electrons. The energetic proton and electron measurements used to characterize the penetrating radiation come from the EPS instrument on the GOES satellites and the SOPA instrument on the LANL satellites, respectively. The high-energy spectrum at geosynchronous orbit during these events can be compared with the AP/AE-8 models of the inner magnetosphere fluxes. Based on the correlation between CEM background and ambient penetrating radiation at geosynchronous, we extrapolate the background response to the inner magnetosphere, a highly relevant instrument design parameter for future missions to this region.