A geometric factor calculation method based on the isotropic flux assumption

One of the instruments onboard the China Seismic Electromagnetic Satellite （CSES） is the Low Energy Particle Detector （LEPD）. The primary objective of LEPD is to provide measurements of the fluxes, energy spectra and pitch angles of 100 keV to 10 MeV electrons and protons from 2 to 50 MeV in the Earth＇s magnetosphere. The geometric factor is one of the principle parameters of a detector, which converts the physical quantity-count rate to the particle quantity-flux. In this paper, we calculated the geometric factor of LEPD via computer modeling of an isotropic radiation environment. It was first demonstrated that the radiation intensity related should obey a cosine-law, then a general sampling method of generating this distribution via GPS of GEANT4 was explained. Furthermore, combined with flux normalization, a comparison of the geometric factor calculation of a set of 2-layer detectors with different shapes （cylinder, truncated cone and rectangle） was performed. Results show a generally good agreement between simulation and analytical calculations for the cylinder and truncated cone detectors, and the result of the rectangular one, for which there is no accurate analytical formula, is consistent with the previous simulated results by others. As a practical instance of the 2-layer rectangle detector, the geometric factor of LEPD is 10.336±0.036 m cm2·sr for 10 MeV proton and 8.211±0.032 m cm2·sr for 8 MeV electron.