The rapid development of X-ray astronomy has been made possible by widely deploying X-ray focusing telescopes on board many X-ray satellites. Geant4 is a very powerful toolkit for Monte Carlo simulations and has remarkable abilities to model complex geometrical configurations. However, the library of physical processes available in Geant4 lacks a description of the reflection of X-ray photons at a grazing incident angle which is the core physical process in the simulation of X-ray focusing telescopes. The scattering of low-energy charged particles from the mirror surfaces is another noteworthy process which is not yet incorporated into Geant4. Here we describe a Monte Carlo model of a simplified wide-angle X-ray focusing telescope adopting lobster-eye optics and a silicon detector using the Geant4 toolkit. With this model, we simulate the X-ray tracing, proton scattering and background detection. We find that: (1) the effective area obtained using Geant4 is in agreement with that obtained using Q software with an average difference of less than 3%; (2) X-rays are the dominant background source below 10 keV; (3) the sensitivity of the telescope is better by at least one order of magnitude than that of a coded mask telescope with the same physical dimensions; (4) the number of protons passing through the optics and reaching the detector by Firsov scattering is about 2.5 times that of multiple scattering for the lobster-eye telescope.
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