  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.
