  The Chasing All Transients Constellation Hunters (CATCH) space mission plans
to launch three types of micro-satellites (A, B, and C). The type-B CATCH
satellites are dedicated to locating transients and detecting their
time-dependent energy spectra. A type-B satellite is equipped with lightweight
Wolter-I X-ray optics and an array of position-sensitive multi-pixel Silicon
Drift Detectors. To optimize the scientific payloads for operating properly in
orbit and performing the observations with high sensitivities, this work
performs an in-orbit background simulation of a type-B CATCH satellite using
the Geant4 toolkit. It shows that the persistent background is dominated by the
cosmic X-ray diffuse background and the cosmic-ray protons. The dynamic
background is also estimated considering trapped charged particles in the
radiation belts and low-energy charged particles near the geomagnetic equator,
which is dominated by the incident electrons outside the aperture. The
simulated persistent background within the focal spot is used to estimate the
observation sensitivity, i.e. 4.22$\times$10$^{-13}$ erg cm$^{-2}$ s$^{-1}$
with an exposure of 10$^{4}$ s and a Crab-like source spectrum, which can be
utilized further to optimize the shielding design. The simulated in-orbit
background also suggests that the magnetic diverter just underneath the optics
may be unnecessary in this kind of micro-satellites, because the dynamic
background induced by charged particles outside the aperture is around 3 orders
of magnitude larger than that inside the aperture.
