  The Chasing All Transients Constellation Hunters (CATCH) space mission is an
intelligent constellation consisting of 126 micro-satellites in three types (A,
B, and C), designed for X-ray observation with the objective of studying the
dynamic universe. Currently, we are actively developing the first Pathfinder
(CATCH-1) for the CATCH mission, specifically for type-A satellites. CATCH-1 is
equipped with Micro Pore Optics (MPO) and a 4-pixel Silicon Drift Detector
(SDD) array. To assess its scientific performance, including the effective area
of the optical system, on-orbit background, and telescope sensitivity, we
employ the Monte Carlo software Geant4 for simulation in this study. The MPO
optics exhibit an effective area of $41$ cm$^2$ at the focal spot for 1 keV
X-rays, while the entire telescope system achieves an effective area of $29$
cm$^2$ at 1 keV when taking into account the SDD detector's detection
efficiency. The primary contribution to the background is found to be from the
Cosmic X-ray Background. Assuming a 625 km orbit with an inclination of
$29^\circ$, the total background for CATCH-1 is estimated to be
$8.13\times10^{-2}$ counts s$^{-1}$ in the energy range of 0.5--4 keV. Based on
the background within the central detector and assuming a Crab-like source
spectrum, the estimated ideal sensitivity could achieve $1.9\times10^{-12}$ erg
cm$^{-2}$ s$^{-1}$ for an exposure of 10$^4$ s in the energy band of 0.5--4
keV. Furthermore, after simulating the background caused by low-energy charged
particles near the geomagnetic equator, we have determined that there is no
need to install a magnetic deflector.
