  The Cosmic Ray Albedo Neutron Decay (CRAND) is believed to be the principal
mechanism for the formation of inner proton radiation belt -- at least for
relatively higher energy particles. We implement this mechanism in a Monte
Carlo simulation procedure to calculate the trapped proton radiation at the low
Earth orbits, through event-by-event interaction of the cosmic ray particles in
the Earth's atmosphere and their transportation in the magnetosphere. We
consider the generation of protons from subsequent decay of the secondary
neutrons from the cosmic ray interaction in the atmosphere and their transport
(and/or trapping) in the geomagnetic field. We address the computational
challenges for this type of calculations and develop an optimized algorithm to
minimize the computation time. We consider a full 3D description of the Earth's
atmospheric and magnetic-field configurations using the latest available
models. We present the spatial and phase-space distribution of the trapped
protons considering the adiabatic invariants and other parameters at the low
Earth orbits. We compare the simulation results with the trapped proton flux
measurements made by PAMELA experiment at low Earth orbit and explain certain
features observed by the measurement.
