The global evolution of an artificially injected relativistic electron beam is simulated and examined. The study focuses on injections originating in the upper ionosphere, magnetically mirroring above the lower atmosphere where significant energy loss occurs, and so a long-lived population arises in the inner magnetosphere from this particle source. This investigation is conducted by solving the bounce-averaged relativistic kinetic equation for the electron distribution function for various L shells. It is found that the beam quickly spreads in MLT due to differential drift rates, eventually morphing into a fairly uniform shell around the Earth. Wave interactions are comparable to collisional losses in reducing the beam content. It is also found that the beam total particle loss rate is a complicated function of L and, for the chosen conditions, the total beam particle counts are 73%, 77%, and 52% of the initial count at t=24 hours after injection for L=2, 3, and 4, respectively. The loss rates at this time are ~1%/hour (of the remaining beam strength) and very slowly decreasing with time. These loss rates and other features of the beam evolution are discussed in detail. There are now four distinct stages recognized in the evolution of an injected relativistic beam: (1) the immediate loss of particles injected at pitch angles mapping to the lower thermosphere; (2) the initial loss of particles injected right next to the loss cone by collisional scattering; (3) the continuation of this collisional loss along with the spread of the beam to all local times by differential drift rates; and (4) the transformation of the beam into a fairly uniform shell covering all energies and all local times, with the loss rate mainly governed by wave scattering. Other stages may exist beyond the 1-day limit set on these simulations. While the study dwells on beam dynamics, it is also a general examination of the leading edge population next to the loss cone. This has implications for the physics of the naturally occurring radiation belt particles, as this region of phase space regulates the actual precipitation of these particles into the atmosphere. The applicability of this model for studying the natural radiation environment around the Earth is also pondered. ¿ 1999 American Geophysical Union