Relativistic effect on substorm particle injections

Injections of high-energy particles to the inner magnetosphere have been regarded as one of the indicators of a substorm onset. The ERG, GOES-15 and GOES-13 spacecraft observe the injection of high-energy electrons associated with the substorm event initiating on Apr. 5, 2017 near geosynchronous orbit. The ERG satellite observes the nearly-dispersionless injection and the subsequent drift echoes while the GOES-15 and GOES-13 capture the dispersion features of the drift echoes. Assuming that a substorm-associated electromagnetic pulse propagates earthward, motions of the high-energy electrons are analyzed in the combined electric and magnetic fields. We improve the previous transport model by considering the relativistic effect on the electron calculations. Considering the relativistic effect, the particle drift motion, the adiabatic invariant and particle magnetic moment differ from the non-relativistic ones. Our simulations successfully reproduce the features of the nearly-dispersionless injection and the subsequent drift echoes observed by the three satellites. We discuss the differences among the results of spacecraft observations, non-relativistic calculations and the relativistic ones.