Energization of electrons at synchronous orbit by substorm-associated cross-magnetosphere electric fields

The time variation of the flux of energetic electrons arriving at synchronous orbit subsequent to a sudden enhancement of a uniform cross-magnetosphere electric field has been calculated by using adiabatic theory and a model time-independent magnetic field. The initial (t = 0) particle distribution was taken to be spatially uniform within the region from which particles are convected to synchronous orbit in 1 hour and was described by a power law in energy for high energies (>50 keV) and as a Maxwellian with a temperature of 1 keV for lower energies. The trajectories of particles of energy W and pitch angle α observed at a given position at time t were followed backward in time to determine their initial (t = 0) energies and pitch angles. Liouville's theorem was then invoked to predict the flux at the desired position and time. As the model does not allow for a time-varying magnetic field, which is known to accompany substorm activity, the predictions have been compared with observations of substorm-associated particle injections during periods of relatively steady local magnetic fields. The model successfully reproduces many of the qualitative changes observed by ATS 1 in the > 50-keV electrons during magnetospheric substorms. In particular, the predicted rapid flux increases in the midnight to dawn quadrant associated with a marked softening of the energy spectrum are observed. The observed energy-dependent delay in the onset of flux enhancements, which is an increasing function of local time, is also predicted. This delay has previously been adduced as evidence that newly accelerated particles are injected near local midnight and then drift in local time. However, the present calculation, which allows continuous acceleration along the particle trajectory, also predicts this delay, which results from the energy dependence of particle drift velocities. The pitch angle dependence of the particle energization depends on the magnetic field model used for the calculation. For a dipole field the model predicts a preferential enhancement of the flux of particles near 90° pitch angle in the morning hours. This may explain the correlation observed between energetic electrons at ATS 1 and precipitating electrons without requiring a local acceleration mechanism. For lower-energy (<20-keV) plasma a marked increase in energy flux accompanied by rapid heating of the plasma in the region near midnight is predicted. This result is consistent with ATS 5 observations. Thus many features of the model which assumes injection of particles in a spatially localized region at the onset of a substorm are present in a model in which a sudden increase in the cross-magnetosphere electric field affects a spatially uniform population of particles. This ambiguity must be considered in interpretation of substorm-associated particle measurements. A complete description of the response of particles to substorms must include the effect of time-varying magnetic fields and possible nonadiabatic acceleration and must also incorporate the response of the particles to the enhancement of large-scale electric fields.