A Physical Interpretation of Moving Sources of ELF/VLF Chorus

Recent observations on the four Cluster spacecraft of upper band chorus emissions near the magnetic equator (at magnetic latitudes between -10° and 10° and L shells ranging between L = 4 and L = 5) with the WBD instrument, have been used to estimate the dimensions of the compact source regions of ELF/VLF chorus emissions. The interpretation of frequency differences exhibited by the same chorus emissions observed on different spacecraft in terms of a differential Doppler shift, has lead to a simple model involving rapidly moving sources traveling at speeds comparable to the parallel resonant velocity of counter-streaming gyroresonant electrons. Even though the chorus source motion was discussed in early models of the generation mechanism of ELF/VLF chorus [Helliwell, 1967], no detailed model has yet been proposed which determines the source motion from fundamental physical principles. In the present paper we construct a physical model describing the rapid motion of sources of chorus waves based on the nonlinear phase bunching of gyroresonant energetic electrons by the chorus waves. We estimate the source characteristics (size, velocity, and frequency dependence) as well as the linear wave growth rate, using energetic electron flux measurements as observed by the PEACE particle instrument on Cluster for selected events in 2003. The energetic electron pitch angle distribution during these events is used to calculate the wave amplitude growth rate due to cyclotron resonance [Bell et al., 2000]. Our results indicate that typical chorus sources emit over a distance of ~6000 km along the Earth's magnetic field lines, and their velocity can reach values as high as ~20,000 km/s. The direction of motion of the source, either away or toward the Cluster spacecraft, is determined predominently by the wave amplitude growth rate and the nonlinear phase bunching time of the gyroresonant electrons.