Fig. 2

Electron PSD measurements, resonant energy analysis and linear growth calculations. a 15-minute-averaged electron PSD versus energy measured by the HOPE spectrometer onboard the Van Allen Probe. Electrons exhibit significant anisotropies over energies of 0.05–2 keV and again at >10 keV, providing energy sources to the upper-band and lower-band chorus waves, respectively. A parallel PSD plateau is seen at ~2 keV, around the equatorial Landau resonant energies. The PSD of 4–6 keV at 18º exceeds the PSDs at 36º and 54º pitch angles, suggesting an acceleration in the parallel direction, possibly caused by Landau resonant accelerations at higher latitudes. b Minimum resonant energies for cyclotron and Landau resonances as a function of wave frequency for various wave normal angles under the plasma condition of f_pe/f_ce = 5.5. The cyclotron resonance occurs over a broad energy range from 0.22 to 24 keV, while the Landau resonant energy is within a small energy range from 1.3 to 2.1 keV. The equatorial Landau resonant energies match the observed PSD plateau. c Chorus wave growth rate (\(\gamma /\omega _{ce}\)) as a function of frequency for three selected wave normal angles, indicating that chorus waves can grow at the lower and upper bands