Fig. 9

Temporal energy variations of 360 particles under the initial conditions of case 1 (500 keV-60°), case 2 (2.1 MeV-80°), and case 3 (5.7 MeV-86°). The energy variations of the 360 particles in three cases by the interactions with the chorus wave. The top line reaching the largest energy increase at the termination of the simulation in each case represents the most successful particle discussed in Fig. 7. a The most successful electron in case 1 gained energy of \( \Delta {\text{K}} = 62.7\,{\text{keV}} \) by the interactions with eight wave subpackets. The energy increase per subpacket, therefore, is 7.84 keV assuming a uniform gradient of the energy increase. b The energy increase of the most successful electron in case 2 is 133.5 keV through interactions with seven subpackets, hence the energy gain per subpacket is calculated as \( 19.1\,{\text{keV}} \). c Similarly, the energy increase of the most successful electron in case 3 is 154.4 keV through interactions with seven subpackets and the energy gain per subpacket is \( 22.1\,{\text{keV}} \)