Fig. 10

Histograms of the final energy levels of 360 test particles in case 1 (500 keV-60°), case 2 (2.1 MeV-80°), and case 3 (5.7 MeV-86°). a Histogram in case 1. About one-third of the particles are accelerated by about 20 keV (energy gain by a few subpackets). Rest of the particles also gain energies less or more than 20 keV depending on the number of the wave subpackets that each particle is entrapped by. b Histogram in case 2, which forms a distribution with the first peak at \( \Delta {\text{K}} \approx 10\;{\text{keV}} \) (energy gain by less than a single subpacket). The second peak is at \( \Delta {\text{K}} \approx 50\;{\text{keV}} \) (energy gain by a few subpackets). c Histogram in case 3, which forms a distribution with the first peak at \( \Delta {\text{K}} \approx 10\;{\text{keV}} \) (energy gain by less than a single subpacket). The second peak is at \( \Delta {\text{K}} \approx 50\;{\text{keV}} \) (energy gain by a few subpackets). The third peak is at \( \Delta {\text{K}} \approx 100\;{\text{keV}} \) (energy gained by four or five subpackets). These distributions indicate that not only a small fraction of successful particles, but also many other particles can be accelerated with various degrees of efficiency