Sub-packet structures in EMIC rising tone emissions observed by the THEMIS probes

We report sub-packet structures found in electromagnetic ion cyclotron (EMIC) rising tone emissions observed by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) probles. We investigate three typical cases in detail. The first case shows a continuous single rising tone with obvious four sub-packets, and the second case is characterized by a patchy emission with multiple sub-packets triggered in a broadband frequency. The third case looks like a smooth rising tone without any obvious sub-packet in the FFT spectrum, while its amplitude contains small peaks with increasing frequencies. The degree of polarization of each sub-packet is generally higher than 0.8 with a left-handed polarization, and the wave direction of the sub-packets is typically field-aligned. We show that the time evolution of the observed frequency and amplitude can be reproduced consistently by nonlinear growth theory. We also compare the observed time span of each sub-packet structure with the theoretical trapping time for second-order cyclotron resonance. They are consistent, indicating that an individual sub-packet is generated through a nonlinear wave growth process which excites an element in accordance with the theoretically predicted optimum amplitude.