Subcritical Growth of Electron Phase-space Holes in Planetary Radiation Belts

The discovery of long-lived electrostatic coherent structures with large-amplitude electric fields (1 <= E <= 500 mV/m) by the Van Allen Probes has revealed alternative routes through which planetary radiation belts' acceleration can take place. Following previous reports showing that small phase-space holes, with q phi/T-e(c) similar or equal to 10(-2)-10(-3), could result from electron interaction with large-amplitude whistlers, we demonstrate one possible mechanism through which holes can grow nonlinearly (i.e., gamma alpha root phi) and subcritically as a result of momentum exchange between hot and cold electron populations. Our results provide an explanation for the common occurrence and fast growth of large-amplitude electron phase-space holes in the Earth's radiation belts.