# Subcritical growth of electron phase-space holes in planetary radiation belts

## TL;DR

This paper explains how electron phase-space holes can grow nonlinearly and subcritically in planetary radiation belts, contributing to the understanding of large-amplitude electrostatic structures observed by the Van Allen Probes.

## Contribution

It introduces a new mechanism for the nonlinear, subcritical growth of electron phase-space holes via momentum exchange between hot and cold electron populations.

## Key findings

- Large-amplitude electron holes can grow nonlinearly in radiation belts.
- Subcritical growth occurs through momentum exchange between electron populations.
- The mechanism explains rapid formation of electrostatic structures observed by probes.

## Abstract

The discovery of long-lived electrostatic coherent structures with large-amplitude electric fields ($1 \leq E \leq 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 $q\phi /T^c_e\simeq 10^{-2}-10^{-3}$, could result from electron interaction with large-amplitude whistlers, we demonstrate one possible mechanism through which holes can grow nonlinearly (i.e. $\gamma \propto \sqrt{\phi}$) 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.