Understanding Non-Gaussian Chorus Wave Statistics via the Benjamin-Feir Index

We derive an extended wave action model for equatorial chorus waves, identifying a wave activity index (a version of the Benjamin-Feir index, BFI) which indicates non-Gaussian frequency spectra emerge when BFI$>$0.5. Global maps of this index indicate the night and dawn sectors ($0<{\rm MLT}<9)$ of the magnetosphere as the primary region for non-Gaussian wave statistics to emerge. Comparisons with events measured by the Van Allen probe A demonstrate good qualitative agreement whilst identifying key aspects for model refinement. A key strength of our model that our work highlights is its ability to account for the asymmetric frequency spectra characteristic of non-Gaussian chorus. This work ultimately establishes the first wave activity index that distinguishes Gaussian and non-Gaussian wave scenarios from first principles, providing the groundwork for a threshold-based quantification for use in space weather modelling.