An Automatic Maximum Entropy Based Wave Distribution Function (AME‐WDF) Method and Its Application on RBSP Data

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Abstract
Accurate determination of the wave propagation direction is essential for understanding wave–particle interactions in space plasmas as well as the source and propagation characteristics of waves. Traditional wave normal angle (WNA) analysis methods rely on the plane‐wave assumption and cannot describe realistic wave fields with a distribution of propagation directions, while existing wave distribution function (WDF) methods are often unstable when applied to spacecraft observations and require manual parameter tuning, limiting their practical applicability on large data sets. In this work, we develop a fully automatic maximum entropy based wave distribution function (AME‐WDF) method that enables stable and accurate inference of WDFs from observed power spectra without manual supervision. The method introduces a modified accuracy metric, an adaptive leap‐frog kernel number update scheme, and an efficient Discrete Region based initial guess generation procedure, which together ensure convergence, robustness, and automation. Tests on artificial data demonstrate excellent reconstruction performance, accurately reproducing wave propagation structures while preserving the total energy with low errors. Application to chorus wave observations from the Van Allen Probes reveals complex multi‐peak and non‐plane‐wave propagation structures that cannot be resolved using traditional WNA analysis methods. By enabling reliable and automatic reconstruction of realistic wave propagation direction distributions beyond the plane‐wave approximation, the AME‐WDF method provides a powerful tool for large‐scale statistical analyses of spacecraft wave observations and enables more accurate characterization of wave source, propagation, and wave–particle interaction processes in planetary space plasmas.

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