Recovering Ion Distribution Functions: II. Gyrotropic Slepian Reconstruction of Solar Wind Electrostatic Analyzer Measurements

TL;DR

This paper introduces an advanced gyrotropic Slepian Basis Reconstruction method to accurately recover ion velocity distribution functions from limited electrostatic analyzer measurements in the solar wind, enhancing kinetic plasma analysis.

Contribution

It extends the previous SBR method by incorporating gyrotropic symmetry, enabling high-fidelity reconstruction of partially measured VDFs with limited field-of-view.

Findings

g-SBR recovers ≥90% of density with only 20% measurement

Method preserves kinetic structures and plasma moments

Three frameworks for g-SBR are introduced and benchmarked

Abstract

Velocity distribution functions (VDF) are an essential observable for studying kinetic and wave-particle processes in solar wind plasmas. To experimentally distinguish modes of heating, acceleration, and turbulence in the solar wind, precise representations of particle phase space VDFs are needed. In the first paper of this series, we developed the Slepian Basis Reconstruction (SBR) method to approximate fully agyrotropic continuous distributions from discrete measurements of electrostatic analyzers (ESAs). The method enables accurate determination of plasma moments, preserves kinetic features, and prescribes smooth gradients in phase space. In this paper, we extend the SBR method by imposing gyrotropic symmetry (g-SBR). Incorporating this symmetry enables high-fidelity reconstruction of VDFs that are partially measured, as from an ESA with a limited field-of-view (FOV). We introduce three frameworks for g-SBR, the gyrotropic Slepian Basis Reconstruction: (A) 1D angular Slepian functions on a polar-cap, (B) 2D Slepian functions in a Cartesian plane, and (C) a hybrid method. We employ model distributions representing multiple anisotropic ion populations in the solar wind to benchmark these methods, and we show that the g-SBR method produces a reconstruction that preserves kinetic structures and plasma moments, even with a strongly limited FOV. For our choice of model distribution, g-SBR can recover $\geq90\%$ of the density when only $20\%$ is measured. We provide the package \texttt{gdf} for open-source use and contribution by the heliophysics community. This work establishes direct pathways to bridge particle observations with kinetic theory and simulations, facilitating the investigation of gyrotropic plasma heating phenomena across the heliosphere.