Pitch-Angle Diffusion in the Earth’s Magnetosphere Organized by the Mozer-Transformed Coordinate System

Joseph E Borovsky,Kateryna N Yakymenko,Gian Luca Delzanno

doi:10.3389/fspas.2022.810792

Joseph E Borovsky, Kateryna N Yakymenko + Show 1 more

Open Access

https://doi.org/10.3389/fspas.2022.810792

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Abstract

In the Earth’s dipole magnetosphere finite-gyroradius effects produce a shift of the atmospheric loss cone away from the direction of the magnetic field. This loss-cone shift is theoretically described by the “Mozer transform” [Mozer, F. S. (1966). Proton trajectories in the radiation belt. J. Geophys. Res. 71:2701], which is based upon the curvature drift of particles crossing the equatorial plane. For positive ions the northern and southern loss cones both shift westward and for electrons the northern and southern loss cones both shift eastward. This loss-cone shift is part of a coordinate-system transform, with the transformed coordinates better organizing the behavior of particle orbits in the dipole magnetic field (e.g. first adiabatic invariants, mirror heights, and bounce times). In this report it is demonstrated that the transformed coordinate system also properly organizes pitch-angle diffusion. This improved organization of the diffusion is true whether the angular scattering is produced by plasma-wave scattering or by field-line-curvature (FLC) scattering. It is shown that FLC scattering and the loss cone shift are linked, so that if FLC scattering is occurring, there is a loss cone shifted away from the magnetic-field direction and the Mozer-transformed coordinates are needed.

Highlights

For energetic charged particles in the Earth’s dipole magnetic field a finite-gyroradius effect causes the atmospheric loss cone to shift away from the direction of the magnetic field (Porazik et al, 2014; Borovsky et al, 2022)
In this report it was demonstrated that the Mozertransformed coordinates organize the bounce motion of charged particles and they organize the behavior of charged particles undergoing pitch angle scattering in the dipole magnetic field, whether that scattering is caused by 1) scattering centers encountered during the bounce motion or 2) finite-gyroradius effects in the dipole
The Mozertransformed coordinate system was explored and shown to be a differential aberration of the commonly used αo-φo pitchangle gyrophase-angle coordinate system. This organization of the angular scattering indicates that there is the possibility that the Mozer-transformed coordinate system can provide a path forward to correct bounce-averaged pitch-anglediffusion calculations in the presence of the displaced atmospheric loss cone

Summary

INTRODUCTION

For energetic charged particles in the Earth’s dipole magnetic field a finite-gyroradius effect causes the atmospheric loss cone to shift away from the direction of the magnetic field (Porazik et al, 2014; Borovsky et al, 2022). When angular scattering is added along the ion’s orbit away from the equator, the aberrated circles organize the description of the scattering in equatorial pitch-angle and gyrophase-angle coordinates Dragt and Finn, 1976; Birmingham, 1984; Tagare, 1986; Jung and Sholz, 1988; Chrikov, 1987; Anderson et al, 1997; Young et al, 2002, 2008; Artemyev et al, 2015; Borovsky et al, 2022) An example of this is shown, where five protons with five different kinetic energies are launched at the geosynchronous-orbit equator with initial equatorial pitch angle of 0o. The magnitude of the loss-cone shift and the FLC scattering are still linked: independent of the value of ε the loss cone shift and the FLC scattering strength both increase monotonically as the value of ε increases

DISCUSSION

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