Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

Abstract

AbstractThe behavior of energetic particles in the Earth's dipole and stretched magnetic‐field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic‐field direction and on non‐adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic‐field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the “Mozer transform” described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch‐angle/gyrophase‐angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss‐cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient‐curvature drift) breaks down and the “central trajectory” theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss‐cone shift. By comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring‐current ions is significantly modified during geomagnetically active times.