Using invariant altitude (h_inv) for mapping of the radiation belt fluxes in the low‐altitude environment

Abstract

[1] Mapping of the radiation belt environment in the classical (B, L) invariant coordinates is rather poorly resolved at low altitudes where the SAMPEX and DEMETER missions are collecting scientific data. This lack of adequate spatial resolution at low altitudes has been pointed out since 1986. A simple solution to this standing problem is proposed in this article. We recall alternative coordinates that were proposed in the 90s to improve the spatial resolution of binning meshes and radiation belt maps in the lowaltitude region, i.e., near the atmospheric cutoff. Next, we define a new coordinate: the ''invariant altitude,'' h inv , that we recommend instead of B or other invariant drift shell coordinates like B/B 0 or a 0 , the equatorial pitch angle. In McIlwain's reference dipole, the new coordinate, h inv , corresponds to the altitude (in units of km) of mirror points of particles which have given values of B and I or L, calculated by using a geomagnetic field model like the International Geomagnetic Reference Field. The advantages and limitations of the new h inv coordinate are presented. For illustration, the distributions of the omnidirectional fluxes of electrons and protons predicted by the standard AE8 and AP8 radiation belt models are displayed using this new invariant coordinate, as well as by using alternative invariant coordinates like B/B 0 or a 0 . A set of orbits of the SAMPEX, DEMETER, and CRRES spacecraft are displayed in these different coordinate systems to illustrate the advantage of using the invariant altitude h inv to map the radiation belt environment at low altitudes.Citation: Cabrera, J., and J. Lemaire (2007), Using invariant altitude (h inv ) for mapping of the radiation belt fluxes in the lowaltitude environment, Space Weather, 5, S04007,

AE9, AP9 and SPM: New Models for Specifying the Trapped Energetic Particle and Space Plasma Environment

“…Cabrera and Lemaire 2007). For AE9/AP9/SPM the primary coordinates are: (a) the particle energy E, (b) the modified second adiabatic invariant K capturing the particle's bounce motion,…”

The Effect of Energetic Ion Dispersionless Injections on the Ring Current Dynamics

“…For proton energy density calculated from 44 to 488 keV, (d) the average energy density 5–15 min after injection is greater than the mean value in the previous 15–5 min. In addition, (e) we require that McIlwain's L value (e.g., Cabrera & Lemaire , 2007 and reference therein; McIlwain , 1961) corresponding to injection onset ( t 0 ) is greater than 3 Re, and the MLT is in the sector of 18‐6; (f) the maximum value of the SME (SME max ) from 10 min before to 30 min after proton dispersionless injection should be greater than 300 nT ( Fu et al., 2021). Moreover, (g) if there are multiple proton dispersionless injections within 30 min after t 0 , we only take into account the first proton dispersionless injection event at t 0 .…”

Proton Flux Variations During Solar Energetic Particle Events, Minimum and Maximum Solar Activity, and Splitting of the Proton Belt in the South Atlantic Anomaly

“…Figure 5 shows maps of proton flux as a function of the invariant altitude (location of the mirror points) versus magnetic latitude for November 2014 (top panels) and October 2019 (bottom panels). This coordinate system was introduced by Cabrera and Lemaire (2007) to map the radiation belt fluxes in the low‐altitude environment. Left panels correspond to west direction, right panels to east direction.…”