Relativistic electrons in the outer radiation belt: Differentiating between acceleration mechanisms

Abstract

[1] Many theoretical models have been developed to explain the rapid acceleration to relativistic energies of electrons that form the Earth's radiation belts. However, after decades of research, none of these models has been unambiguously confirmed by comparison to observations. Proposed models can be separated into two types: internal and external source acceleration mechanisms. Internal source acceleration mechanisms accelerate electrons already present in the inner magnetosphere (L < 6.6), while external source acceleration mechanisms transport and accelerate a source population of electrons from the outer to the inner magnetosphere. In principle, the two types of acceleration mechanisms can be differentiated because they imply that different radial gradients of electron phase space density expressed as a function of the three adiabatic invariants will develop. Model predictions can be tested by transforming measured electron flux (given as a function of pitch angle, energy, and position) to phase space density as a function of the three invariants, m, K, and F. The transformation requires adoption of a magnetic field model. Phase space density estimates have, in the past, produced contradictory results because of limited measurements and field model errors. In this study we greatly reduce the uncertainties of previous work and account for the contradictions. We use data principally from the Polar High Sensitivity Telescope energetic detector on the Polar spacecraft and the Tsyganenko and Stern [1996] field model to obtain phase space density. We show how imperfect magnetic field models produce phase space density errors and explore how those errors modify interpretations. On the basis of the analysis we conclude that the data are best explained by models that require acceleration of an internal source of electrons near L* $ 5. We also suggest that outward radial diffusion from a phase space density peak near L* $ 5 can explain the observed correspondence between flux enhancements at geostationary orbit and increases in ULF wave power.

Relativistic electron response to the combined magnetospheric impact of a coronal mass ejection overlapping with a high‐speed stream: Van Allen Probes observations

“…A strong indication of the occurrence of local energization is the appearance of localized peaks in radial profiles of phase space density [e.g., Green and Kivelson, 2004]. As discussed earlier (section 4), measurements from both Probe A and Probe B show such localized peaks in the PSD radial profiles on 11 November.…”

“…The peaked structure is evident for electrons with higher values of the first adiabatic invariant, , with PSD profiles at lower values showing a smoother monotonic behavior. The latter behavior is indicative of radial diffusion [Green and Kivelson, 2004;Reeves et al, 2013]. Although, as Green and Kivelson [2004] point out, such localized peaks in PSD may arise due to losses at higher L shells, that does not seem to be the case on 11 November.…”

“…The full details of the PSD calculations for electrons measured by MagEIS and REPT, including the geomagnetic field models used and quantitative estimates of uncertainties on the PSD values, are described in the supplementary materials of Reeves et al [2013]. Differentiation between radial transport and in situ modes of energization is obtained by examining the radial profiles of the PSD; energization predominantly by in situ processes results in a local "bump" in the radial profiles of the PSD, whereas radial transport leads to a monotonic increase in PSD with increasing L * [e.g., Reeves et al, 2013 andreferences therein andKivelson, 2004]. "lower" energy (see quantitative description below) electrons than the bottom row.…”

Identifying the radiation belt source region by data assimilation

“…This data set is used as input for the ensemble Kalman Filter. We made L* profile cuts for Figure 4 at the indicated arrows similar to the work by Green and Kivelson [2004].…”

“…Recently, new observations and increased monitoring evidenced that other processes play an important role as well [Reeves et al, 1998]. For a review, see the studies of Friedel et al [2002], Brautigam and Albert [2000], and Green and Kivelson [2004]. Reeves et al [2003] show that the net effect of geomagnetic activity on radiation belt dynamics is a delicate balance of acceleration, transport, and losses that can lead to either increased or decreased fluxes or to almost no changes at all.…”