Electron Acceleration in the Heart of the Van Allen Radiation Belts

See allHide authors and affiliations

Science  30 Aug 2013:
Vol. 341, Issue 6149, pp. 991-994
DOI: 10.1126/science.1237743

Local Acceleration

How the electrons trapped in Earth-encircling Van Allen radiation belts get accelerated has been debated since their discovery in 1958. Reeves et al. (p. 991, published online 25 July) used data from the Van Allen Radiation Belt Storm Probes, launched by NASA on 30 August 2012, to discover that radiation belt electrons are accelerated locally by wave-particle interactions, rather than by radial transport from regions of weaker to stronger magnetic fields.


The Van Allen radiation belts contain ultrarelativistic electrons trapped in Earth’s magnetic field. Since their discovery in 1958, a fundamental unanswered question has been how electrons can be accelerated to such high energies. Two classes of processes have been proposed: transport and acceleration of electrons from a source population located outside the radiation belts (radial acceleration) or acceleration of lower-energy electrons to relativistic energies in situ in the heart of the radiation belts (local acceleration). We report measurements from NASA’s Van Allen Radiation Belt Storm Probes that clearly distinguish between the two types of acceleration. The observed radial profiles of phase space density are characteristic of local acceleration in the heart of the radiation belts and are inconsistent with a predominantly radial acceleration process.

Radial diffusion of geomagnetically trapped electrons occurs continuously in Earth’s time-varying magnetic field. Early theories of the formation of the Van Allen radiation belts focused on betatron and Fermi acceleration processes that act when electrons are transported from the outer magnetosphere where magnetic fields are weak (<100 nT) to the radiation belts, in the inner magnetosphere, where the magnetic fields are strong (1, 2). The single-point measurements and low time resolution of early satellite observations suggested that radial diffusion could generally explain the equilibrium structure of the radiation belts and its evolution on the longer time scales (days to weeks) revealed in early satellite observations. In the 1990s, a growing network of satellites provided multipoint measurements with temporal and spatial resolutions, revealing complex structure and rapid dynamics that were difficult to explain with conventional theory.

In January 1997, a solar coronal mass ejection produced a strong geomagnetic storm and a dramatic intensification of radiation belt electron fluxes at energies up to several MeV (3, 4). Comparison of the dynamics at geosynchronous orbit [~6.6RE (RE is Earth’s radius, 6372 km) or 42,000 km geocentric distance] and in the heart of the electron belt (~4.2RE or 27,000 km) showed that the intensification of relativistic electron fluxes occurred first in the heart of the belts and on extremely rapid time scales (~12 hours) and only later and more slowly at higher altitudes. In contrast with radial diffusion theory, these observations strongly suggested an energization process operating locally in the heart of the radiation belts (3). A leading candidate for that process was proposed to be acceleration by resonant interactions between radiation belt electrons and naturally occurring electromagnetic very low frequency (VLF) (≳ 1 kHz, i.e., radio) waves (510). However, around the same time other observations (11) showed a strong correlation between radiation belt electron enhancements and the power in global ultralow frequency (ULF) waves, which are enhanced during geomagnetic storms. Subsequent studies suggested that rapid enhancements of the radiation belts could be explained by acceleration from rapid, time-varying radial diffusion driven by the strong ULF field fluctuations (1217).

Measurements of electron flux (electrons cm–2 s–1 sr–1 MeV–1) cannot distinguish between local acceleration and acceleration by radial transport because both can produce radial peaks in electron flux. However, phase space density, which is the electron flux divided by the square of the momentum, does show unique signatures for local versus radial acceleration when expressed as a function of “magnetic coordinates.” NASA’s recently launched Van Allen Radiation Belt Storm Probes (RBSP) mission was designed to make the measurements needed to distinguish whether local or radial acceleration is the primary driver behind radiation belt electron acceleration events (18). Here, we report on the radial profiles of phase space density observed during the first major radiation belt enhancement event of the RBSP mission.

In Earth’s magnetic field, the motion of electrons is constrained to “drift shells” where electrons bounce between northern and southern magnetic mirror points and drift azimuthally around Earth (Fig. 1). To distinguish between local and radial acceleration, we must express phase space density not as it is measured—as a function of energy, pitch angle, and position—but rather as a function of the magnetic coordinates, μ, K, and L*, that constrain electron motion (figs. S1 and S2). For radiation belt electrons, the quantity L* defines their radial location, as measured from the center of Earth. Radial diffusion moves electrons in L* while conserving the quantities μ and K. Because it is a stochastic process, diffusion moves electrons from regions of higher to lower phase space density. Therefore, enhanced radial diffusion from a source population at high L* can increase the phase space density at lower L*, but the gradients will still exhibit a monotonic decrease from the source or, equivalently, a monotonic increase with increasing L* (Fig. 1A). In contrast, local acceleration processes keep an electron’s position (L*) essentially constant while increasing its energy. Therefore, local acceleration processes produce increases in phase space density over a limited range of L*, which, if sufficiently strong, will lead to a local peak in the radial profile with negative radial gradients at higher L* (Fig. 1B).

Fig. 1 The geometry of the radiation belts and RBSP orbits shown to scale.

The positions of the RBSP satellites at 07:57 UT on 9 October are indicated. Also shown, in a cut-away view, is a single drift shell for electrons with 15° equatorial pitch angles starting at the position of RBSP-A at a radial distance L* ≈ 4.2. Representative magnetic field lines are plotted in light blue between the northern and southern magnetic mirror points. The radial profiles of phase space density expected from radial-diffusive acceleration (A) and local wave-particle acceleration (B) are indicted schematically.

Beginning with the January 1997 radiation belt electron event, studies have analyzed the radial profiles of phase space density and have provided growing evidence for local acceleration (4, 1922). However, those studies were limited by a number of factors, including detector limitations, high backgrounds from penetrating radiation, poor energy coverage or resolution, limitations imposed by the satellite inclination or orbital period, and limited radial coverage (23). The RBSP mission was designed specifically to overcome those limitations by providing measurements near the magnetic equator, with broad and continuous energy coverage and rapid radial cuts through the heart of the radiation belts, and simultaneous measurements from spatially separated satellites (24). The two RBSP satellites were launched on 30 August 2012 into a near-equatorial, elliptical orbit with apogee at 5.7RE.

On 9 October 2012, the twin RBSP satellites measured an intense relativistic electron acceleration event (Fig. 2). Geomagnetic storms can either intensify or deplete the fluxes of MeV electrons in the outer belt (25). A storm on 1 October strongly depleted the outer electron belt (26), and electron fluxes remained exceptionally low and fairly constant until 8 October. The fluxes of outer belt electrons continued to gradually decrease until early on 9 October, when the fluxes of MeV electrons began to rapidly increase. In many radiation belt electron acceleration events, the fluxes rise gradually over the course of a day or two. This event more closely resembles the January 1997 event in that the fluxes rose nearly three orders of magnitude in a period of less than 12 hours.

Fig. 2 An overview of the October 2012 geomagnetic storm and radiation belt electron event.

The top graph shows the flux (intensity) of 2.5 MeV electrons from the MagEIS magnetic spectrometer (30) on NASA’s twin RBSP satellites. The second graph shows the fluxes at a radial distance of L = 4.2. The bottom three graphs show solar wind speed (Vsw), the interplanetary magnetic field north-south component (IMF Bz), and the disturbance storm time index (Dst, a measure of geomagnetic storm intensity). The geomagnetic activity late on 8 October and into 9 October produced a very intense and very rapid increase in fluxes. More information on solar wind, geomagnetic, and VLF wave conditions is in the supplementary materials.

We plotted the time-dependent radial profiles of phase space density in order to look for the characteristic signatures of either radial or local acceleration (Fig. 3). In the first pass on 8 October (labeled 18:22), the RBSP-A spacecraft was outbound starting at L* = 3.6 at 17:32 UT, reaching an apogee of L* = 5.2 at 21:17 UT. Comparison with the subsequent profiles at 18:27 and 23:17 UT shows that there was little temporal evolution, and each pass can essentially be considered a snapshot of the phase space density profile.

Fig. 3 Phase space density profiles for relativistic radiation belt electrons.

Profiles were measured by the Relativistic Electron-Proton Telescope instrument (31) on 8 and 9 October. Phase space density, f, is in units of (c/cm MeV)3 where c is the speed of light. By plotting f(L*) at fixed magnetic invariants, μ = 3433 MeV/G, and K = 0.11 REG1/2, we can plot both inbound and outbound portions of the orbit for each satellite on a common basis, vastly increasing the spatial and temporal resolution relative to previous observations. We used the TS04 magnetic field model to calculate the invariants (32). Curves for RBSP-A (squares) and RBSP-B (circles) are color-coded and labeled by the time at which each satellite crossed L* = 4.2. The rapid increase in phase space density in the vicinity of L* = 4.2 and the slower, more delayed increase at higher L* produce signatures of local acceleration: a peak in phase space density with positive radial gradients at lower L* and negative radial gradients at higher L*. The average uncertainty on the calculation of phase space densities at fixed μ and K is a factor of 1.4, and the maximum uncertainty is a factor of 2 as discussed in the supplementary materials and figs. S8 and S9.

Between the passes labeled 23:17 (8 October) and 03:32 UT (9 October), the radiation belts experienced a rapid increase in phase space density that continued for the next 10 hours. The increase in phase space density is most rapid in the heart of the radiation belts, in the vicinity of L* = 4.2. In the early stages of the event, the phase space densities at higher L* (e.g., 4.8) change only slightly to produce a pronounced peak in the radial profiles. In the passes labeled 4:12 and 7:57 UT, the radial peak in phase space density and the negative gradients at high L* continue to grow. The pass labeled 3:32 UT is complicated because the magnetosphere was changing on time scales that are comparable to the transit of the RBSP-A satellite through the belt (figs. S6 and S7).

In the passes labeled 8:22 and 13:02 UT, the negative radial gradients at high L* began to smooth out even as the peak phase space density increased, indicating that, in addition to local acceleration, radial diffusion also affected the radiation belt electrons by transporting them radially outward (and inward) from the newly formed peak. From 10:22 UT on 9 October through 12 October (labeled “late times”), the phase space density profiles show very little change, which is consistent with the abrupt decrease of energy input into the magnetosphere as the IMF turned northward (Fig. 2).

As noted in previous studies (18, 20, 22), single-satellite studies of phase space density gradients are subject to some spatial-temporal ambiguity because of the finite time for a single satellite to move from one L* to another. By using simultaneous measurements of the phase space density measured at different L* by the two RBSP satellites, we can further test whether instantaneous gradients are consistent with those seen in a finite-duration satellite pass. Starting at 05:57, RBSP-A was on the inbound leg of its orbit (labeled 7:57 in Fig. 3). RBSP-A measured a negative radial gradient with phase space densities that increased from 2.2 × 10−9 at L* = 4.9 to 5.4 × 10−8 at L* = 4.2. At about 07:22, RBSP-B entered the outer electron belt moving outward (orbit labeled 8:22 in Fig. 3). RBSP-B measured a positive radial gradient with phase space densities that increased from 1.6 × 10−12 at L* = 3.4 to 6.5 × 10−8 at L* = 4.2. Starting at 07:22, the two satellites were making simultaneous observations on opposite sides of the peak (Fig. 4). From 7:22 to 8:12 UT, RBSP-A moved inward from L* = 4.5 to 4.1 and measured phase space densities went from 3.0 × 10−8 to 4.4 × 10−8. Although this is on the order of the uncertainty in the measurements, the inward-directed gradients are a smooth continuation of the gradients measured earlier. The twin RBSP measurements confirm that the radial peak in phase space density is indeed a real spatial structure and not the result of spatial-temporal aliasing.

Fig. 4 Simultaneous measurements of phase space density from RBSP-A (squares) and RBSP-B (circles).

Points are color-coded as a function of time when the two satellites were making simultaneous measurements of the radial gradients (07:22 to 08:12 UT). (Inset) The satellite orbits with RBSP-A inbound from apogee and RBSP-B outbound from perigee.

Numerical simulations (27) and other analyses (20) have shown that radial peaks in phase space density can in some cases be produced by radial diffusion in combination with a boundary condition at the outer edge of the belts that first increases to levels higher than the observed peak at lower L* then decreases to levels below it. The shortness of the time between subsequent RBSP apogee passes provides stringent constraints on such a scenario but does not disprove it. Comparison between RBSP and geosynchronous phase space densities from five geosynchronous satellites that orbit outside RBSP’s apogee and provide near-continuous monitoring of the outer boundary of the radiation belts confirms the negative radial gradient at high L*, the lack of a potential source population at the outer boundary, and the necessity of an internal local acceleration process (fig. S10).

Although it is possible that radial acceleration may dominate in other relativistic acceleration electron events (28), the RBSP measurements of phase space density profiles on 8 and 9 October show signatures of local acceleration by wave-particle interactions in the heart of the radiation belts (29). The entire acceleration took place over a period of ≈ 11 hours between 23:17 UT on 8 October and 13:02 UT on 9 October. The primary acceleration was centered at L* ≈ 4 with evidence of acceleration observed between L* = 3.5 to 4.5.

Supplementary Materials

Supplementary Text

Figs. S1 to S10

References (3344)

References and Notes

  1. We note that at lower values of μ, corresponding to electrons in the 10s- to 100s-keV energy range, the dynamics are dominated by processes such as enhanced convection and substorm injections that are important precursors to relativistic (MeV) electron enhancements.
  2. Acknowledgments: This work was supported by RBSP–Energetic Particle, Composition, and Thermal Plasma funding under NASA’s Prime contract no. NAS5-01072. All Van Allen Probes (RBSP) observations used in this study, along with display and analysis software, are publicly available at the Web site
View Abstract

Navigate This Article