Volume 16, Issue 12 p. 2022-2037
Research Article
Free Access

Solar Energetic Proton Access to the Magnetosphere During the 10–14 September 2017 Particle Event

T. P. O'Brien

Corresponding Author

T. P. O'Brien

Space Sciences Department, The Aerospace Corporation, El Segundo, CA, USA

Correspondence to: T. P. O'Brien,

[email protected]

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J. E. Mazur

J. E. Mazur

Space Sciences Department, The Aerospace Corporation, El Segundo, CA, USA

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M. D. Looper

M. D. Looper

Space Sciences Department, The Aerospace Corporation, El Segundo, CA, USA

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First published: 02 August 2018
Citations: 20

Abstract

We explore the penetration of >60 MeV protons into the magnetosphere during the 10–14 September 2017 solar energetic particle event. Solar energetic particles can cause single event effects and total dose degradation in spacecraft electronics. Therefore, it is important for satellite anomaly analysis to understand how deep into the magnetosphere these particles penetrate. Whereas most studies of geomagnetic cutoffs use low-altitude data, we use data from the Relativistic Proton Spectrometer on National Aeronautics and Space Administration's Van Allen Probes, which is in a high-altitude, elliptical orbit. We determine how the penetration depends on particle energy, location, and direction of incidence. We evaluate multiple published models of the geomagnetic cutoff to determine how well these models constrain the spectrum at the location of a spacecraft inside the magnetosphere given data outside the magnetosphere. We show that, compared to cutoff models, low-altitude proton measurements are far superior for near-real-time monitoring of the geomagnetic cutoff in support of high-altitude anomaly resolution.

Key Points

  • The angular distribution of SEPs in the magnetosphere is dominated by the east-west effect
  • Geomagnetic cutoff models do not capture the idiosyncratic and dynamic particle access to a satellite's location inside the magnetosphere
  • Observed low-altitude cutoffs correlate well with high-altitude observations

Plain Language Summary

Energetic particles that originate from interplanetary space can travel into the region governed by Earth's magnetic field and cause problems for satellites, aircraft, and radio communications. Using data from National Aeronautics and Space Administration and National Oceanic and Atmospheric Administration, we analyze how particle access to a high-altitude satellite (apogee > ~2,000 km) in near-Earth space depends on particle energy and direction. We evaluate how well models and low-altitude observations perform as estimates of this access. We find potential for significant improvement in our ability to specify solar energetic particle access to high-altitude satellite orbits if we use near-real-time low-altitude observations rather than only models parameterized by global measures of geomagnetic activity.

1 Introduction

During a solar energetic particle (SEP) event, energetic electrons, protons, and heavy ions flood the heliosphere. The protons and heavy ions can adversely affect satellites (see Koons & Fennell, 2006, and references therein), and the protons contribute to radiation hazards at aviation altitudes (e.g., Mertens et al., 2010) and interfere with radio communications (e.g., Rogers et al., 2016; Sauer & Wilkinson, 2008). The Earth's magnetic field controls access of these particles to near-Earth space (Störmer, 1955). Particle access is usually described through the concept of a geomagnetic cutoff, which either specifies the minimum energy or rigidity (momentum per charge) that can reach a given location, or the deepest location in the magnetosphere that can be reached by a given energy. We will explore how these cutoffs and associated concepts may be used to understand the SEP environment at high altitudes, where the SEPs can contribute to satellite anomalies, mainly single event effects (SEEs) in which a single particle disrupts the state or function of an electronic part. Although SEEs can be caused by both heavy ions and protons, we have more extensive proton observations, and so protons will be the subject of our investigation. Fortunately, proton cutoffs apply to heavy ions at the same rigidity. Solar energetic protons can also cause total dose degradation, and can be the primary source of solar array damage for geosynchronous and some other high-altitude orbits.

The 10–14 September 2017 SEP event was unique among recent events because it included a relatively high intensity of >100-MeV protons. This makes it the first SEP event suitable for extensive study by the Relativistic Proton Spectrometer (RPS; Mazur et al., 2012) flown on National Aeronautics and Space Administration (NASA)'s Van Allen Probes (Mauk et al., 2012). Before we delve into the RPS data, however, it is necessary to review some of the background science on energetic particle access to the magnetosphere and on geomagnetic cutoffs.

1.1 Theoretical Considerations

First, we consider the theoretical argument (Smart et al., 2000; Smart & Shea, 2005; Störmer, 1955) that near-Earth space can be divided into regions to which energetic particle access from interplanetary space is allowed or forbidden. Störmer's result can be summarized in a single equation that provides the cutoff rigidity as a function of direction of incidence and location in a purely dipole field (adapted from Smart & Shea, 2005):
urn:x-wiley:15427390:media:swe20737:swe20737-math-0001(1)
where L is a dimensionless field line label, analogous to McIlwain's Lm (McIlwain, 1961), ζ is the zenith angle relative to the dipole center, θ is the azimuth angle measured clockwise from magnetic north, and λ is the magnetic latitude. R0 is an epoch-dependent vertical (ζ=0°) cutoff at the geomagnetic equator at L = 1 (i.e., at the Earth's surface, neglecting the dipole offset), and currently has a value of ~15 GV (for historical reasons, rigidity is often presented as having units of gigavolts, rather than the gigavolts per speed of light one would expect in the more recent conventions of space science). For the vertical cutoff, Störmer's equation reduces to
urn:x-wiley:15427390:media:swe20737:swe20737-math-0002(2)
which can be easily inverted to obtain a cutoff L at a given rigidity (or energy given a known species and charge state):
urn:x-wiley:15427390:media:swe20737:swe20737-math-0003(3)
For studies at low altitudes, the L parameter, which is approximately the radial distance at which the local magnetic field line crosses the magnetic equatorial plane, is often replaced by an invariant latitude, which is the magnetic latitude of that field line where it intersects the Earth's surface in a centered dipole:
urn:x-wiley:15427390:media:swe20737:swe20737-math-0004(4)

There are two major considerations that prevent a straightforward implementation of Störmer's equation for practical use: the need to account for all directions simultaneously, and the nondipolar, dynamic nature of the Earth's magnetic field. A lesser consideration is that, especially early in the SEP event, the angular and spatial distribution of the SEPs is not uniform and isotropic in the region beyond the influence of Earth's magnetic field. Taken together, these considerations lead toward a reliance on empirical models of the magnetic field, the cutoff rigidity, and the effective sharpness of the cutoff with L or Λ, all of which will be discussed in more detail later in our analysis.

1.2 Particle Trajectories

Another question worth considering is tied to the converse relationship between particles being magnetically trapped in the radiation belts and external SEP access: Is the radius of curvature of the particle's motion in the magnetic field small enough that it can complete a circle before traveling into a different region of the magnetic field? Figure 1a provides this gyroradius as a function of energy for several different L values. The figure shows that a 100-MeV proton gyrating about a center at L = 5 has a gyroradius of about 1 RE, meaning that it wanders down to L = 4 and up to L = 6 over the course of its gyromotion. A 100-MeV proton has a rigidity of about 0.5 GV, meaning it has a Störmer vertical cutoff around L = 5.5, and our example particle thus wanders outside its cutoff, or else it could have originated outside the magnetosphere. Except where noted, when we write about a particle's L value we will refer to the location at which it is measured, that is, the spacecraft location Lsc, rather than its gyrocenter location, which we will denote by Lgc.

Details are in the caption following the image
Panel (a) shows the gyroradius for protons mirroring at the magnetic equator in a dipole, for several values of the dipole field line label L. Panel (b) shows how geomagnetic cutoffs vary with L for several values of Dst, using the Leske et al. (2001) dependence. SAMPEX = Solar, Anomalous, and Magnetospheric Particle Explorer.

In the frame of the spacecraft, the large gyroradius effect manifests itself as an east-west asymmetry in the particle flux. Particles entering from the east arrive from lower altitudes, while particles entering from the west arrive from higher altitudes. Named primarily for an analogous effect seen at low altitudes (see, e.g., Lenchek & Singer, 1962; Ginet et al., 2007; Mazur et al., 2014, and references therein), the effect manifests during some parts of SEP events as substantially different fluxes observed by east facing and west facing proton telescopes at geostationary orbit (Blake et al., 1974; Rodriguez et al., 2010). The east-west effect can also be exploited to infer the local radial gradient (Buck et al., 1973) from a single observing spacecraft.

Because SEPs accessing the magnetosphere are not stably trapped, understanding their access often requires tracing their trajectories through realistic magnetic fields. Several studies have explained specific events by tracing particles from interplanetary space into event-specific simulations of the magnetosphere (Hudson et al., 1997, 2004; Kress et al., 2004, 2005, 2010; Richard et al., 2002; Weygand & Raeder, 2005). These kinds of studies are generally able to reproduce the qualitative SEP access and sometimes capture how magnetic field dynamics lead to quasi-trapped protons or even new proton belts that last for weeks or longer (Lorentzen et al., 2002; Selesnick et al., 2010). For the time being, these large-scale numerical simulations are impractical for use in satellite anomaly analysis because of the computational burden associated with running the field simulation and tracing many energetic particles through it.

A more practical approach is to pretabulate cutoffs on a spatial grid using a parameterized empirical magnetic field model. This is the approach taken by Smart and Shea (2001, 2005), who trace particles in a field model that varies only with the Kp geomagnetic index. We will return to this model later to evaluate how well it describes cutoffs observed at high altitude by RPS.

1.3 Empirical Analytical Models

Even simpler than the Smart and Shea (2005) approach is an analytical expression based on the Störmer equation but with parameters determined empirically, including additional terms for magnetic activity dependence. Multiple studies have shown empirical correlation between cutoffs and geomagnetic activity (e.g., Adriani et al., 2016; Leske et al., 2001; Mazur et al., 1999; Ogliore et al., 2001). Throughout the paper, we will rely on a hybrid cutoff model owing to Ogliore et al. (2001) and Leske et al. (2001):
urn:x-wiley:15427390:media:swe20737:swe20737-math-0005
where Λc is the cutoff invariant latitude in degrees and Dst is in nanotesla. Ogliore et al. developed the model without a Dst dependence, and Leske et al. added the Dst correction. These kinds of empirical cutoffs can be thought of as analogous to the effective cutoffs of the Smart and Shea type models that account for some of the directional structure of the cutoff. We note that Leske et al. were not presenting the Dst correction as a model in itself, but rather as a correction they needed in order to further their analysis of other details of the events they were studying. However, we will use the Leske et al. description because it has among the strongest magnetic activity dependences of the available simple analytical cutoff functions. We note that there can be substantial local time dependence in the cutoffs (Cayton et al., 2007; Fanselow & Stone, 1972; Leske et al., 2001), but we will not explicitly address those here. Figure 1b shows a set of cutoff energies versus L for differing values of the Dst index. Both Ogliore et al. and Leske et al. were analyzing low-altitude data from NASA's SAMPEX mission. A more recent analysis by Neal et al. (2013) used data from National Oceanic and Atmospheric Administration (NOAA)'s Polar-orbiting Operational Environmental Satellite (POES) vehicles. However, the Neal model has a weaker dependence on magnetic activity (via Dst or Kp indices) than Leske et al., and it only applies to protons at three specific energies. Selesnick et al. (2015) combined the Ogliore et al. and Neal et al. models into a unified Kp-dependent model of cutoff rigidity versus invariant latitude. It is telling that these studies rely heavily on low Earth orbit (LEO) data, and LEO data are the basis of the empirical models. Highly inclined LEO vehicles pass through the cutoff region 4 times per orbit, or about every 20–25 min, making LEO a convenient place to monitor cutoffs. One of the goals of our study is to determine how useful such LEO monitoring is for drawing inferences about cutoffs at high altitude for use in high-altitude satellite anomaly resolution and situational awareness.
Another aspect of cutoff modeling that has given way to empirical approaches is the shape of the cutoff with L or Λ. Because the cutoff depends on look direction, the shape of a flux profile in L or Λ is necessarily smooth compared to the idealized step function implied by the vertical cutoff formulae. Benck et al. (2016) introduced a Weibull function to capture that smoothness and defined the cutoff as the location at which the flux dropped to 10% of its free space value (L = ∞). The Weibull function can be written as
urn:x-wiley:15427390:media:swe20737:swe20737-math-0006(5)

The L0 parameter controls the location of the cutoff, the γ parameter controls the sharpness of the cutoff (higher γ means sharper), and j provides the free-space flux. We note that while Benck et al. used the 10% level, Ogliore et al. and Leske et al. used the 50% level. For satellite anomaly analysis, a level far lower than even 10% would likely be needed to exonerate SEPs as the cause of an anomaly via a SEE, because even a few percent of the free-space flux during a large SEP event would be larger than the quiescent cosmic ray flux, which represents the baseline SEE hazard.

With these preliminaries behind us, we may now begin our analysis. First, we will describe the three satellite data sets used in this paper. Next, we will explore the angular distribution observed by RPS at high altitude to gain an understanding of how to use narrow field-of-view in situ data. Then we will assess how well several cutoff models capture the cutoffs seen by RPS. Finally, we will explore how well low-altitude data can be used to infer the high-altitude cutoffs.

2 Satellite Data

We use data from three satellites: Van Allen Probes B, GOES-15, and MetOp-A (also known as MetOp-2). The Van Allen Probes were launched in August 2012 into a ~600 × 33,000-km orbit with an inclination of ~10o. The mission is made up of two identically-instrumented satellites. We note that NASA uses the acronym RBSP to reflect the mission's original designation: Radiation Belt Storm Probes. Our study uses data from the RPS instrument on the B spacecraft because a partial failure on the RPS-A sensor prior to September 2017 impacts its correction for >400-MeV proton arrival direction. The RPS-B sensor provides clean measurements of protons with energies from ~60 MeV to ~1 GeV. RPS has a 13.4o half-angle field of view, and a cylindrical detector geometry (Mazur et al., 2012). The sensor telemetry is set up to downlink details for individual particles entering the field of view, and these details are used to compute fluxes in a posteriori constructed energy channels during ground processing. A quota system throttles the rate of events captured and telemetered to the ground. Because RPS is designed to study the inner radiation belt, its telemetry is highly constrained for L > 3, where the SEPs have access. Therefore, we must compute fluxes from accumulations over several minutes to obtained accurate fluxes in this region. However, by binning the data in both energy and spin phase angle, we can resolve the energy-angle spectrum about every 10 min with reasonable accuracy.

For this study, we use the first 15 of the standard 20 RPS energy channels (which are constructed entirely on the ground from direct event data). The higher energy channels are not used in this study because their low fluxes for a relatively short duration during the event limit how much we can learn about access given RPS's limited telemetry allocation in the SEP access region. During the SEP event, the RPS apogee was just post noon, meaning RPS was taking its high-altitude measurements on the dayside of the magnetosphere. Figure 2 depicts the octagonal RBSP vehicle, which is Sun pointing and spinning at approximately 5.5 rpm. The RPS sensor is mounted on the anti-sunward deck with a field of view pointing outward, perpendicular to the spin axis. Particles entering the sensor with momentum urn:x-wiley:15427390:media:swe20737:swe20737-math-0007 at vehicle spin phase ϕ have an associated pitch angle α and gyrophase angle β relative to the magnetic field direction urn:x-wiley:15427390:media:swe20737:swe20737-math-0008, which is roughly northward throughout the near-equatorial RBSP orbit. The Relativistic Electron-Proton Telescope (REPT) on RBSP provides proton fluxes in energies ranging from ~20 MeV to >100 MeV (Baker et al., 2012; Selesnick et al., 2014), but those data are not used in this study.

Details are in the caption following the image
An illustration of the RBSP spacecraft and the Sun-Earth system with the RBSP and MetOp-A satellites. The vehicle is located at radial position urn:x-wiley:15427390:media:swe20737:swe20737-math-0009, and the RPS FOV axis is urn:x-wiley:15427390:media:swe20737:swe20737-math-0010. A particle entering the RPS sensor with momentum urn:x-wiley:15427390:media:swe20737:swe20737-math-0011 (opposite to urn:x-wiley:15427390:media:swe20737:swe20737-math-0012 at spin phase ϕ has pitch angle α and gyrophase β relative to the magnetic field urn:x-wiley:15427390:media:swe20737:swe20737-math-0013. The inset table relates the gyrophase angle to a positively charged particle's direction of motion, the RPS FOV axis, and the gyrocenter offset from the vehicle. Red and bold lines relate to coloring used in later plots. RBSP = Radiation Belt Storm Probes; RPS = Relativistic Proton Spectrometer; FOV = field of view.

Geostationary Operational Environmental Satellite 15 (GOES-15) was launched into a geostationary orbit in March 2010, and was at a longitude of ~135oW during the September 2017 solar particle event. We use two sensors from GOES-15: the energetic proton, electron, and alpha detector (EPEAD), and the high-energy proton and alpha detector (HEPAD; Boeing Satellite Systems, Inc, 2010). EPEAD consists of an east looking and a west looking sensor head. We use the top three dome detector energy channels from EPEAD, covering protons from 38 to 900 MeV. HEPAD only has one look direction, with a 34o half angle. We use the first three HEPAD proton energy channels covering 330–700 MeV (the fourth is an integral channel above 700 MeV). All six of the GOES channels we use have wide energy response, meaning it can be difficult to convert them to differential flux at a specified energy. For our purposes, we use GOES data mostly to determine the timing of the SEP event onset and the qualitative time evolution of the free space energetic proton flux. Thus, we are not concerned with obtaining absolute flux values from GOES. Attempts to harmonize the GOES fluxes to each other and to other sensors have been published and are ongoing (Jiggens et al., 2018; Rodriguez et al., 2017; Sandberg et al., 2014).

The final satellite data set we use is the medium-energy proton and electron detector (MEPED) on EUMETSAT's MetOp-A. MetOp-A was launched in October 2006. It is in a Sun-synchronous orbit at ~800-km altitude and 98.7° inclination. During the SEP event, MetOp-A had one leg of its orbit on the dayside, prenoon, and the other on the nightside, premidnight. This was the closest local time alignment with RBSP-B among the operating satellites carrying the MEPED sensor, including the POES fleet that also carries the MEPED sensor. From MEPED on MetOp-A, we use three fluxes extracted from the omni sensor heads: 25, 50, and 100 MeV. These differential fluxes are derived from a piecewise spectral fit of the four original omni, integral sensor outputs covering the range from 16 to 250 MeV (Machol, 2012; Redmon et al., 2015).

GOES and POES/MetOp provide only limited angular information. However, RPS, having a comparatively narrow field of view and being on a spinning platform, provides detailed angular information. That brings us to the first part of our analysis: the angular distribution of protons at high altitude.

3 Angular Distribution

The first issue we explore is the importance of sensor look direction on the inferred local flux environment. For anomaly resolution, one typically employs an omnidirectional flux average for two reasons: first, the full calculation accounting for the true angular distribution is often overly complex, involving spacecraft attitude as well as shielding geometry and materials; second, most radiation effects are not strongly dependent on the angle of incidence because particles incident from a variety of directions can reach the sensitive solid-state circuit volume with enough energy to do harm. Previous studies (Blake et al., 1974; Rodriguez et al., 2010) have shown that at geostationary orbit, proton flux sensors looking in opposite directions can produce measurements of SEP fluxes that differ by as much as an order of magnitude. With RPS's ability to make energy- and angle- resolved measurements, we have a unique opportunity to examine how the angular distribution behaves during a solar particle event.

Figure 3 shows GOES-15 and RBSP-B RPS data for the main part of the SEP event. Panel (a) provides the six GOES-15 channels to show the timing of the event. The EPEAD west (solid) and east (dashed) sensors agree fairly well over the course of the event, but there are times when the two sensors measure fluxes that differ by more than a factor of 2. Panels (b)–(f) show the RPS data in selected energy channels. In each panel, the vertical axis is the spin phase angle ϕ, which is 90° when particles coming into RPS along the instrument axis have pitch angles passing through α = 90° during the half of the spin when RPS is sweeping through increasing pitch angles. The spin phase is 0° at the minimum pitch angle observed over the sensor's spin, and it is 180° when the pitch angle is closest to 180°. However, unlike the pitch angle, the spin phase continues to increase after passing through 180, so that again at ϕ = 270°, α = 90°, but α is decreasing with ϕ (and time). The gyrophase angle β is indicated by black and red contours, giving β = 90° and β = 270°, respectively. The final panel of Figure 3 shows the McIlwain L value according to the Olson-Pfitzer quiet magnetic field (Olson & Pfitzer, 1977) for locally mirroring particles (α = 90°) with gyrocenters at the RBSP-B vehicle.

Details are in the caption following the image
An overview of the 10–14 September 2017 solar particle event. Panel (a) shows GOES-15 proton flux in several sensor channels as a function of time. Solid lines depict west facing EPEAD channels and HEPAD. Dashed lines indicate east facing EPEAD channels. Panels (b)–(f) shows RPS proton flux in five energy channels (colored background) as functions of time and spin phase angle (vertical axis, described in main text). Black contours indicate gyrophase of β = 90°, and red traces indicate β = 270°. The vertical color bar to the right relates color to flux. Below panel (f) there are three colored horizontal bars indicating the spans of time plotted in later figures as labeled. Panel (g) provides the McIlwain L value for locally mirroring particles with gyrocenters at the spacecraft. GOES = Geostationary Operational Environmental Satellite; EPEAD = energetic proton, electron, and alpha detector; HEPAD = high-energy proton and alpha detector; RPS = Relativistic Proton Spectrometer; RBSP = Radiation Belt Storm Probes.

Comparing panels (b)–(f) with panel (g), one can see that when L > ~3, the spin phase structure of the RPS data is smooth over most of the range of spin phase, but has a divot around ϕ = 90°, which often coincides with β = 270° (red contours). When particles are entering RPS with β = 90° their curved trajectories are bringing them from higher altitude to RPS. Conversely, when particles are entering RPS with β = 270° their curved trajectories are bringing them from lower altitude to RPS. This is the east-west effect in action and is illustrated in Figure 4a. At β = 270°, the sensor is facing east, and the particles are moving west into its aperture, coming from lower altitude. The short periods near perigee (minimum L) show a very different angular structure in Figures 3b–3f: peaks at ϕ = 90° and 270°. As noted before, both these points correspond to α = 90°, reflecting the magnetically trapped structure of the inner zone proton belt. The troughs at ϕ = 0° and 180° likewise correspond to the trapped angular distribution, which tends to zero near the atmospheric loss cones at α = 0° and 180°. In fact, the presence or absence of local minima at α = 0° and 180° is a useful way to distinguish trapped particles from untrapped ones, and the same usually also applies for minima at ϕ = 0° and 180°.

Details are in the caption following the image
Panel (a) illustrates how the finite gyroradius effect leads to different particle fluxes when viewing different directions with the RPS sensor. Lgc is the McIlwain L value of the particle's gyrocenter, whereas Lsc is the McIlwain L value for a locally mirroring particle with its gyration centered on the spacecraft. Panel (b) shows how Lgc organizes the RPS fluxes much better than does Lsc during one apogee interval. RPS = Relativistic Proton Spectrometer; RBSP = Radiation Belt Storm Probes.

Although the protons observed at RPS for L > 3 are not geomagnetically trapped, we can still organize them by their gyrocenter Lgc. Figure 4b shows how the gyrocenter Lgc does a much better job of organizing the L > 3 fluxes for an example orbit than does the spacecraft location (Lsc). The fluxes have a spread of about 2 orders of magnitude for the same value of Lsc. However, the spread is closer to a factor of 2 using Lgc. The red dots are also marked with vertical measurement error bars, at 1 σ, which are barely visible, indicating that the remaining scatter is likely not instrumental, but might be caused by temporal variation or local time anisotropy in the primary population or the cutoff.

In Figure 5, we add white contours of Lgc to a subset of the interval shown in Figure 2. The flux levels closely follow the Lgc contours throughout the event, showing that the Lgc parameter is a good organizing parameter for the L > 3 fluxes throughout the event. As we move from panels (b) to (f), the energy increases and we see how that narrows the spacing of the Lgc contours—the vehicle samples a larger range of Lgc at higher energy. The first few hours of the event show unusual evolution—perhaps a peak in flux at Lgc ~ 6. We will return to this in section 8, where we can corroborate it with LEO data.

Details are in the caption following the image
A zoomed in view of the 10 September 2017 solar particle event. The panels are the same as in Figure 3 with the following exceptions: White contours have been added to panels (b)–(f) to show the guiding center McIlwain L (Lgc), and horizontal bars in panel (g) indicate time intervals plotted in other figures as labeled. GOES = Geostationary Operational Environmental Satellite; EPEAD = energetic proton, electron, and alpha detector; HEPAD = high-energy proton and alpha detector; RBSP = Radiation Belt Storm Probes.

Figure 5 suggests that we can represent much of the angular distribution in terms of the Lgc dependence. Figure 6a shows a dial plot of RPS-B flux versus energy and spin phase angle ϕ, averaged over times when Lsc > 5.5 in one apogee traversal. We can see that at high energy, the flux is fairly symmetric around the dial plot. However, at lower energy, there is a local minimum at ϕ ~ 90°. This happens to also be where α ~ 90° and β ~ 270° (over the chosen apogee period, β ~ 270° occurs at a range of ϕ values bounded by the red dashed lines). Although particles at all energies exhibit an east-west effect, the asymmetry shown in Figure 6a reflects both that effect and the energy-dependent L profile. Higher-energy particles reach deeper into the magnetic field (have lower cutoff L) and as a result their gradient in L local to the spacecraft is smaller, meaning there is less east-west asymmetry at Lsc > 5.5 at high energies.

Details are in the caption following the image
Panel (a) provides a dial plot of the 58- to 261-MeV proton flux observed by RPS during an apogee interval for Lsc > 5.5. Clock angle is spin phase (ϕ), and radius is energy. The black dashed lines bound the range of spin phases for which β ~ 90°, and the red dashes bound the range of spin phases for which β ~ 270°. There is a local minimum flux for β ~ 270°. Panel (b) is a reconstruction of the observed flux using the average radial profile versus Lgc and the angular dependence of Lgc. Panel (c) shows that the degree of anisotropy is strongest at lower energies near β ~ 270°. RPS = Relativistic Proton Spectrometer.

We can actually model the energy angular profile by using the flux versus Lgc profiles for each energy channel and knowledge of Lgc as a function of energy and ϕ. We compute flux versus Lgc in each energy channel by averaging all points in each Lgc bin for the entire orbit. Using this approach, we can reconstruct the energy-angle dial plot, obtaining Figure 6b. It is obvious that the bulk of the energy-angle variation in the observations (Figure 6a) is simply a reflection of the finite gyroradius effect superimposed on the energy-dependent flux versus L profile. Finally, in Figure 6c, we show the observed energy-angle pattern, normalized by the spin-averaged flux at each energy. This depiction highlights the depressed flux at lower energies where β~270o. (Again, we note that this asymmetry is due the local magnetic field and is not a result of anisotropy outside the magnetosphere.) A sensor with a ~14° field of view like RPS can expect to underestimate the omnidirectional flux by as much as a factor of 4–5 if it is fixed looking in just the wrong direction (eastward).

In this part of the analysis, we have shown that the high-altitude angular distribution as a function of energy is well described by accounting for the finite gyroradius and the radial (L) gradient. Now we turn to the spatial distribution: how deep do the particles go into the magnetosphere as a function of energy, and how is the local energy spectrum affected by that depth of access?

4 High-Altitude Cutoffs

Much of the analysis of SEP access is focused on the cutoff latitude (Λ) or L value at a fixed energy. In this section, we will see how several models of that cutoff perform at the RBSP location in the RPS energy range. We begin this analysis with an overview of the event. Figure 7 shows flux versus Lgc and time for each RBSP pass through the magnetosphere. Panel (a) provides the GOES-15 measurements for context, and panel (g) provides the geomagnetic indices Dst and Kp. The SEP event was not accompanied by strong magnetic activity: minimum Dst of −50 nT, and maximum Kp of 5. This is only moderate activity, and so we should not expect to see dramatic motion of the geomagnetic cutoffs in response to it. In panels (b)–(f), we see the evolution of the SEP event at RPS: the intensity at L > ~3.5 primarily follows the rise and fall of conditions at GOES. Changes in the geomagnetic cutoff are not readily apparent but will become so later in our analysis. Colored traces provide the Ogliore et al., Leske et al., and Smart and Shea models. The Ogliore et al. model is constant, and Leske et al. is parameterized by Dst. For Smart and Shea, we used their RCUT3/CUTOFF2005 software provided by Air Force Research Laboratory, which uses precomputed tracings of cutoffs in the T89 (Tsyganenko, 1989) empirical model, which is parameterized by Kp. Smart and Shea provide nine different cutoffs in their model, and we have drawn contours at the L value for which the lowest-energy proton reaching the spacecraft from the east and west matches the RPS energy channel in each panel. We note that cutoff L value for particles arriving from the east is higher than for those arriving from the west. With only modest magnetic activity as occurred during this event, there is not a strong association between either the observed fluxes and the static Ogliore et al. cutoff or the dynamic Leske et al. or Smart and Shea cutoffs. As we will see, much of the observed cutoff variation is idiosyncratic to this particular geomagnetic storm.

Details are in the caption following the image
Another overview of the 10–14 September 2017 solar particle event. Panel (a) is repeated from Figure 3. Panels (b)–(f) show RPS proton flux versus guiding center Lgc. The color bar at right relates color to proton flux. In each channel, four cutoff values are plotted: Ogliore et al., Leske et al., and the highest and lowest from Smart and Shea. Panel (g) shows the Dst index (left axis, black) and Kp index (right axis, green). GOES = Geostationary Operational Environmental Satellite; EPEAD = energetic proton, electron, and alpha detector; HEPAD = high-energy proton and alpha detector; RPS = Relativistic Proton Spectrometer; RBSP = Radiation Belt Storm Probes.

Digging deeper, we have selected four legs of the RBSP-B orbit to plot as L profiles in Figure 8. In each case, we have fit a Weibull function to the L profile and we have marked various model cutoffs on the profile. We included all nine Smart and Shea cutoffs: the effective, lower, and upper vertical cutoff, the effective, lower, and upper east looking cutoff, and the effective, lower, and upper west looking cutoff. The effective cutoff attempts to account for the dependence of the cutoff on angle of incidence. It is important to note that in the figure, the model provides only the horizontal location for the cutoff points; the vertical location is chosen only for convenience of visual association and is not an indicator of goodness of fit. Again, we have included 1 σ RPS flux error bars, which are very small, except at the lowest fluxes. As in Figure 7, there is not much of a relationship between the L value of the cutoff models and the location where the flux versus L profile starts to drop off from the high L (free space) value.

Details are in the caption following the image
Observed RPS proton flux for four passes during the September 2017 solar particle event. Solid traces indicate observed particle flux, with 1 σ error bars. Dashed traces indicate Weibull fits. Light symbols indicate multiple cutoffs from the Smart and Shea model, while the thick symbols indicate cutoffs from Ogliore et al. and Leske et al. models. For these cutoff indicators, only the horizontal location is meaningful, with the vertical location having been chosen arbitrarily to be near the associate observed flux while also avoiding overlap of symbols. RPS = Relativistic Proton Spectrometer; RBSP = Radiation Belt Storm Probes.

Another way to look at the cutoffs is through energy spectra. Figure 9 shows energy spectra in several Lgc bins for the first full RBSP-B orbit during the event. We have drawn in lines at approximately 50% and 10% of the free space values. The cutoff models again do not give specific insight into where the spectrum will depart from the free space value at high L. We note, however, that at Lgc ~ 4.5 the cutoff phenomenon has led to an inverted spectrum (i.e., one that increases with energy). This increasing spectrum is important because the spectral inversions (i.e., deconvolutions) that are sometimes used to compute differential flux from broad or integral energy channels often assume a monotonically decreasing spectrum. Such an assumption breaks down where the cutoff creates an increasing spectrum over part of the sensor's energy response.

Details are in the caption following the image
Solid traces provide RPS spectra in several Lgc bins early in the solar particle event. Dashed traces mark approximately 50% and 10% of the free space flux. Symbols indicate cutoffs from the Ogliore et al. and Leske et al. models. The vertical position of the cutoffs is arbitrary, chosen only for visual association. RPS = Relativistic Proton Spectrometer.

Returning to the L profiles, we performed the Weibull fitting for every pass for which RPS-B had good observations of the cutoff (visually inspected to confirm). Figure 10 summarizes what the earlier figures suggested: the various model cutoffs do not capture the motion of the cutoff. In fact, the cutoff moves over a range of about 1.5 L, while the models tend to only vary by ~0.2 L or less (even though we chose Leske et al. because of its relatively strong dependence on Dst). In the figure, we have chosen to plot the 50% level from the Weibull for the 58.1 MeV channel, but we obtain similar lack of correlation for other energies and for the 10% level (not shown).

Details are in the caption following the image
Model L cutoffs versus the 50% point on the Weibull fits to observed fluxes, for all passes with accepted Weibull fits. Blue, green, and brown symbols indicate cutoffs from Smart and Shea, while the two red symbols indicate the Ogliore et al. and Leske et al. cutoff models. RPS = Relativistic Proton Spectrometer.

In Figure 11, we explore whether a fit to Dst different from that provided by Leske et al. might perform better. We plot the 50% cutoff from the Weibull fit for all the accepted passes versus Dst. We also provide a linear fit with 1 σ error bars. Our fits are considerably shallower than Leske et al. (see Figure 1b, above), and, taken together, are not indicative of a statistically significant relationship. We performed the same analysis for the 10% cutoffs as well (not shown). Between the two analyses, all the energy channels had very shallow dependence on Dst, and about half were in the wrong direction. Thus, the issue is not with the Leske et al. Dst factor being incorrect—rather, for this storm, with only modest Dst variation, the issue is simply that Dst is not a good parameter for the idiosyncratic variation of the cutoff. Because the high-altitude cutoff does vary by ~1.5 L over the course of the event, satellite anomaly forensics and situational awareness require some kind of routinely-available indicator of where the high-altitude cutoff is. For that, we turn to the routine polar LEO observations from MetOp.

Details are in the caption following the image
The observed cutoffs (symbols) versus Dst for five RPS energy channels. Solid lines provide a linear fit of L versus Dst for each energy channel. Fit errors in the legend are 1 σ. RPS = Relativistic Proton Spectrometer.

5 Comparison of High- and of Low-Altitude Cutoffs

Unlike geostationary observations, lower-altitude data, like those from RBSP and low-Earth orbit, cut through many L values routinely, providing a regular observation of the geomagnetic cutoffs during a SEP event. The MetOp series carries the MEPED sensor as described above and, together with NOAA's POES fleet, provides continuous, long-term monitoring of the polar LEO space environment. One useful feature of the LEO data is the rapid revisit time. Each vehicle makes four passes through the cutoff each orbit, leading to a revisit cadence of about 20–25 min. RPS can mimic this rapid revisit time by binning fluxes by Lgc in 10-min intervals. That is, RBSP-B uses its spin to sample flux versus Lgc, whereas MetOp-A moves through the L values over the course of its orbit.

Figure 12 shows a sequence of RPS-B and MetOp-A passes through the first several hours of the SEP event on 10 September. Panel (a) shows a series of L profiles from RPS-B, with the first one showing flux above background being at 16:35, which is corroborated in panel (b) by MetOp-A, showing no flux at 16:33 and then measurable flux 25 min later in the 16:58 pass. Both vehicles show a peak in flux near L ~ 6, consistent with the peaks noted earlier in Figure 5. These kinds of nonmonotonic signatures are thought to arise from a combination of interplanetary anisotropy in the SEP intensity and complex particle trajectories into Earth's magnetic field (Evans & Stone, 1969; Morfill & Quenby, 1971; Van Allen et al., 1971). After the first 2 hr of the event, the L profiles settle into a more typical shape that can be fit by the Weibull function. We note that the MetOp-A cutoff appears to vary more and to penetrate deeper than the RPS cutoff. This is likely because the calculation of differential energy channels from the MEPED sensor data necessarily assumes that the proton flux is isotropic, whereas the cutoff dependence on angle of incidence leads to potentially strong energy-angular structure (as in Figures 3, 5, and 6). Therefore, the MEPED fluxes may blend together particles with different cutoffs. For both vehicles, by the end of the period plotted (red) the peak flux at high L has stabilized, but the roll-off at lower L continues to evolve. To study this further, we fit the individual RPS and MetOp-A flux versus L profiles to Weibull functions.

Details are in the caption following the image
Panel (a) shows Lgc profiles inferred from the spin-resolved RPS flux data in the 58.1 MeV channel. Panel (b) shows Lsc profiles observed from the 50-MeV flux channel from MetOp on multiple passes into and out of the polar cap. In both panels, color indicates time, as indicated by the color bar at right. RPS = Relativistic Proton Spectrometer.

Figure 13a shows how the cutoffs derived from the Weibull fits to RPS and MetOp-A fluxes vary over the course of the event. There is considerable high-frequency variation in the RPS spins (blue dots) and MetOp-A passes (black, red, and green dots). But, on the timescale of RBSP passes (blue circles), the evolution is fairly smooth. We have also smoothed the MetOp-A passes with a four-point trailing average to produce an orbit-averaged cutoff (solid traces), which also evolves fairly smoothly over the course of the event. (We use a trailing average to simulate what might plausibly be done in real time.) Nonetheless, the Leske et al. model, which is representative of all the models, does not track the variation very well. It sometimes moves in the right direction at the right time, but rarely does it move by enough to match the observed variations. Figure 13b shows Dst and Kp. While neither index alone tracks all the changes in the cutoff, it appears that some cutoff variations may be correlated with one index, while other variations are correlated with the other. It may be possible to improve upon Leske et al. and models like it by fitting to both Dst and Kp (using more than just this one event, of course).

Details are in the caption following the image
Panel (a) shows cutoff L estimated several different ways. The thick blue line with circles indicates whole RPS passes, whereas the small blue dots indicate cutoffs inferred from 10-min spin-resolved Lgc accumulations. Black, red, and green dots indicate cutoffs from individual MetOp passes in each energy channel. Thin black, red, and green traces indicate four-point trailing averages of the cutoffs (i.e., orbit averages). The thin magenta line indicates the Leske et al. model cutoff evaluated at 58 MeV. Panel (b) provides the Dst (left axis, black) and Kp (right axis, green) geomagnetic indices. RPS = Relativistic Proton Spectrometer.

Figure 13a also shows that the low- and high-altitude cutoffs track each other fairly well over the course of the event. Figure 14 confirms this with a scatter plot. The 10% cutoff observed by RPS at 58 MeV is correlated (r = 0.92) with the cutoffs observed by MetOp-A at 50 MeV. Using the 25-MeV or 100-MeV channel from MetOp-A, the correlation drops to ~0.8 (not shown). Using the 50% cut off instead (not shown), the correlation drops from 0.85 at 25 MeV to 0.57 at 50 MeV to essentially zero at 100 MeV. That is, the deeper (10%) cutoff in LEO is a better indicator of the high-altitude cutoff than is the 50% cutoff in LEO. Other POES and MetOp-A vehicles have similar correlation coefficients with RPS. We also note that using the raw, rather than four-point smoothed, MetOp-A value typically reduces the correlation coefficient by about 0.2 (not shown).

Details are in the caption following the image
Cutoffs observed by RPS passes versus smoothed MetOp cutoffs. The red trace provides a linear regression. RPS = Relativistic Proton Spectrometer.

From this analysis, we conclude that low-altitude cutoff observations exhibit a robust correlation with high-altitude cutoffs, superior to the empirical parametric models based on Dst or Kp, and superior to the trajectory-tracing model in T89. A routine, near-real-time low-altitude cutoff determination would likely be very useful for assessing high-altitude cutoffs, a vital input to satellite anomaly investigations for vehicles lacking their own particle sensors. What we cannot assess in this moderate storm is how well the cutoff relationships hold up during larger geomagnetic storms (Dst < −50, Kp > 5).

6 Summary and Conclusion

We have examined >60-MeV solar energetic proton access to the magnetosphere through energetic proton observations of the 10–14 September 2017 SEP event. We have shown that, although the particles are not usually magnetically trapped, their gyrocenter Lgc is a useful organizing parameter relative to the L value at which they are observed. This finite gyroradius effect, coupled with a measured L profile, can be used to explain most of the energy-angle dependence observed at high altitude. The angular asymmetry can lead narrow field-of-view sensors to give large (factors of ~5) underestimates of the omnidirectional flux, even after fluxes outside the magnetosphere have reached isotropy. We observed that the deeper penetration of more energetic particles can lead to inverted spectra at some L values in the magnetosphere, complicating interpretation of integral energy channel data.

We have also shown that for the moderate geomagnetic activity that occurred during this SEP event, the analytical fits and trajectory tracing models of the cutoff do not describe much, if any, of the cutoff variation. However, near-simultaneous low-altitude cutoff observations are, at least for this event, strongly correlated with high-altitude cutoff variations.

A single SEP event is not a stressing test of cutoff models, but our analysis illustrates the improved utility of LEO observations for satellite anomaly assessments. We conclude that a cutoff monitor derived from polar LEO observations would likely be useful for real-time and forensic anomaly assessment for high-altitude vehicles (aside from GEO, which is adequately covered by GOES). This would, for example, extend the SEE and total dose aspects of the Spacecraft Environmental Anomalies Expert System (O'Brien, 2009), which is running live at www.swpc.noaa.gov/products/seaesrt, from its current domain of geostationary orbit to any Earth orbit. Any monitoring system built from LEO data will have to account explicitly or implicitly for the fact that LEO sensors with finite energy response and field of view will not perfectly represent cutoffs at higher altitude. Further, satellite local time, the direction of the interplanetary magnetic field, and initial solar particle anisotropy may also need to be accommodated. Additional insights may also be gained from investigation of lower-energy sensor data from RBSP and MEPED.

Acknowledgments

The authors thank S. Young for fruitful discussions and assistance in locating background literature. This work was supported by NASA Van Allen Probes science funding through JHU/APL on contract NNN06AA01C. RPS sensor data are available from the Virtual Radiation Belt Observatory at virbo.org/RBSP/RPS. Kp and Dst data are available from NASA Goddard Spaceflight Center at omniweb.gsfc.nasa.gov. POES/MetOp and GOES data are available from NOAA's National Center for Environmental Information at satdat.ngdc.noaa.gov. The authors thank R. Hilmer and AFRL Space Vehicles Directorate for providing the RCUT3/CUTOFF2005 software, which is available to the public as part of AF-GEOSpace.