Radiation belt modeling for spacecraft design: model comparisons for common orbits

We present the current status of radiation belt modeling, providing model details and comparisons with AP-8 and AE-8 for commonly used orbits. Improved modeling of the particle environment enables smarter space system design.

the release of AP-8 and AE-8. Importantly, we offer comparisons of these models to AP-8 and AE-8 for four different representative orbits. This information will assist model users in understanding the tools presently available and how they differ from the old standards.

A . The Standard Radiation Belt Models, AP-8 and AE-8
In order to appreciate the need for new models and to assess their potential, the strengths and limitations of the current standard models, AP-8 and AE-8, must be understood. Perhaps the biggest factor driving the continued use of these models lies in the number of years that they have been used to successfully design spacecraft. Their spatial coverage is unmatched by recent modeling efforts: AP-8 is valid from L = 1.15 to 6.6; AE-8 covers L = 1.2 to 11. The data used to develop them come from 38 satellites [16]; thus, radiation measurements have some degree of inter-instrument validation. This strength is also a source of error in the models due to the challenge of inter-calibrating the instruments. Many of the detector systems whose data were used for these models were never properly calibrated and/or did not have welldefined energy sensitivities [3].
AP-8 and AE-8 are more than 20 years old. The data used to build these models were collected between 1958 and 1979. Due to the dynamic nature of the space environment, the models may no longer portray the environment that today's space systems encounter. Importantly, the inner zone electron flux data are known to be contaminated from high-altitude nuclear-device detonations during the late 1950's and early 1960's [4].
The models must be run with the same internal geomagnetic field models used to analyze the data [5]; as a result, secular changes in the magnetic field that affect the location of the South Atlantic Anomaly (SAA) are not accounted for, resulting in incorrect positions for flux values at low altitudes. Additional low-altitude error results from the absence of eastwest asymmetry in the models; while this effect averages out in non-oriented spacecraft, it is important for missions with fixed orientations such as the International Space Station. Dyer presents MIR data highlighting this anisotropy in [6]. At low altitudes, the particle flux gradient becomes very steep due to interactions with the upper atmosphere. Daly and Evans [7] report problems with the interpolation method used in AP-8 for this region and provide an improved method of interpolation over the gradient.
Limitations of the AP-8 and AE-8 models also stem from their energy range and temporal resolution. The models do not include fluxes at plasma energies, and stop far short of covering the up to 30 MeV electrons recorded by the CRRES satellite [SI. AP-8 has an energy range of 100 keV to 400 MeV protons, and AE-8 covers 40 keV to 4.5 MeV inner zone electrons and 40 keV to 7 MeV outer zone electrons. The models are static, providing only long-term averages for solar maximum or solar minimum. This division of the cycle into two models does not necessarily parlay into a separation of maximum and minimum flux: there is evidence that the longterm fluctuation of the trapped proton environment is out of phase with the solar cycle [6]. In addition, long-term averaging removes the effects of storm injections and solar wind on flux distributions, preventing use of the models for worst-case analysis and for missions of short duration (<6 months). A clear example of this shortcoming can be found in [9], in which Mazur compares AE-8 with GOES 7 data.
The space systems of today are built using higherperformance technologies that can be more sensitive to radiation. Smaller margins of error in environment estimates will prevent costly over-design and will aid in the decision to use or forego a particular capability.

B. Currently Available Models
General information about the seven publicly available models that this paper addresses can be found in  [20].

C. Proposed Standards
While ultimately a single model of the radiation belts is desirable, the development of regional models will be pursued in the near-term. A Low Altitude Proton (LAP) model based on TPM-I and PSB97 has been proposed for standardization. TPM-I, developed with support from the NASA Space Environment Effects Program, is the result of combining elements of LATRM, a low-altitude model from polar data covering almost two solar cycles, with the Air Force Research Laboratory's CRRESPRO, a medium Earth orbit model based on the 14 months of data from the CRRES satellite. PSB97 was developed using one year of data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) satellite with support from the European Space Agency (ESA); additional SAMPEX data are available from 1992 to the present [ 171. The addition of PSB97 and data to the LAP model will extend the low altitude energy coverage to 500 MeV. POLE, a model of geostationary electrons, has also been proposed for standardization. The model is a result of the collaboration between LANL, with support from NASA's LWS Targeted Research and Technology (TR&T) Program, and ONERA. POLE is based on datasets from 13 LANL geostationary satellites covering the period 1976-200 1. In the future, the energy range of the model will likely be extended beyond the current 2.5 MeV upper limit [23].
The decision to standardize new models will be made by the Committee on Space ResearcWPanel for Radiation Belt Environment Modeling (COSPAWPRBEM); inclusion of models in this paper should not be viewed as an endorsement. Details about the PRBEM and standardization process can be found at http://www.cosparhq.ore/scistr/prbem.htm and links therein.

A. Proton Models
We have generated average flux spectra from the trapped proton models for three commonly used orbits in order to present meaningful comparisons between the models. Orbits include an International Space Station (1SS)-like low Earth orbit (LEO), a low Earth polar orbit, and an elliptical medium  Fig. 1 shows the results for an ISS-type circular low Earth orbit of 400 km altitude and 51.6' inclination during solar minimum. Both differential flux (filled symbols) and integral flux (unfilled symbols) are graphed according to model capability. The consensus of the post-AP8 models suggests that AP-8 under-predicts proton flux above 10 MeV by more than a factor of two for this orbit. Actual factor differences from AP-8 can be found in Table 2 for 1.5 MeV, 20 MeV, 60 MeV, and 100 MeV protons. In the table, the integral and differential flux predicted by AP-8 are given, along with the ratio of each post-AP-8 model flux versus the AP-8 predicted flux. When a model is not valid for a given energy value, a line is drawn through the table cell. As can be seen by the factor differences in Table 2 for energies 20 MeV and above, previously reported factor of two corrections [e.g. IO] may be too low.

1) Low Earth Orbit
For lower energies, TPM-I predicts as much as a factor of nine (at 1.5 MeV-2 MeV) less average flux than does AP-8 during solar minimum, and a factor of two less during solar maximum (see Fig. 2 and Table 2). The validity of the AP-8 model for energies below 10 MeV is uncertain [lo], [24].
Armstrong and Colborn [IO] suggest using data from the S3-3 satellite as an alternative to AP-8 for very low energy spectra.
It is notable therefore that TPM-1 's under-prediction of AP-8 for low energies is in contrast to these S3-3 data which overpredict AP-8 at low altitude [24]. Our findings are in keeping with those of the TPM-1 developer [ 191.
In Fig. 2, TPM-1 is compared to AP-8 for periods of both solar minimum (grey symbols) and solar maximum (black symbols). For 10 MeV and lower energy protons, TPM-I suggests a smaller variation of flux with the solar cycle than does AP-8. Fig. 3 shows the results for a low Earth polar orbit of 800 km altitude and 98" inclination during solar minimum. Both differential flux (filled symbols) and integral flux (unfilled symbols) are graphed according to model capability. Newer models predict a harder proton flux spectrum for this orbit than does AP-8, suggesting a factor of two or more greater flux for energies above 8 MeV. See Table 3 for comparisons at specific energies. As can be seen in Fig. 3, for energies above 100 MeV, PSB97 predicts more than a factor of five greater flux at solar minimum for this orbit.
For lower energies, TPM-1 predicts as much as a factor of nine (at 1.5 MeV) less average flux than does AP-8 during solar minimum, and a factor of seven less during solar maximum, as shown in Fig. 4 and Table 3. For this orbit, both AP-8 and TPM-I show similar variation between solar maximum and solar minimum proton flux (Fig. 4).

3) Medium Earth Orbit
Average differential proton flux was determined from AP-8, TPM-1, and CRRESPRO for an elliptical orbit of 2000 km perigee, 26,750 km apogee, 63.4" inclination, and 270" argument of perigee. CRRESPRO is valid for solar maximum only; comparisons are therefore made for this part of the solar cycle. Both TPM-I and CRRESPRO (on which TPM-I is partly based) contain models for normally quiet geomagnetic periods and for active geomagnetic periods such as the March 1991 event that occurred during the CRRES mission.
For quiet geomagnetic periods of solar maximum (Fig. 5), CRRESPRO predicts about a factor of three lower average proton flux than AP-8. The difference peaks to a factor of nine in the 15-20 MeV range. Conversely, for active periods of solar maximum (Fig. 6), CRRESPRO shows agreement with AP-8, though with a divergence in the 15-20 MeV range of up to a factor of six less flux. Table 4 provides factor differences between the CRRESPRO models and AP-8 at 1.5 MeV, 10 MeV, 20 MeV, and 60 MeV energy levels.
TPM-1 suggests an order of magnitude less flux than AP-8 for quiet periods of solar maximum (Fig. 5). The difference grows to a factor of 40 less flux at 10 MeV. For active geomagnetic periods, TPM-1 predicts lower flux by more than a factor of four for <IO MeV, and at most a factor of 20 in the 15-20 MeV range (Fig. 6). See Table 4 for factor differences with AP-8 at specific energy levels.

B. Electron Models
Average integral flux spectra for the trapped electron models were generated for two common orbits: an elliptical medium Earth orbit and a geostationary orbit (GEO).  Fig. 7 shows a comparison of the electron flux predicted by the CRRESELE Average model to that predicted by AE-8. In Fig. 8, the CRRESELE Worst-case model and FLUMIC, also a worst-case model, are compared to AE-8. CRRESELE Average model differs only by a factor of 1.5 from AE-8 for energies below 1 MeV; however, CRRESELE Worst-case model suggests flux in this energy range can be more than a factor of ten greater than that predicted by AE-8 for this orbit. Conversely, FLUMIC suggests AE-8 may be a factor of three or more too high at energies below I MeV.
For electron energies above 1 MeV at this orbit, CRRESELE Average model under-predicts AE-8 by as much as a factor of 16 (at 4 MeV). The CRRESELE Worst-case model over-predicts AE-8 by a factor of two before significantly diverging from AE-8 above 4 MeV (Fig. 8). FLUMIC hovers below AE-8 by about a factor of 2.5 before gradually converging at energies above 5 MeV.
The integral flux values predicted by AE-8 MAX for electron energy minima of 0.5 MeV, 1 MeV, 2 MeV, and 4 MeV are shown in Table 5 , along with the factor differences between the newer model predictions and AE-8.

2) Geostationary Orbit
Average integral electron flux was determined from AE-8 MAX, POLE, CRRESELE Average and Worst-case models, and FLUMIC, for a geostationary orbit of 35,790 km altitude at 82"W longitude. POLE consists of three models: Best-case, Average, and Worst-case; we show results from only the Average and Worst-case models.
The CRRESELE Average and POLE Average models are compared with AE-8 in Fig. 9 for solar maximum. Fig. IO shows the CRRESELE Worst-case, POLE Worst-case, and FLUMIC flux predictions for solar maximum compared to AE-8. At the 40 keV terminus of AE-8, POLE Average model predicts a factor of 1.5 greater flux, with POLE Worst-case model approaching a factor of 2.5 greater. For energies between 70 keV and 2.5 MeV, POLE Average model predicts less average flux by as much as a factor of five (at 1 MeV). POLE Worst-case model reduces this factor to between two and three, over a smaller energy range. See Table 6 for factor differences with AE-8 at specific energy levels.
The CRRESELE models tell a different story. The Average model under-predicts AE-8 by a factor of ten initially, then drops to as much as 690 times below AE-8 at 3.5 MeV. On the other hand, the Worst-case CRRESELE model varies within a factor of three above or below AE-8 for most of the shared energy range for this orbit.
FLUMIC, a worst-case model, under-predicts AE-8 by as much as a factor of 28 at 0.2 MeV, before coming within a factor of 3 below AE-8 at about 1.5 MeV. Both CRRESELE Worst-case model and FLUMIC predict greater average flux at 5 MeV and higher at this orbit. Once again, a table of selected energy points is provided that shows the AE-8 MAX predicted average flux along with the factors by which the newer models differ (Table 6).
At geostationary orbits, AE-8 MIN and AE-8 MAX do not differ. The proposed standard model for this region, POLE, demonstrates higher average electron flux during solar minimum than during solar maximum [23]. This result is also seen with the FLUMIC model [22]. Fig. 11 shows the POLE Average model predictions for solar minimum and solar maximum as compared to AE-8 (MAX) for the GEO orbit examined here. Based on the POLE model results, the difference between solar cycle periods becomes more pronounced with increasing electron energy.

Iv. SUMMARY
Since the release of AP-8 and AE-8, initiatives by both NASA's Living With a Star Targeted Research and Technology Program and its Space Environments and Effects Program, ESA's Technology Research Programme, and the U.S. Air Force Space Radiation Effects Program have stimulated further model development. We have examined some of these newer models with respect to AP-8 and AE-8, for specific orbits. This paper is intended to assist spacecraft designers; for this end, we have chosen commonly used orbits that lie within the bounds of each model's validity. Providing model comparisons comes with the risk that the results will be extracted from their context and used for orbits other than those to which they apply; however, as we anticipate the standardization of new models, it is important to understand how these models differ from the tools currently available.
All of the proton models evaluated suggest that during solar minimum periods at an ISS-like orbit, AP-8 under-predicts flux for protons greater than 10 MeV. For protons having less than 10 MeV of energy, TPM-1 indicates that AP-8 may overpredict the flux at solar minimum. This pattern is seen for the polar LEO used in this paper, though with 8 MeV being the crossing point. At the ME0 examined in this paper, both TPM-1 and CRRESPRO predict less flux than AP-8 during quiet geomagnetic conditions at solar maximum, for the entire shared energy range. For active geomagnetic conditions at solar maximum, CRRESPRO tends towards agreement with AP-8, though TPM-1 continues to suggest lower flux levels.
The electron flux graphs for ME0 show a murkier picture.
The CRRESELE Average model indicates a softer spectrum for solar maximum at the sampled orbit. The worst-case model, FLUMIC, suggests that AE-8 MAX over-predicts electron flux for energies less than 5 MeV. Conversely, CRRESELE Worst-case model suggests that AE-8 greatly under-predicts the worst-case electron flux below 1 MeV and above 5 MeV during solar maximum. At 82"W longitude GEO, AE-8 may over-predict the flux of electrons between 100 keV to 2.5 MeV during average solar maximum conditions. The POLE models suggest that AE-8 may under-predict electron flux at energies below 70 keV. The worst-case models do not form a consensus as to whether AE-8 under-or over-predicts electron flux during more extreme conditions of solar maximum. Finally, we note that, as expected from the literature [22]- [23], the post-AE-8 models POLE and FLUMIC demonstrate a solar cycle variation in flux for this GEO orbit, with higher flux occurring at solar minimum.

V. CONCLUSION
Accurate space radiation environment models are crucial to planning and operating missions. Models with smaller margins of error in radiation environment estimates will prevent costly over-design and will aid in the decision to use or forego a particular capability. This paper provides an overview of advances made in these efforts, including model comparisons for commonly used orbits.
At this time, we cannot make an endorsement of any particular model. The international COSPAWPRBEM will play a central role in decisions to standardize new models. Until new standards have been established, the information provided in this paper can be used to assist spacecraft designers in deciding appropriate design margins of error. 400 km altitude,         Fig. 1 1, Proposed standard POLE model predictions for solar maximum and solar minimum at 82"W longitude geostationary orbit.