A Comparison of Trapped Particle Models in Low Earth Orbit
aa r X i v : . [ a s t r o - ph . I M ] J a n A Comparison of Trapped Particle Models in Low EarthOrbit
Jakub ˇR´ıpa a,b,c , Giuseppe Dilillo d , Riccardo Campana e,f , and G´abor Galg´oczi aa Institute of Physics, E¨otv¨os Lor´and University, Budapest, Hungary b Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University,Brno, Czech Republic c Astronomical Institute of Charles University, Prague, Czech Republic d Universita di Udine, Dipartimento di Matematica, Informatica e Fisica, Udine, Italy e INAF/OAS, Via Gobetti 101, I-40129, Bologna, Italy f INFN-Sezione di Bologna, Viale Berti Pichat 6/2, I-40127, Bologna, Italy
ABSTRACT
Space radiation is well-known to pose serious issues to solid-state high-energy sensors. Therefore, radiation modelsplay a key role in the preventive assessment of the radiation damage, duty cycles, performance and lifetimes ofdetectors. In the context of HERMES-SP mission we present our investigation of AE8/AP8 and AE9/AP9specifications of near-Earth trapped radiation environment. We consider different circular Low-Earth orbits.Trapped particles fluxes are obtained, from which maps of the radiation regions are computed, estimating dutycycles at different flux thresholds. Outcomes are also compared with published results on in-situ measurements.This study is done on behalf of the HERMES-SP collaboration.
Keywords: x-ray and gamma rays, CubeSats, constellation of small satellites, radiation belts, solid-state sensors,radiation damage
1. INTRODUCTION
Thanks to features such as compactness, light-weight, small power consumption and low cost, silicon-based high-energy sensors are enabling miniaturised spacecraft to pursue ambitious scientific objectives, once reachable onlyby larger missions. However, space is an hazardous environment: the effect of space radiation lead to damageof solid-state sensors and to a consequent worsening of its performance.
1, 2
Space radiation models play a keyrole in the preventive assessment of the radiation damage and henceforth detector duty cycle, performance andlifetime.In the context of
High Energy Rapid Modular Ensemble of Satellites - Scientific Pathfinder (HERMES-SP)mission we present an investigation of the AE8/AP8 and IRENE (International Radiation EnvironmentNear Earth) AE9/AP9 models specifications of near-Earth trapped radiation environment. We consider36 different circular Low-Earth Orbits (LEO) at three different altitudes (500, 550 and 600 km) and twelveinclinations (0 ◦ , 5 ◦ , 10 ◦ , 15 ◦ , 20 ◦ , 30 ◦ , 40 ◦ , 50 ◦ , 60 ◦ , 70 ◦ , 80 ◦ and 90 ◦ ).For each simulated orbit we obtain differential and integral trapped particles fluxes, from which we computemaps of the trapped particles region and estimate duty cycles at different flux thresholds.Differences between AE8/AP8 and AE9/AP9 models are quantified. Trapped particles fluxes computed byAP9/AE9 models are found to be generally higher than its AP8/AE8 counterparts, especially at low inclinations. Further author information: (Send correspondence to J.R.)J.R.: E-mail: [email protected]
G.D.: E-mail: [email protected]
G.G.: E-mail: [email protected]
R.C.: E-mail: [email protected] he models are also compared with published results on in-situ measurements performed by the Particle Monitorinstrument onboard BeppoSAX. The outcomes of this study are used in an investigation of GAGG:Ce scintillator afterglow emission (seeRef. 12) and in a software toolkit to simulate activation background for high energy detectors onboard satellites(see Ref. 13).
2. METHODS2.1 AE8/AP8 and AE9/AP9 models
The fluxes of geomagnetically trapped electrons and protons inside the inner van Allen radiation belt contributeto the overall detected instrumental background and they are especially important when a satellite at LEO passesthrough the South Atlantic Anomaly (SAA) or polar regions.Several models describing the fluxes of the trapped particles around the Earth, based on measurements fromseveral space missions, have been developed over last decades, for example the NASA’s AE8 and AP8 modelsof trapped electrons and protons, respectively. These models are based on data from more than 20 satellitesfrom the early sixties to the mid-seventies and are available on the ESA’s SPace ENVironment InformationSystem (SPENVIS) ∗ . The SPENVIS tool is an Internet interface to models of the space environment and itseffects, developed by a consortium led by the Royal Belgian Institute for Space Aeronomy (BIRA-IASB). Themore recent AE9 and AP9 models of trapped electrons and protons are based on 33 satellite datasets from1976 to 2011, and currently are available on SPENVIS only for evaluation purposes. At variance with respectto the AE8/AP8 models, the AE9/AP9 models include the flux uncertainties due to the statistical variations,instrument errors as well as the variations due to the changing space weather. The AE9/AP9 models also providea more detailed spatial resolution.For the AE8 model we choose the MAX condition which means the solar cycle maximum. The flux of trappedelectrons is on average highest near the maximum of the solar activity. For the AP8 model we choose the MINcondition which means the solar cycle minimum. The flux of protons is on average highest near the minimumof the solar activity. Therefore, this is a conservative estimation of fluxes. For the AE8/AP8 models theMAX/MIN of the solar cycle are the only two available versions.For the AE9/AP9 models the 50 % confidence level (CL 50) and 90 % confidence level (CL 90) of fluxes werecalculated using the Monte Carlo (MC) mode with 100 runs. The MC mode accounts for the uncertainty due tothe random perturbations as well as the flux variations due to the space weather. We employed the software provided by the U.S. Air Force Research Laboratory † v1.50 to calculate the differentialand integral fluxes (flux of particles with energy higher than a given energy) of both the AE8/AP8 and theAE9/AP9 models.For the geomagnetic field, the International Geophysical Reference Field (IGRF) model for the “main” mag-netic field was used, in conjunction with the Olson-Pfitzer Quiet (OPQ77) model for the “external” magneticfield, fixed at 2020 January 01. The basic “Kepler” orbit propagator with “J2” perturbation effects was used to generate the ephemeris of asatellite with a given altitude and inclination. The “J2” perturbation accounts for long-term variations in theorbit due to oblateness of the Earth. The time sampling of the trapped particle fluxes was every 10 s with the total orbit duration of 60 days forthe time period from 2020-01-01 to 2020-03-01. In order to have a more uniform sampling of the trapped particleregions, i.e. to avoid repeat ground-track orbits, the right ascension of ascending node (RAAN) was increasedby 5 ◦ in a stepwise manner every 10 days starting from RAAN = 0 ◦ and ending with RAAN = 25 ◦ . ∗ † . TRAPPED PARTICLE MAPS Maps of the radiation regions were computed using the trapped particle models. Figure 1 shows maps of theintegral fluxes of trapped electrons for AE8 MAX model compared with the flux maps for AE9 50 % CL modelfor various low energy thresholds at 550 km altitude. Figure 2 shows maps of the integral flux maps of trappedprotons for AP8 MIN model compared with the flux maps for AP9 50 % CL model at the same altitude.
4. ORBIT AVERAGED SPECTRA
The mean fluxes averaged along the whole 60-days long trajectory have been calculated for three differentaltitudes (500, 550 and 600 km). Figure 3 shows total-trajectory-averaged differential fluxes of trapped electronsfor AE8 MAX and AE9 50 % CL models for different inclinations and comparing different altitudes. Similarly,Figure 4 shows averaged differential fluxes of trapped protons for AP8 MIN and AP9 50 % CL models.
Figure 5 compares the differential fluxes of trapped electrons for AE8 MAX, AE9 50 % CL and 90 % CL modelsand fluxes of trapped protons for AP8 MIN, AP9 50 % CL and 90 % CL models. Figure 6 shows the ratio ofthe integral fluxes given by models AE9 50 % CL / AE8 MAX of trapped electrons and the ratio of the integralfluxes given by models AP9 50 % CL / AP8 MIN of trapped protons for different altitudes and inclinations.The standard Ax8 models and the recent IRENE Ax9 models give dramatically different trapped particlefluxes, especially for low inclinations and low energies.
5. DUTY CYCLE
We define the duty cycle as the fraction of time a satellite spends in a region with particle flux lower than agiven flux threshold. From simulations of different circular orbits with different altitudes and inclinations andfrom the integral fluxes given by the trapped particle models, we computed the duty cycles for various particleflux thresholds and low-energy thresholds.Figure 7 shows a comparison of duty cycles as a function of orbital inclination for different models of trappedelectrons for low-energy threshold of 0.04 MeV and for different flux thresholds and altitudes. Similarly, Figure 8shows a comparison of duty cycles for trapped protons for low-energy threshold of 0.1 MeV.Figure 9 shows duty cycle for particle flux < − s − for different orbital inclination as a function of thelow-energy threshold for models of trapped electrons and protons at 550 km altitude.
6. IN-SITU MEASUREMENTS
Figure 10 shows a comparison of proton fluxes in SAA by AP8 MIN and AP9 Mean models with the count ratemeasured by the particle monitor (PM) instrument onboard BeppoSAX satellite at mean altitudes of 474 km,548 km and 597 km. The energy threshold for proton detections with the PM was 20 MeV. The actuallymeasured flux is somewhat in-between the predictions of both models.
7. CONCLUSIONS
The AE8/AP8 and AE9/AP9 models of near-Earth trapped radiation environment were investigated. We con-sidered 36 different circular low-Earth orbits at three different altitudes (500, 550 and 600 km) and twelveinclinations (0 ◦ , 5 ◦ , 10 ◦ , 15 ◦ , 20 ◦ , 30 ◦ , 40 ◦ , 50 ◦ , 60 ◦ , 70 ◦ , 80 ◦ and 90 ◦ ). The main results can be summarized asfollows: • AP8 MIN and AP9 models give dramatically different trapped particle fluxes. For low inclinations ( I ≤ ◦ for e − , I ≤ ◦ for p + ) and low energies ( E . − , E .
10 MeV for p + ) the AE9 and AP9 50 %CL models give up to ∼ × (for e − ) and up to ∼
40 000 × (for p + ) higher fluxes than the AE8 MAXand AP8 MIN models, respectively. For I & ◦ different models give comparable results (i.e. within thesame order of magnitude). igure 1. Integral flux maps of trapped electrons for AE8 MAX model (top panels) compared with the flux maps for AE950 % CL model (bottom panels) at 550 km altitude with low energy thresholds of 40 keV, 1 MeV and 5 MeV, respectivelyfrom left to right.Figure 2. Integral flux maps of trapped protons for AP8 MIN model (top panels) compared with the flux maps forAP9 50 % CL model (bottom panels) at 550 km altitude with low energy thresholds of 0.1 MeV, 10 MeV and 200 MeV,respectively from left to right.igure 3. Orbit averaged differential fluxes of trapped electrons for mean AE8 MAX (top panels) and AE9 50 % CL(bottom panels) models computed for altitudes 500, 550 and 600 km altitudes, respectively, from left to right and fordifferent orbital inclinations I .Figure 4. Orbit averaged differential fluxes of trapped protons for mean AP8 MIN (top panels) and AP9 50 % CL (bottompanels) models computed for altitudes 500, 550 and 600 km altitudes, respectively, from left to right and for differentorbital inclinations I .igure 5. Comparison of mean differential fluxes of trapped electrons (top panels) and protons (bottom panels) for AE8MAX and AP8 MIN and 50 % CL fluxes for AE9 and AP9 models.Figure 6. Ratio of integral fluxes of trapped electrons (AE9 50 % CL / AE8MAX) in the top panels and protons (AP950 % CL / AP8MIN) in the bottom panels for altitudes 500, 550 and 600 km, respectively from left to right, and fordifferent inclinations I .igure 7. Comparison of duty cycle as a function of orbital inclination for different models of trapped electrons forlow-energy threshold of 0.04 MeV and for different flux thresholds and altitudes.Figure 8. Comparison of duty cycle as a function of orbital inclination for different models of trapped protons for low-energythreshold of 0.1 MeV and for different flux thresholds and altitudes.igure 9. Duty cycle for particle flux < − s − for different orbital inclination as a function of the low-energy thresholdfor AE8MAX (top left), AE9 50 % CL (bottom left) models of trapped e − and AP8MIN (top right), AP9 50 % CL (bottomright) models of trapped p + .Figure 10. Comparison of trapped proton fluxes in the South Atlantic Anomaly by the AP8 MIN (top panels) and AP9mean (middle panels) models with the count rate measured by the particle monitor on the BeppoSAX satellite (bottompanels) with the energy threshold of 20 MeV for altitude of 474 km (left), 548 km (middle) and 597 km (right). Higher altitude gives higher flux. A 50 km difference in orbital altitude gives a factor of roughly 2 × difference in orbit-averaged integral flux for the same orbital inclination. • Deepest SAA passings are for I = 40 − ◦ (AP8 MIN model) or for I = 30 − ◦ (AP9 50 % CL model).Orbits with I & ◦ (for e − ) or & ◦ (for p + ) face highest average fluxes of particles (up to 6 orders ofmagnitude higher than near equator). • For e − by AE8 MAX model, typical duty cycle is 60 −
90 %, maximal at I . ◦ , minimal at I = ∼ − ◦ .For p + by AP8 MIN model, typical duty cycle is 80 −
100 %, maximal at I . ◦ , minimal at I = ∼ − ◦ .Lowering altitude by 50 km increases the duty cycle by about 2 − I and low flux thresholds since AE9 has excess of low-energy, low-flux e − near equator comparedto AE8. • The measurements from the BeppoSAX satellite indicate that AP9 likely severely overestimate the actualflux values for altitudes below 600 km and inclinations below 5 ◦ , while AP8 is a likely underestimate. ACKNOWLEDGMENTS
This work has been carried out in the framework of the HERMES-TP and HERMES-SP collaboration. Weacknowledge support from the European Union Horizon 2020 Research and Innovation Framework Programmeunder grant agreement HERMES-Scientific Pathfinder n. 821896 and from ASI-INAF Accordo Attuativo HER-MES Technologic Pathfinder n. 2018-10-HH.0. The research has been supported by the European Union, co-financed by the European Social Fund (Research and development activities at the E¨otv¨os Lor´and University’sCampus in Szombathely, EFOP-3.6.1-16-2016-00023).
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