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APEXRAD

APEXRAD is a new low-altitude dose model for solar minimum, developed at the USAF Phillips Laboratory. It is an empirical model, based on direct measurements from the APEX satellite (70o inclination, 362 km perigee, 2544 km apogee) in 1994-1996. APEXRAD results should be significantly more accurate than those based on the AP8MIN/AE8MIN models, which are outdated and known to have limited accuracy at low altitudes.

For more information on APEXRAD, see:

M.S. Gussenhoven et al. "APEXRAD: Low Altitude Orbit Dose as a Function of Inclination, Magnetic Activity, and Solar Cycle", IEEE Transactions on Nuclear Science 44, 2161-2173 (1997).

The APEXRAD code runs on a PC; it is not presently available over the WWW. Users interested in obtaining a copy of APEXRAD are instructed to contact Dr. E.G. Mullen by mail [Geophysics Directorate, Phillips Laboratory, Hanscom AFB, MA 01731 USA], by e-mail [mullen@plh.af.mil], or by FAX [617-377-3160].

The CREME/TRP software is not recommended for dose calculations (see limitations), especially since the CREME software does NOT include trapped electrons. Nevertheless, as a test of the AP8MIN implementation in CREME/TRP, we compared dose predictions from APEXRAD and from CREME96/TRP. The tables below show these comparisons for various orbits and depths of shielding.

  • The CREME results were calculated using the TRP routine to determine the orbit-integrated proton flux, the TRANS module to transport through Al shielding, and the DOSE module to convert the proton flux into a dose value.
  • The APEXRAD results shown below were read from the figures given in the above-cited paper and then multiplied by two, since the APEXRAD doses are for a hemispherical acceptance (2-pi steradians) and the CREME calculations are for a spherical (4-pi steradians) acceptance.

Discrepancies can be very large for light shielding (the "no shielding limit"), where the trapped electrons (included in APEXRAD but neglected in TRP) dominate.

In most other cases, AP8MIN predicts a dose which is only ~50-70% of that predicted by APEXRAD. Part of this discrepancy may also be due to energetic trapped electrons. However, the discrepancy primarily reflects the systematic error in the AP8 model at low-altitudes:

  • Comparable discrepancies have been reported in comparisons between AP8/AE8 predictions and dose measurements on LDEF and aboard the Space Shuttle.
  • The AP8 models also typically underpredicts SEU-rates in low-altitude Earth orbits by a similar factor. [See Figure 7 of E.L. Petersen, IEEE Trans. Nucl. Sci. 44, 2174-2187 (1997).]
Table 1: Orbit: 70o Inclination, 1000 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 2.6 E+5 5.60 E+4 0.22
82 mils Al 3600 1846 0.51
232 mils Al 2000 1266 0.65
457 mils Al 1600 958 0.59
Table 2: Orbit: 70o Inclination, 500 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 1.4 E+3 4468 0.32
82 mils Al 200 122 0.61
232 mils Al 140 88.5 0.63
457 mils Al 80 68.4 0.85
Table 3: Orbit: 70o Inclination, 300 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 3600 340 0.09
82 mils Al 40 7.1 0.18
232 mils Al 16 5.0 0.31
457 mils Al 10 3.7 0.37
Table 4: Orbit: 35o Inclination, 1000 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 5.0 E+5 2.60 E+4 0.05
82 mils Al 5200 3746 0.72
232 mils Al 4000 2576 0.64
457 mils Al 3600 1950 0.54
Table 5: Orbit: 35o Inclination, 500 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 2.2 E+4 931 0.04
82 mils Al 360 261 0.73
232 mils Al 300 201 0.67
457 mils Al 180 159 0.88
Table 6: Orbit: 35o Inclination, 300 km Altitude
Shielding APEXRAD Dose (rad/year) TRP/AP8MIN (rad/year) Ratio: AP8MIN/APEXRAD
No Shielding Limit 2000 29.3 0.014
82 mils Al 24 13.4 0.56
232 mils Al 20 11.0 0.55
457 mils Al 16 8.8 0.55
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