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AP8MIN and AP8MAX Trapped Proton Models

The AP8 Trapped Proton Models are empirical models of the omnidirectional trapped proton flux in Earth's magnetosphere. The models were derived from measurements accumulated by numerous satellites in the 1960s and 1970s. [Sawyer & Vette 1976]. The AP8 models are the culmination of a series of modeling efforts undertaken by Drs. J. I. Vette and D.M. Sawyer, first at the Aerospace Corporation and later at NASA' National Space Science Data Center (NSSDC). [See Fung 1996 for a review.]

The AP8 models return trapped proton fluxes at energies of 0.1-400 MeV and at McIlwain L values between 1.15 and 6.6. These fluxes are extracted from tabulations of the integral proton fluxes as a functions of geomagnetic coordinates B (or B/B0) and L.

Although the AP8 models are now more than 20 years old, they are still the most comprehensive trapped proton models available. Due to changes in the geomagnetic field, the AP8 models no longer provide reliable maps of the geographic distribution of trapped protons. Nevertheless, comparisons with on-orbit dose and SEU observations suggest that these models generally provide omnidirectional orbit-averaged quantities which are accurate to within a factor of two. See additional information on AP8 accuracy.

The AP8 models exist in two versions:

  • AP8MIN for evaluating trapped proton fluxes near solar minimum conditions.
  • AP8MAX for evaluating trapped proton fluxes near solar maximum conditions.

AP8MAX fluxes are generally smaller: at solar maximum, increased solar UV input to the atmosphere causes the atmosphere to expand. This increased atmospheric scale height causes more trapped protons to be removed from the radiation belts, through increased energy loss and scattering in the residual atmosphere. The AP8 models do not provide any means of interpolating to intermediate points in the solar cycle.

Our implementation of the AP8 models follows the recommendations from a comprehensive review of trapped radiation models conducted by Dr. Tony Armstrong et al. of Science Applications International Corporation (; 931-468-2603), sponsored by the NASA Space Environments and Effects (SEE) Program under NASA/MSFC Contract No. NAS8-40294.

In this implementation, we have taken care to avoid errors which have caused problems in the past. In particular:

  • We interrogate the AP8 models using magnetic field maps appropriate for the epoch of the data used to build the models: - For AP8MIN (epoch 1964), we use the IGRF 1965 magnetic model. - For AP8MAX (epoch 1970), we use the USC&GS 1970 magnetic field model .
  • In determining the value of B0 needed to extract fluxes from the tabulations, the value of Earth's magnetic moment (M0) is required, where B0 = M0 RE3/L3. We determine M0 from the field model at the appropriate epoch. (Some versions of AP8 use a fixed value for M0.)

We also employ the "ESA interpolation algorithm" to extract more accurate flux values when interpolating between table entries covering regions in which the proton fluxes show strong gradients in B and L. [See Daly et al. (1996) for further details.]

The AP8 models are known to have their greatest uncertainties at low altitudes (250-1000 km and L < 1.5). Efforts to develop new low-altitude trapped proton models, using data from the TIROS/NOAA polar orbiting spacecraft, are currently underway. [See Huston et al. 1996].

Finally, there are also companion models for trapped electrons, known as AE8MIN and AE8MAX, which are not included here. Trapped electrons are important for dose-related effects but do not cause single-event effects. See further discussion of limitations of the trapped particle models included in this website.


E.J. Daly, J. Lemaire, D. Heynderickx, and D.J. Rodgers, "Problems with Models of the Radiation Belts", IEEE Transactions on Nuclear Science 43, 403-415 (1996).

S.F. Fung, "Recent Development in the NASA Trapped Radiation Models" in Radiation Belts: Models and Standards, AGU Geophysical Monograph 97, 79-91 (1996).

S.L. Huston, G.A. Kuck, and K.A. Pfitzer, "Low Altitude Trapped Radiation Model Using TIROS/NOAA Data" in Radiation Belts: Models and Standards, AGU Geophysical Monograph 97, 119-122 (1996).

D.M. Sawyer and J.I. Vette, "Trapped Particle Environment for Solar Maximum and Solar Minimum (AP8)", NSSDC Report 76-06, (1976).

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