Omnidirectional Trapped Proton Fluxes

The AP8 Models provide omnidirectional trapped proton fluxes, which means that the fluxes are averaged over the entire range of arrival directions, covering 4p steradians.

However, it is important to note that omnidirectional does not imply isotropic, that is, having the same flux arriving from all directions.

In fact, the low-altitude trapped proton flux is highly anisotropic, with the flux concentrated about a plane which is perpendicular to the local magnetic field line.

In addition, there is also the so-called "east-west effect", by which more protons arrive from westerly directions than from easterly directions. This anisotropy arises because of energy loss in the residual high-altitude atmosphere. Protons arriving from the west have trajectories which gyrate about a point located above the observation point and thus encounter less residual atmosphere. Protons arriving from the east, on the other hand, have trajectories which gyrate about a point located below the observation point and thus encounter more residual atmosphere.

Anisotropies are more pronounced at high energies, where the protons have larger gyroradii and hence sample larger ranges of atmospheric density. Anisotropies also decrease with increasing altitude, where atmospheric density gradients are smaller.

For many spacecraft in low-Earth orbits, in which spinning and random spacecraft orientations wash out the proton anistotropies, directionality in the trapped proton flux is generally ignored and these omnidirectional fluxes are used for radiation-effect calculations. However, neglecting anisotropies may not be a good approximation for orientation-stabilized spacecraft.

For more information on trapped proton anisotropies, see

• J.W. Watts, T.A. Parnell, and H.H. Heckman, "Approximate Angular Distribution and Spectra for Geomagnetically Trapped Protons in Low-Earth Orbit", Proceedings of the High-Energy Radiation Background in Space Conference, AIP Conference Proceeding 186, AIP, New York (1989).
• 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).