Rigidity Cutoff Calculations:

Cosmic rays reaching the top of the atmosphere have to penetrate through the geomagnetic shield, which prevents charged particles below a certain energy entering the atmosphere by deflecting them away from the Earth, an effect known as rigidity cutoff. So the determination of the rigidity cut-off at the given location and time is one essential component of a model for cosmic rays at the top of the atmosphere. A cosmic ray trajectory tracking and rigidity cut-off calculation code MAGCOS based on the Geant4 toolkit has been developed [1]. It is capable of computing the rigidity cut-offs at a user-defined location, time and direction of incidence. Various inner field models, such as the latest IGRF[2], and outer field models, such as the Tsyganenko2001[3], can be used. The use of a dynamic outer field model makes this code different from the widely used Shea and Smart calculations [4], as the actual rigidity cut-off at a given time is highly dependent on the geomagnetic field condition (Kp index) at the time [5], as shown in Example 2 .

The calculation of the rigidity cut-off at a given location and time for one geomagnetic condition takes a few seconds of CPU time on a fast PC. This is fast enough for simple applications of MAIRE involving the calculation of rigidities at a few locations only. For applications in radiation dose calculations following a flight path, which may consist of hundreds or even thousands of points, it can be a significant computation task. It is even more of a problem when several geomagnetic conditions may have to be considered. To speed up this process for such applications we have pre-calculated a large number of rigidity maps at the top of the atmosphere (i.e. 100 km in our model) for different epochs and geomagnetic conditions. These precalculated data come in the format of a set of 49 maps at 5 ×5 resolutions for the 1950, 1960, 1970, 1980, 1990, 2000, 2005 epochs, and for each epoch maps are determined for different Kp indices (0 - 6+). Example 3 shows such a map based on the geomagnetic field models of IGRF and Tsyganenko89. It took ~10 hrs CPU time on an Athlon 3000+ machine to produce a single map. With these pre-calculated maps, the required rigidities can be quickly calculated by interpolation between locations and epochs.

Although MAGCOS is capable of calculating the angular-dependent cutoffs, currently only a vertical cutoff is applied in MAIRE for performance reasons.

The rigidity calculation capability of MAIRE is offered as an independent tool, Single Point Rigidity Calculation, so the user can determine the rigidity cut-off at a given location, time and geomagnetic condition.


[1] Desorgher, L., MAGNETOCOSMICS Users Manual. 2003. http://reat.space.qinetiq.com/septimess/magcos
[2] http://www.iugg.org/IAGA/iaga_pages/pubs_prods/igrf.htm
[3] http://nssdc.gsfc.nasa.gov/space/model/magnetos/data-based/modeling.html
[4] Smart, D.F., and Shea, M.A., Calculated cosmic ray cutoff rigidities at 450km for epoch 1990, Proc. 25th ICRC, 2, 397-400,1997.
[5] Dyer, C.S., et al., Calculations and Observations of Solar Particle Enhancements to the Radiation Environment at Aircraft Altitudes, Adv. Space Res. 32(1), 81-93,2003.