Models of Galactic Cosmic Radiation:

The radiation in the atmosphere is mainly the product of the galactic cosmic ray interactions with the atmosphere. Cosmic radiation consists primarily of energetic proton (~ 89%) and ~ 10% helium (alpha) particles. In the solar system the cosmic ray radiation is modulated by the interplanetary magnetic field and its intensity at the Earth is in anti-correlation to the solar activity over the 11 year solar cycle.

Many cosmic ray models have been developed over the years and most of them are based on the diffusion-convection theory [1]. Two of the best known to the space radiation effects community are the Badhwar & O'Neill model [2] and CREME96/Nymmik model [3]. The former uses ground-based neutron monitor data to estimate the solar modulation while the latter relates the solar cycle variation to the sunspot numbers. Although results of both models have been widely quoted, and the CREME96/Nymmik model is available on-line, we found that it is in fact not straightforward to have a local implementation of either model as some of the key information, such as the parameters for the local interstellar spectra, is proprietary and therefore not available openly. As a result we have developed a simple alternative model based on the original solution of Gleeson & Axford [4]:

where J(E,t) is the differential cosmic ray flux at Earth, Φ(t) is the solar modulation parameter, E, E0 and Z are the total energy, mass and charge of the particle respectively. Jis(E') is the stationary interstellar flux for particles with energy E' = Z Φ(t)+E outside the Heliosphere, and it is assumed to follow the simple power-law form:

In MAIRE we used α = 2.84 and C = 106 cm-2s-1sr-1MeV1.84 for the protons and α = 2.90 and C = 1.7×107 cm-2s-1sr-1MeV1.90 for the alpha particles. As for the solar modulation parameter Φ(t), which is not easy to determine, we found Davies et al [5] provide an on-line service which calculates the monthly based Φ(t) values from the years 1952 to 2020. These values are derived from the ACE measured oxygen spectra, which are then fitted to the averaged Climax neutron monitor data. The Φ(t) value for a given time is obtained by first looking up the Climax neutron monitor average for the appropriate time and then calculating the value from the fit of v Φ(t) vs. the neutron monitor data.

In Example-1 we plot the proton and alpha spectra without the shielding effect of the Earth's magnetosphere, i.e. for 0 GV rigidity cut-off, as predicted by our model for the date 01/07/2001. Also shown in the figure are the spectra predicted by the CREME96/Nymmik model and the alpha spectrum from reference [5]. The good agreement between these spectra is clear to see. Similar comparisons have been performed for many other dates, with very good agreement for the alpha spectra but to a lesser degree for the protons.

The design of MAIRE allows it to be interfaced to any cosmic radiation model. At the moment the predicted spectra of the Badhwar & O'Neill model or the CREME96/Nymmik model can be used via the "User Defined Spectrum" option.


[1] Parker, E.N., The Passage of Energetic Charged Particles Through Interplanetary Space, Planet. Space Sci., 13, 9-49, 1985
[2] Badhwar, G.D. and O'Neill, P.M., Galactic Cosmic Radiation Model and Its Applications. Adv. Space Res. 17(2), 7-17, 1996.
[3] Nymmik, R. A., et al., Galactic cosmic ray flux simulation and prediction, Adv. Space Res. 17(2), 19-30, 1996.
[4] Gleeson, L. J., & Axford, W. I., ApJ, 154, 1011, 1968.
[5] Davies, A. J., et al., The Evolution of Galactic Cosmic Ray Element Spectra from Solar Minimum to Solar Maximum: ACE Measurements, Proceedings of the 27th International Cosmic Ray Conference, Hamburg, 10, 3971, 2001.