MAIRE: The Response Matrices

Atmospheric radiation response matrices have been generated by detailed MC simulations of mono-energetic proton and alpha particles incident on the geometrical model of the atmosphere discussed above. The transport code can be any of the three we have evaluated, and the resulting response matrices produced by the different codes are interchangeable in MAIRE.

In the actual simulation tallying boundaries (shells) are placed in the geometry model and the secondary particles, i.e. protons, neutrons, charged pions, charged muons, electrons and gammas, crossing a specified tallying boundary are recorded into separate histograms. Furthermore, upward and downward moving particles are separated into two histograms to give a limited angular capability in the response matrix.

The first response matrices were produced with MCNPX simulations. These have 30 energy channels covering the energy range from 100 MeV to 100 GeV in equal logarithmic intervals and 150 tallying boundaries were placed in the geometry model. So in total, the response matrices consist of 6 particle types x 30 incident particle energies x 2 up/down directions x 150 boundaries = 54000 histograms for the protons and the same number of histograms for the alphas. The histograms for secondary neutrons covering the energy range from 10-6 to 105 MeV in 110 channels, and the histograms for all the other particles are in 60 channels covering the energy range between 0.1 and 105 MeV. Simulations of a large number of incident particles are required in order to achieve good statistics for each of the histograms in the matrices. The production of the first version of the response matrices took an equivalent of 1 month CPU time on a Athlon 3000+ machine, but with a local Linux cluster of several such machines, such a task can be completed in a matter of days.

Proton flux normalised to per incident proton, as a function of the altitude in the atmosphere. Each curve corresponds to an incident proton energy, as colour coded in the legends on the right.

In the figure above we plot the normalised (per incident proton) number of protons crossing the boundary recorded as a function of altitude for different incident proton energies. From this figure, one can see a clear separation between the primary proton and the secondary proton contributions in the recorded flux in the low energy proton incident cases (below ~ 1.4 GeV). It also shows that only energetic primary protons, (> ~ 500 MeV) can make a significant contribution to the proton flux at sea-level, but the lower energy incident protons of a few hundreds of MeVs will contribute to the flux at passenger jet flight altitudes. Similar conclusions can be reached for other particle types.

The alpha particle response matrices have been generated in the same way as those for the protons. We show in the figure below an example of the number of secondary neutrons crossing the tally boundaries as a function of altitude and each curve in the figure corresponds to specific primary alpha particle energy. Similar to what we saw in the proton response matrices, even relatively low energy alphas, i.e. in hundreds of MeVs, have a detectable chance (>10-6) of contributing to the neutron flux at ground level. Compared to a proton incidence, an alpha particle leads to less secondary radiation when compared on equal energy per nucleon basis. The current MCNPX code, however, can only properly simulate alpha particle interactions up to the energy of 1 GeV per nucleon; hence our current alpha particle response matrices are incomplete. We will switch to using the Geant4 and FLUKA codes, as they have better treatments of the ion-nuclear interactions. It is our plan to eventually produce independent response matrices using all three codes.

Secondary proton flux normalised to per incident alpha, as a function of the altitude in the atmosphere. Each curve corresponds to an incident alpha energy, as colour coded in the legends on the right.