• Current standard NASA AE8/AP8 models of Earth’s radiation belts have known limitations, mostly due to limited range of (1960s) observations incorporated
• Some energies and spatial regions were not sampled, so extrapolation needed
• Only simple (MIN/MAX) account taken of dependence on 11-year solar cycle
• Models incorporating newer data also limited (e.g., Heynderickx et al. 1999)
•
Missions to gather more comprehensive measurements in inner zone planned
• Advances in theoretical and computational tools allow construction of “full physics,” time-dependent model of inner zone, for pure-science or applied use
•
GEANT4 simulations of CRAND (Cosmic Ray Albedo Neutron Decay) and other processes an important part of this NSF-funded project (ATM-0518190)

•
Source: Cosmic Ray Albedo Neutron Decay (CRAND)
• Cosmic ray protons modulated by solar activity (F10.7), e.g., Usoskin et al. 2002
•
Geomagnetic access to atmosphere modeled using vertical rigidity cutoff plus transmission function to account for off-vertical variation

•
Monoenergetic protons incident isotropically at 200 km altitude
• Atmosphere modeled with average of NRLMSISE-00
N, O, and Ar densities over latitude, longitude, local time, and season, with typical geomagnetic conditions: F10.7 = 150, Ap
= 4 (Picone et al. 2002)
• GEANT4 physics list
LHEP_PRECO_HP seemed reasonable…
•
Neutrons exiting top of simulation tabulated
•
Mac OS X, dual 2.5GHz G5

•
Neutron production convolved with incident modulated/cut-off proton spectrum
• Agreement with observations pretty good, especially at crucial higher energies

•
Tangent to a given proton orbit traced back to top of atmosphere
•
Neutron flux integrated along line of sight to give source term (drift averaged)
•
Assumes decay proton acquires neutron flight direction and energy
• Losses include drift-averaged energy loss and scattering, parametrized by the real time history of solar activity in realistic atmospheric/ionospheric models
• Adiabatic energization/de-energization due to secular changes in magnetic field
(with real time history) also included; important for long-lived particles (centuries)
•
Loss and adiabatic terms integrated back in time to give proton energy history at given K, and L (adiabatic invariants for bounce and drift motion)
•
Energy histories convolved with source function and integrated along path to give temporal and spatial dependence of fluxes

• Model results are solid curves, with AP8 shown as dashed curves
• Note AP8 stops at 400 MeV, but actual data that were used to build it only went to 150 MeV
•
These results were from a oneyear preliminary study; we are now in a multi-year project to improve the model
• Long residence times at high altitudes mean that slower processes (nuclear scattering, radial diffusion) will need to be added to the model

• Other improvements include addition of neutrons from cosmic-ray helium to
CRAND source (about 10% of proton incident flux, but higher yield)
• Light-ion secondaries
(deuterium, tritium, alphas and helium-3, e.g., Looper et al. 1996) have been observed and modeled (with
AP8 inputs), Selesnick &
Mewaldt 1996
• Both of these, as well as nuclear scattering of protons off atmospheric and exospheric nuclei, require
GEANT4

•
I am a relatively new (1-2 years) GEANT4 user
•
The addition of pre-packaged physics lists has been a huge help to me!
•
Suggestions as to the best ones, for CRAND process and others we hope to add, would help
•
We are looking for secondaries (neutrons, light ions) in the energy range of a few MeV to a few GeV, from proton (and later, alpha and other light ion) primaries of tens of MeV to tens of GeV incident on atmospheric nuclei
• We are also interested in the losses of “fragile” secondaries like deuterium at energies of tens to hundreds of MeV due to breakup on atmospheric nuclei

References
• Heynderickx, D., M. Kruglanski, V. Pierrard, J. Lemaire, M. D. Looper, and J. B. Blake, A low altitude trapped proton model for solar minimum conditions based on SAMPEX/PET data,
IEEE Trans. Nucl. Sci., 46, 1475 –1480, 1999
• Kanbach, G. C. Reppin, and V. Schonfelder, Support for Crand theory from measurements of Earth albedo neutrons between 70 and 250 MeV, J. Geophys. Res., 79, 5159, 1974
• Looper, M. D, J. B. Blake, J. R. Cummings, and R. A. Mewaldt, SAMPEX observations of energetic hydrogen isotopes in the inner zone, Radiation Meas., 26, 967 –978, 1996
• Picone, J. M., A. E. Hedin, D. P. Drob, NRLMSISE-00 empirical model of the atmosphere:
Statistical comparisons and scientific issues, J. Geophys. Res., 107, 1468, doi:10.1029/2002JA009430, 2002
• Preszler, A. M., S. Moon, and R. S. White, Atmospheric neutrons, J. Geophys. Res., 81,
4715, 1976
• Selesnick, R. S. and R. A. Mewaldt, Atmospheric production of radiation belt light isotopes,
J. Geophys. Res., 101, 19,745 –19,757, 1996
• Usoskin, I. G., K. Alanko, K. Mursula, and G. A. Kovaltsov, Heliospheric modulation strength during the neutron monitor era, Sol. Phys., 207, 389 –399, 2002