Theoretical Modeling of the Inner Zone Using GEANT4 Simulations as Inputs

1. Theoretical Modeling of theInner Zone Using GEANT4 Simulations as Inputs R. S. Selesnick and M. D. Looper The Aerospace Corp., Los Angeles, CA USA R. A. Mewaldt Caltech, Pasadena, CA USA

2. 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)

4. 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

5. 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

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

8. 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

10. 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 one-year 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

11. 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

12. Suggestions would be appreciated • 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

13. 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