Theoretical modelling of the Inner Zone Using Geant4 Simulations


Theoretical Modeling of the

Inner 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

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


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


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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

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–399, 2002