Elsevier

Advances in Space Research

Volume 51, Issue 12, 15 June 2013, Pages 2251-2260
Advances in Space Research

An extension of HZETRN for cosmic ray initiated electromagnetic cascades

https://doi.org/10.1016/j.asr.2013.01.021Get rights and content

Abstract

Safe and efficient mission operations in space require an accurate understanding of the physical interactions of space radiation. As the primary space radiation interacts with intervening materials, the composition and spectrum of the radiation environment changes. The production of secondary particles can make a significant contribution to radiation exposure. In this work, the NASA space radiation transport code, HZETRN, is extended to include the transport of electrons, positrons, and photons. The production of these particles is coupled to the initial cosmic ray radiation environment through the decay of neutral pions, which produce high energy photons, and through the decay of muons, which produce electrons and positrons. The photons, electrons, and positrons interact with materials producing more photons, electrons and positrons generating an electromagnetic cascade. The relevant cross sections, transport equation, and solution method are introduced. Electron and positron production in Earth’s atmosphere is investigated and compared to experimental balloon-flight measurements. Reasonable agreement is seen between HZETRN and data.

Introduction

Space radiation protection is an important consideration for human space flight (NCRP, 2006) and for occupational exposure for airline crews (Mertens et al., 2011, NCRP, 2009, ICRP, 1991). The radiation environment of space is much more intense than the terrestrial radiation environment and can be dangerous to electronics and biological tissue. To mitigate the potential adverse effects of space radiation, sensitive systems must be shielded. However, the addition of unnecessary shielding mass can be costly and should be avoided if possible. Therefore, it is advantageous and cost effective to develop tools to design efficient radiation shielding which can optimize materials and configurations. To accomplish this task, fast and efficient radiation transport codes are required.

In order to accurately characterize the radiation environment inside a spacecraft, radiation transport codes need to include all relevant sources of damaging radiation, including secondary particles produced through the interaction of the primary radiation environment with the intervening spacecraft shielding. Pions and muons account for some of the produced secondary particles. Previous work was done to update the NASA space radiation transport code HZETRN (Slaba et al., 2010b, Slaba et al., 2010c, Wilson et al., 1991) to include charged pions and muons (Norman et al., 2012). HZETRN is a one-dimensional, deterministic radiation transport code developed for fast and efficient transport calculations. However, in Norman et al. (2012) muon decay was modeled simply as a loss term, with no subsequent particle production as a result of the decay. Physically, it is known that first generation leptons (electrons and positrons) are produced from the decay of muons. In addition to the charged pions, the neutral pion, π0, that decays very quickly to two photons (Nakamura et al., 2010), was previously unaccounted for in HZETRN.

With the production of electrons, positrons, and photons through these channels, an electromagnetic cascade can develop in shielding materials. The subsequent cascade particles can make an important contribution to radiation dose (O’Brien et al., 1996, Aghara et al., 2009) and should therefore be included in radiation transport codes. To address this deficiency, an extension to HZETRN to include the decay of muons into positrons and electrons, the production and decay of neutral pions, and the subsequent electromagnetic cascade is presented. Section 2 details the transport models used. Section 3 presents the formalism for the production and decay of the neutral pion. Muon decay is discussed in Section 4. In Section 5, a comparison is presented of electron and positron production in Earth’s atmosphere as measured by the CAPRICE98 (Mocchiutti, 2003) experiment to the newly developed transport model including the full electromagnetic cascade.

Section snippets

Radiation transport model

For neutrons, protons, and heavy ions (Z > 2), HZETRN provides a fast and accurate solution to the Boltzmann transport equation within the continuous slowing down and straight ahead approximations given by (Wilson et al., 1991)B¯[ϕj(x,T)]=kTσjk(T,T)ϕ(x,T)dT,with the linear differential operatorB¯[ϕj(x,T)]x-1AjTSj(T)+σj(T)ϕj(x,T),and the boundary conditionϕj(0,T)=fj(T).In Eqs. (1), (2), (3), ϕj(x,T) is the fluence of type j particles at depth x with kinetic energy T, Aj is the atomic

Results

With all components of the electron, positron, and photon transport model defined and coupled to HZETRN, the extended version was compared to electron and positron production in Earth’s atmosphere measured by the CAPRICE (Cosmic AntiProton Ring Imaging Cherenkov Experiment) balloon-borne experiment in 1998 (Mocchiutti, 2003). The detector consisted of a solid ring imaging Cherenkov (RICH) detector, an imaging calorimeter, a time-of-flight system, and a superconducting magnet spectrometer with

Conclusions

A deterministic method for the transport of electrons, positrons, and photons produced from cosmic rays was presented. Electrons and positrons were produced from the decay of like-charged muons, which were produced from charged pion decay. Neutral pion production was also introduced into the model and the subsequent photons from the decay were also transported. Relevant cross sections and decay rates were also presented.

The extended version of HZETRN was compared with electron and positron

References (32)

  • G. Barr et al.

    Flux of atmospheric neutrinos

    Phys. Rev. D

    (1989)
  • Blattnig, S.R., Norbury, J.W., Norman, R.B., Wilson, J.W., Singleterry, R.C., Tripathi, R.K., MESTRN: A Deterministic...
  • S.R. Blattnig et al.

    Parametrizations of inclusive cross sections for pion production in proton-proton collisions

    Phys. Rev. D

    (2000)
  • M. Durante et al.

    Physical basis of radiation protection in space travel

    Rev. Mod. Phys.

    (2011)
  • ICRP, 1990 Recommendations of the International Commission on Radiological Protection. ICRP Publication 60,...
  • Mertens, C.J., Kress, B.T., Wiltberger, M., Tobiska, W.K., Grajewski, B., Xu, X., Atmospheric ionizing radiation from...
  • Cited by (29)

    • DDFRG2: Double-Differential FRaGmentation model for pion production in high energy nuclear collisions

      2023, Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
    • Updated deterministic radiation transport for future deep space missions

      2020, Life Sciences in Space Research
      Citation Excerpt :

      Nonetheless, a focused nuclear cross section measurement program would be needed to significantly reduce light ion nuclear cross section uncertainties. Finally, pion production and the associated electromagnetic (EM) cascade (hereafter referred to as π/EM) was partially included in HZETRN in previous work (Blattnig et al., 2004; Norman et al., 2012, 2013). Comparisons with ISS and MSL/RAD data showed the significant impact of adding the π/EM interactions on dose.

    • Advances in space radiation physics and transport at NASA

      2019, Life Sciences in Space Research
      Citation Excerpt :

      The combination of HZETRN with deterministic muon/pion transport and coupled EM transport was described by Norbury et al. (2012), Norbury (2013). Comparison against atmospheric measurements (Norman et al., 2012; Norman et al., 2013), ISS data (Slaba et al., 2013a) and recent comparisons to MSLRAD data (Matthia et al., 2016; Matthia et al., 2017) suggest the model is reasonably accurate, as shown in Fig. 12. However, coupling of the pion field to the nucleon field was neglected.

    View all citing articles on Scopus
    View full text