An extension of HZETRN for cosmic ray initiated electromagnetic cascades
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, , 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)with the linear differential operatorand the boundary conditionIn Eqs. (1), (2), (3), is the fluence of type j particles at depth x with kinetic energy T, 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
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