An improved neutron transport algorithm for HZETRN

Long-term human presence in space requires the inclusion of radiation constraints in mission planning and the design of shielding materials, structures and vehicles. It is necessary to expose the numerical tools commonly used in radiation analyses to extensive verification, validation and uncertainty quantification. In this paper, the numerical error associated with energy discretization in HZETRN is addressed. An inadequate numerical integration scheme in the transport algorithm is shown to produce large errors in the low energy portion of the neutron and light ion fluence spectra. It is further shown that the errors result from the narrow energy domain of the neutron elastic cross section spectral distributions and that an extremely fine energy grid is required to resolve the problem under the current formulation. Since adding a sufficient number of energy points will render the code computationally inefficient, we revisit the light ion and neutron transport theory developed for HZETRN and focus on neutron elastic interactions. Two numerical methods (average value and collocation) are developed to provide adequate resolution in the energy domain and more accurately resolve the neutron elastic interactions. An energy grid convergence study is conducted to demonstrate the improved stability of the new methods. Based on the results of the convergence study and the ease of implementation, the average value method with a 100 point energy grid is found to be suitable for future use in HZETRN.     

Comparison of the transport codes HZETRN,HETC and FLUKA for galactic cosmic rays

The HZETRN deterministic radiation code is one of several tools developed to analyze the effects of harmful galactic cosmic rays (GCR) and solar particle events on mission planning and shielding for astronauts and instrumentation. This paper is a comparison study involving the two Monte Carlo transport codes, HETC–HEDS and FLUKA and the deterministic transport code, HZETRN. Each code is used to transport an ion from the 1977 solar minimum GCR spectrum impinging upon a 20 g/cm² aluminum slab followed by a 30 g/cm² water slab. This research is part of a systematic effort of verification and validation to quantify the accuracy of HZETRN and determine areas where it can be improved. Comparisons of dose and dose equivalent values at various depths in the water slab are presented in this report. This is followed by a comparison of the proton and forward, backward and total neutron flux at various depths in the water slab. Comparisons of the secondary light ion ²H, ³H, ³He and ⁴He fluxes are also examined.     

A procedure for benchmarking laboratory exposures with 1 A GeV iron ions.

A new version of the HZETRN code capable of simulating HZE ions with either laboratory or space boundary conditions is under development. The computational model consists of combinations of physical perturbation expansions based on the scales of atomic interaction, multiple scattering, and nuclear reactive processes with use of asymptotic/Neumann expansions with non-perturbative corrections. The code contains energy loss with straggling, nuclear attenuation, nuclear fragmentation with energy dispersion and downshifts, and off-axis dispersion with multiple scattering under preparation. The present benchmark is for a broad directed beam for 1 A GeV iron ion beams with 2 A MeV width and four targets of polyethylene, polymethyl metachrylate, aluminum, and lead of varying thickness from 5 to 30 g/cm2. The benchmark quantities will be dose, track averaged LET, dose averaged LET, fraction of iron ion remaining, and fragment energy spectra after 23 g/cm2 of polymethyl metachrylate.     

An extension of HZETRN for cosmic ray initiated electromagnetic cascades

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.     

Pion and electromagnetic contribution to dose: Comparisons of HZETRN to Monte Carlo results and ISS data

Recent work has indicated that pion production and the associated electromagnetic (EM) cascade may be an important contribution to the total astronaut exposure in space. Recent extensions to the deterministic space radiation transport code, HZETRN, allow the production and transport of pions, muons, electrons, positrons, and photons. In this paper, the extended code is compared to the Monte Carlo codes, Geant4, PHITS, and FLUKA, in slab geometries exposed to galactic cosmic ray (GCR) boundary conditions. While improvements in the HZETRN transport formalism for the new particles are needed, it is shown that reasonable agreement on dose is found at larger shielding thicknesses commonly found on the International Space Station (ISS). Finally, the extended code is compared to ISS data on a minute-by-minute basis over a seven day period in 2001. The impact of pion/EM production on exposure estimates and validation results is clearly shown. The Badhwar–O’Neill (BO) 2004 and 2010 models are used to generate the GCR boundary condition at each time-step allowing the impact of environmental model improvements on validation results to be quantified as well. It is found that the updated BO2010 model noticeably reduces overall exposure estimates from the BO2004 model, and the additional production mechanisms in HZETRN provide some compensation. It is shown that the overestimates provided by the BO2004 GCR model in previous validation studies led to deflated uncertainty estimates for environmental, physics, and transport models, and allowed an important physical interaction (π/EM) to be overlooked in model development. Despite the additional π/EM production mechanisms in HZETRN, a systematic under-prediction of total dose is observed in comparison to Monte Carlo results and measured data.     

Comparison of the transport codes HZETRN,HETC and FLUKA for a solar particle event

The protection of astronauts and instrumentation from galactic cosmic rays and solar particle events is one of the primary constraints associated with mission planning in low earth orbit or deep space. To help satisfy this constraint, several computational tools have been developed to analyze the effectiveness of various shielding materials and structures exposed to space radiation. These tools are now being carefully scrutinized through a systematic effort of verification, validation, and uncertainty quantification. In this benchmark study, the deterministic transport code HZETRN is compared to the Monte Carlo transport codes HETC-HEDS and FLUKA for a 30 g/cm² water target protected by a 20 g/cm² aluminum shield exposed to a parameterization of the February 1956 solar particle event. Neutron and proton fluences as well as dose and dose equivalent are compared at various depths in the water target. The regions of agreement and disagreement between the three codes are quantified and discussed, and recommendations for future work are given.     

Statistical validation of HZETRN as a function of vertical cutoff rigidity using ISS measurements

Measurements taken in Low Earth Orbit (LEO) onboard the International Space Station (ISS) and transit vehicles have been extensively used to validate radiation transport models. Primarily, such comparisons were done by integrating measured data over mission or trajectory segments so that individual comparisons to model results could be made. This approach has yielded considerable information but is limited in its ability to rigorously quantify and differentiate specific model errors or uncertainties. Further, as exploration moves beyond LEO and measured data become sparse, the uncertainty estimates derived from these validation cases will no longer be applicable. Recent improvements in the underlying numerical methods used in HZETRN have resulted in significant decreases in code run time. Therefore, the large number of comparisons required to express error as a function of a physical quantity, like cutoff rigidity, are now possible. Validation can be looked at in detail over any portion of a flight trajectory (e.g. minute by minute) such that a statistically significant number of comparisons can be made. This more rigorous approach to code validation will allow the errors caused by uncertainties in the geometry models, environmental models, and nuclear physics models to be differentiated and quantified. It will also give much better guidance for future model development. More importantly, it will allow a quantitative means of extrapolating uncertainties in LEO to free space. In this work, measured data taken onboard the ISS during solar maximum are compared to results obtained with the particle transport code HZETRN. Comparisons are made at a large number (∼77,000) of discrete time intervals, allowing error estimates to be given as a function of cutoff rigidity. It is shown that HZETRN systematically underestimates exposure quantities at high cutoff rigidity. The errors are likely associated with increased angular variation in the geomagnetic field near the equator, the lack of pion production in HZETRN, and errors in high energy nuclear physics models, and will be the focus of future work.     

Deterministic pion and muon transport in Earth’s atmosphere

An accurate understanding of the physical interactions and transport of space radiation is important for safe and efficient space operations. Secondary particles produced by primary particle interactions with intervening materials are an important contribution to radiation risk. Pions are copiously produced in the nuclear interactions typical of space radiations and can therefore be an important contribution to radiation exposure. Charged pions decay almost exclusively to muons. As a consequence, muons must also be considered in space radiation exposure studies. In this work, the NASA space radiation transport code HZETRN has been extended to include the transport of charged pions and muons. The relevant transport equation, solution method, and implemented cross sections are reviewed. Muon production in the Earth’s upper atmosphere is then investigated, and comparisons with recent balloon flight measurements of differential muon flux are presented. Muon production from the updated version of HZETRN is found to match the experimental data well.     

Comparisons of several transport models in their predictions in typical space radiation environments

We have used several transport codes to calculate dose and dose equivalent values as well as the particle spectra behind a slab or inside a spherical shell shielding in typical space radiation environments. Two deterministic codes, HZETRN and UPROP, and two Monte Carlo codes, FLUKA and Geant4, are included. A soft solar particle event, a hard solar particle event, and a solar minimum galactic cosmic rays environment are considered; and the shielding material is either aluminum or polyethylene. We find that the dose values and particle spectra from HZETRN are in general rather consistent with Geant4 except for neutrons. The dose equivalent values from HZETRN and Geant4 are not far from each other, but the HZETRN values behind shielding are often lower than the Geant4 values. Results from FLUKA and Geant4 are mostly consistent for considered cases. However, results from the legacy code UPROP are often quite different from the other transport codes, partly due to its non-consideration of neutrons. Comparisons for the spherical shell geometry exhibit the same qualitative features as for the slab geometry. In addition, results from both deterministic and Monte Carlo transport codes show that the dose equivalent inside the spherical shell decreases from the center to the inner surface and this decrease is large for solar particle events; consistent with an earlier study based on deterministic radiation transport results. This study demonstrates both the consistency and inconsistency among these transport models in their typical space radiation predictions; further studies will be required to pinpoint the exact physics modules in these models that cause the differences and thus may be improved.     

Assessment and requirements of nuclear reaction databases for GCR transport in the atmosphere and structures

The transport properties of galactic cosmic rays (GCR) in the atmosphere, material structures, and human body (self-shielding) are of interest in risk assessment for supersonic and subsonic aircraft and for space travel in low-Earth orbit and on interplanetary missions. Nuclear reactions, such as knockout and fragmentation, present large modifications of particle type and energies of the galactic cosmic rays in penetrating materials. We make an assessment of the current nuclear reaction models and improvements in these model for developing required transport code data bases. A new fragmentation data base (QMSFRG) based on microscopic models is compared to the NUCFRG2 model and implications for shield assessment made using the HZETRN radiation transport code. For deep penetration problems, the build-up of light particles, such as nucleons, light clusters and mesons from nuclear reactions in conjunction with the absorption of the heavy ions, leads to the dominance of the charge Z = 0, 1, and 2 hadrons in the exposures at large penetration depths. Light particles are produced through nuclear or cluster knockout and in evaporation events with characteristically distinct spectra which play unique roles in the build-up of secondary radiation's in shielding. We describe models of light particle production in nucleon and heavy ion induced reactions and make an assessment of the importance of light particle multiplicity and spectral parameters in these exposures.     

An analytical model for the prediction of a micro-dosimeter response function

A rapid analytical procedure for the prediction of a micro-dosimeter response function in low Earth orbit (LEO), correlated with the Space Transportation System (STS, shuttle) Tissue Equivalent Proportional Counter (TEPC) measurements is presented. The analytical model takes into consideration the energy loss straggling and chord length distribution of the detector, and is capable of predicting energy deposition fluctuations in a cylindrical micro-volume of arbitrary aspect ratio (height/diameter) by incoming ions through both direct and indirect (δ ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCRs) and/or trapped protons at LEO as input. On a desktop PC, the response function of TEPC for each ion in the GCR/trapped field is computed at the average rate of 30 s/ion. The ionizing radiation environment at LEO is represented by O’Neill’s GCR model (2004), covering charged particles in the 1 ? Z ? 28 range. O’Neill’s free space GCR model is coupled with the Langley Research Center (LaRC) angular dependent geomagnetic cutoff model to compute the transmission coefficient in LEO. The trapped proton environment is represented by a LaRC developed time dependent procedure which couples the AP8MIN/AP8MAX, Deep River Neutron Monitor (DRNM) and F10.7 solar radio frequency measurements. The albedo neutron environment is represented by the extrapolation of the Atmospheric Ionizing Radiation (AIR) measurements. The charged particle transport calculations correlated with STS 51 and 114 flights are accomplished by using the most recent version (2005) of the LaRC deterministic High charge (Z) and Energy TRaNsport (HZETRN) code. We present the correlations between the TEPC model predictions (response function) and TEPC measured differential/integral spectra in the lineal energy (y) domain for both GCR and trapped protons, with the conclusion that the model correctly accounts for the increase in flux at low y values where energetic ions are the primary contributor. We further discuss that, even with the incorporation of angular dependency in the cutoffs, comparison of the GCR differential/integral flux between STS 51 and 114 TEPC measured data and current calculations indicates that there still exists an underestimation by the simulations at low to mid range y values. This underestimation is partly related the exclusion of the secondary pion particle production from the current version of HZETRN.     

Transport of light ions in matter

A recent set of light ion experiments are analyzed using the Green's function method of solving the Boltzmann equation for ions of high charge and energy (the GRNTRN transport code) and the NUCFRG2 fragmentation database generator code. Although the NUCFRG2 code reasonably represents the fragmentation of heavy ions, the effects of light ion fragmentation requires a more detailed nuclear model including shell structure and short range correlations appearing as tightly bound clusters in the light ion nucleus. The most recent NUCFRG2 code is augmented with a quasielastic alpha knockout model and semiempirical adjustments (up to 30 percent in charge removal) in the fragmentation process allowing reasonable agreement with the experiments to be obtained. A final resolution of the appropriate cross sections must await the full development of a coupled channel reaction model in which shell structure and clustering can be accurately evaluated.     

Heavy ion contributions to organ dose equivalent for the 1977 galactic cosmic ray spectrum

Estimates of organ dose equivalents for the skin, eye lens, blood forming organs, central nervous system, and heart of female astronauts from exposures to the 1977 solar minimum galactic cosmic radiation spectrum for various shielding geometries involving simple spheres and locations within the Space Transportation System (space shuttle) and the International Space Station (ISS) are made using the HZETRN 2010 space radiation transport code. The dose equivalent contributions are broken down by charge groups in order to better understand the sources of the exposures to these organs. For thin shields, contributions from ions heavier than alpha particles comprise at least half of the organ dose equivalent. For thick shields, such as the ISS locations, heavy ions contribute less than 30% and in some cases less than 10% of the organ dose equivalent. Secondary neutron production contributions in thick shields also tend to be as large, or larger, than the heavy ion contributions to the organ dose equivalents.     

A space radiation transport method development.

Improved spacecraft shield design requires early entry of radiation constraints into the design process to maximize performance and minimize costs. As a result, we have been investigating high-speed computational procedures to allow shield analysis from the preliminary design concepts to the final design. In particular, we will discuss the progress towards a full three-dimensional and computationally efficient deterministic code for which the current HZETRN evaluates the lowest-order asymptotic term. HZETRN is the first deterministic solution to the Boltzmann equation allowing field mapping within the International Space Station (ISS) in tens of minutes using standard finite element method (FEM) geometry common to engineering design practice enabling development of integrated multidisciplinary design optimization methods. A single ray trace in ISS FEM geometry requires 14 ms and severely limits application of Monte Carlo methods to such engineering models. A potential means of improving the Monte Carlo efficiency in coupling to spacecraft geometry is given in terms of re-configurable computing and could be utilized in the final design as verification of the deterministic method optimized design.     

Utilization of CAM,CAF, MAX,and FAX for space radiation analyses using HZETRN

To estimate astronaut health risk due to space radiation, one must have the ability to calculate various exposure-related quantities that are averaged over specific organs and tissue types. Such calculations require computational models of the ambient space radiation environment, particle transport, nuclear and atomic physics, and the human body. While significant efforts have been made to verify, validate, and quantify the uncertainties associated with many of these models and tools, relatively little work has focused on the uncertainties associated with the representation and utilization of the human phantoms. In this study, we first examine the anatomical properties of the Computerized Anatomical Man (CAM), Computerized Anatomical Female (CAF), Male Adult voXel (MAX), and Female Adult voXel (FAX) models by comparing the masses of various model tissues used to calculate effective dose to the reference values specified by the International Commission on Radiological Protection (ICRP). The MAX and FAX tissue masses are found to be in good agreement with the reference data, while major discrepancies are found between the CAM and CAF tissue masses and the reference data for almost all of the effective dose tissues. We next examine the distribution of target points used with the deterministic transport code HZETRN (High charge (Z) and Energy TRaNsport) to compute mass averaged exposure quantities. A numerical algorithm is presented and used to generate multiple point distributions of varying fidelity for many of the effective dose tissues identified in CAM, CAF, MAX, and FAX. The point distributions are used to compute mass averaged dose equivalent values under both a galactic cosmic ray (GCR) and solar particle event (SPE) environment impinging isotropically on three spherical aluminum shells with areal densities of 0.4 g/cm², 2.0 g/cm², and 10.0 g/cm². The dose equivalent values are examined to identify a recommended set of target points for each of the tissues and to further assess the differences between CAM, CAF, MAX, and FAX. It is concluded that the previously published CAM and CAF point distributions were significantly under-sampled and that the set of point distributions presented here should be adequate for future studies involving CAM, CAF, MAX, or FAX. It is also found that the errors associated with the mass and location of certain tissues in CAM and CAF have a significant impact on the mass averaged dose equivalent values, and it is concluded that MAX and FAX are more accurate than CAM and CAF for space radiation analyses.     

Galactic cosmic ray radiation levels in spacecraft on interplanetary missions.

Using the Langley Research Center galactic cosmic ray (GCR) transport computer code (HZETRN) and the computerized anatomical man (CAM) model, crew radiation levels inside manned spacecraft on interplanetary missions are estimated. These radiation-level estimates include particle fluxes, LET (linear energy transfer) spectra, absorbed dose, and dose equivalent within various organs of interest in GCR protection studies. Changes in these radiation levels resulting from the use of various different types of shield materials are presented.