Search

Astronauts are exposed to ionizing radiation that may pose significant health risks from missions to low Earth orbit (LEO) and beyond. The National Aeronautics and Space Administration (NASA) uses the deterministic radiation transport code, High charge (Z) and Energy TRaNsport (HZETRN), to estimate particle fluxes inside shielded vehicles to evaluate risk of radiation exposure to crew members. Highly efficient radiation transport algorithms and cross section models are needed to perform calculations in realistic vehicles with complex geometrical configurations. The HZETRN code uses the NUClear FRaGmentation (NUCFRG) model to evaluate fragmentation cross section products from nucleus–nucleus collisions. Although highly efficient, the NUCFRG model has some limitations that are based on its unique implementation of the abrasion–ablation formalism. NUCFRG performs well in predicting fragmentation cross sections on the average when compared to experimental data; however, even–odd nuclear structure effects observed in laboratory measurements are absent. The aim of the present work is to formulate a self-consistent theory that produces accurate nuclear fragmentation cross sections while maintaining numerical efficiency. To that end, the Relativistic Abrasion–Ablation FRaGmentation (RAADFRG) model has been developed. The theoretical framework for nuclear interaction is multiple scattering theory (MST), where relativistic kinematics may be included in the momentum–space representation of the Lippmann–Schwinger equation. The nuclear abrasion model employs the Eikonal (Eik) approximation and is used to predict prefragment cross sections. A novel approach is utilized for the excitation energy of prefragment, where in addition to differences of binding energies between two nuclei, energy is transferred to the prefragment from subsequent multiple scattering of abraded nucleons with the spectator nucleon constituents of the prefragment. Next, the excited prefragment liberates particles through the nuclear ablation process, and a nuclear coalescence model that forms aggregate particles for each prefragment channel is included in the yield. The ElectroMagnetic Dissociation FRaGmentation (EMDFRG) model is also included for peripheral interactions that stimulates particle emission via nuclear-photon field interactions. When compared to NUCFRG3, uncertainty quantification analysis shows that RAADFRG is better able to predict experimental nuclear fragmentation cross sections. RAADFRG is also shown to produce the even–odd nuclear structure effects, which is achieved by modification of isospin pairing correction in the prefragment excitation energy model.

The space radiation environment consists of a complex mixture of ionizing particles that pose significant health risks to crew members. NASA currently requires that an astronaut's career Risk of Exposure Induced Death (REID) for cancer mortality should not exceed 3% at the upper 95% confidence level. This career radiation limit is likely to be exceeded for even the shortest round-trip mission scenario to Mars. As such, NASA has begun to pursue more vigorously approaches to directly reduce radiation risks, despite the large uncertainties associated with such projections. A recent study considered cohort studies of aspirin and warfarin as possible medical countermeasures (MCMs) acting to reduce background cancer mortality rates used in astronaut risk projections. It was shown that such MCMs can reduce the REID for specific tissues in restricted time intervals over which the drugs were administered; however, the cumulative effect on total lifetime REID was minimal. As an extension, the present work addresses more general MCM requirements that would be needed to meet current NASA radiation limits for a Mars mission scenario. A sensitivity analysis is performed within the major components of the NASA cancer risk model that would likely be modified by MCM interventions. This includes the background cancer incidence and mortality rates, epidemiologically based hazard rates derived from acute terrestrial exposures, and radiation quality factors used to translate terrestrial exposures to space radiation. Relationships between possible MCMs and each of these components are discussed. Results from this study provide important information regarding MCM requirements needed to meet NASA limits for planned Mars missions. Insight into the types of countermeasures expected to yield greatest reductions in crew risk is also gained.

Transport codes used for space radiation protection require accurate nuclear fragmentation cross sections as input. The fragmentation process is modeled in two stages: a fast step, called abrasion or knockout, and a slower step, called evaporation or ablation. In this work, the ablation step is calculated via Monte Carlo (MC) methods using the recently modified legacy EVAporation (EVA) code. The code is based on the Weisskopf-Ewing particle emission formalism and has been extensively overhauled and modernized. Updates include a new nuclear mass table and modifications to the nuclear level density expression. The new formulation enables calculated results to exhibit the odd-even effect observed in experimental measurements. The revised ablation code, EVAporation-University of Tennessee, Knoxville (EVA-UTK), has been coupled with the quantum multiple scattering abrasion formalism incorporated in the nuclear fragmentation code, Optical PoTential FRAGmentation (OPTFRAG), and resulted in substantial improvements in agreement between fragmentation cross section estimates and experimental measurements.

A program of comparing American (NASA) and Russian (ROSCOSMOS) space radiation transport codes has recently begun, and the first paper directly comparing the NASA and ROSCOSMOS space radiation transport codes, HZETRN and SHIELD respectively has recently appeared. The present work represents the second time that NASA and ROSCOSMOS calculations have been directly compared, and the focus here is on models of pion production cross sections used in the two transport codes mentioned above. It was found that these models are in overall moderate agreement with each other and with experimental data. Disagreements that were found are discussed.

NASA's deterministic transport code HZETRN, and its three-dimensional (3D) counterpart, 3DHZETRN, are being used to characterize the space radiation environment over a wide range of scenarios, including future planned missions to the moon or Mars. Combined with available spaceflight measurements, these tools provide the fundamental input for risk models used to quantify possible astronaut health decrements and satisfy agency limits in support of exploration initiatives. Further research is therefore needed to improve radiation transport and nuclear physics models while at the same time continuing to expand the available measurement database (ground-based and spaceflight) to validate such efforts. In this work, significant updates to the deterministic radiation transport models are presented. Charged muons and pions are fully coupled with the existing solutions developed for neutron and light ion (Z ≤ 2) transport. This update includes the 3D nature of pion production as well as the pion interactions, resulting in further production of energetic nucleons within shielding. Additional updates related to low energy proton recoils in hydrogenous materials and capture/decay processes associated with charged pions at rest are also described. Included in this work is the coupling of single and double-differential cross sections from Geant4 into HZETRN and 3DHZETRN. This enables a direct comparison of deterministic and Monte Carlo transport methodologies using the same nuclear databases for specific interactions. Comparisons between Geant4 and 3DHZETRN are shown and establish that the transport methodologies are in excellent agreement when the same cross sections are used. The deterministic codes are also compared to ISS data, and it is found that the updated 3D procedures are within measurement uncertainty (±5%) at cutoff rigidities below 1 GV, which approaches free space conditions.

3DHZETRN-v2 includes a detailed three dimensional (3D) treatment of neutron/light-ion transport based on a quasi-elastic/multiple production assumption allowing improved agreement of the neutron/light-ion fluence compared with results of three Monte Carlo (MC) codes in the sense that the variance with respect to the individual MC results is less than the variance among the MC code results. The current numerical methods are no longer the main limitation to HZETRN code development and further changes in the nuclear model are required. In a prior study, an improved quasi-elastic spectrum based on a solution of the transport approximation to nuclear media effects showed promise, but the remaining multiple-production spectrum was based on a database derived from the Ranft model that used Bertini multiplicities. In the present paper, we will implement a more complete Serber first step into the 3DHZETRN-v2 code, but we retain the Bertini-Ranft branching ratios and evaporation multiplicities. It is shown that the new Serber model in the 3HZETRN-v2 code reduces the variance with individual MC codes, which are largely due to nuclear cross section model differences. The code will be available through the software system, OLTARIS, for shield design and validation and provides a basis for personal computer software capable of space shield analysis and optimization.

The space radiation environment comprises all of the nuclei in the periodic table with energies that extend from a fraction of an MeV/n to TeV/n. The vast range of projectile–target and energy combinations necessitates highly efficient and accurate cross section codes for use in radiation transport codes. As particles in the space radiation environment impinge on shielding materials, nuclear reactions, such as nuclear fragmentation, occur. One way of estimating nuclear fragmentation cross sections is to use an abrasion–ablation model, which describes how nucleons are dislodged from the nuclei as a result of nuclear collisions and the mechanism by which excited pre-fragments decay via particle emission to more stable states. The well-known partial wave solution method cannot be used directly for the computation of abrasion cross sections. Instead, abrasion cross sections may be computed by slightly altering the Eikonal solution method, which is a high energy (small scattering angle) approximation that depends on the nucleus–nucleus optical potential. The aim of the current work is to present two efficient methods for the computation of the Eikonal phase shift function. Analytic formulas of the optical potential are presented in the position-space representation for nuclei that are well-represented by harmonic-well nuclear matter densities (A < 20), which reduces the Eikonal phase factor to an integration over a single dimension. Next, the Eikonal phase function is presented in the momentum-space representation, which is particularly useful when the Fourier transform of the position-space optical potential is known. These new methods increase the computational efficiency by three orders of magnitude and allow for rapid prediction of elastic differential, total, elastic, and reaction cross sections in the Eikonal approximation.

The space radiation field is composed of energetic particles that pose both acute and long-term risks for astronauts in low earth orbit and beyond. In order to estimate radiation risk to crew members, the fluence of particles and biological response to the radiation must be known at tissue sites. Given that the spectral fluence at the boundary of the shielding material is characterized, radiation transport algorithms may be used to find the fluence of particles inside the shield and body, and the radio-biological response is estimated from experiments and models. The fidelity of the radiation spectrum inside the shield and body depends on radiation transport algorithms and the accuracy of the nuclear cross sections. In a recent study, self-consistent nuclear models based on multiple scattering theory that include the option to study relativistic kinematics were developed for the prediction of nuclear cross sections for space radiation applications. The aim of the current work is to use uncertainty quantification to ascertain the validity of the models as compared to a nuclear reaction database and to identify components of the models that can be improved in future efforts.

The space radiation environment is composed of ionizing particles that may pose health risks to crew members during Low Earth Orbit (LEO) and deep space missions. NASA has established astronaut career radiation limits for cancer of 3% Risk of Exposure Induced Death (REID) at the 95% confidence level. The REID is the increased lifetime risk of death from cancer due to radiation exposure in comparison to an unexposed background population and has been traditionally mitigated by passive shielding design concepts and limiting safe days in space. Additional reduction in radiation exposure risk may be achieved with Medical Countermeasures (MCM). Recent meta-analyses have demonstrated the efficacy of aspirin in the reduction of the background colorectal cancer incidence and mortality rates for specific cohorts. Additional studies of warfarin in patients greater than 50 years of age have indicated statistically significant decreases in stomach, bladder, brain, prostate, and lung cancer incidence as compared to control groups. While ultimate selection of suitable countermeasures will be the responsibility of flight surgeons, this paper presents a general methodology for incorporating MCM into the NASA Space Radiation Cancer Risk model and includes modifications of the background mortality rates (hazard rates) and the radiation risk coefficients to numerically quantify the benefits of MCM. As examples of the method, aspirin and warfarin will be employed as MCM in a sensitivity analysis to compute the REID for astronauts embarking on a one-year deep space mission scenario.

The space radiation environment is a complex mixture of particle types and energies originating from sources inside and outside of the galaxy. These environments may be modified by the heliospheric and geomagnetic conditions as well as planetary bodies and vehicle or habitat mass shielding. In low Earth orbit (LEO), the geomagnetic field deflects a portion of the galactic cosmic rays (GCR) and all but the most intense solar particle events (SPE). There are also dynamic belts of trapped electrons and protons with low to medium energy and intense particle count rates. In deep space, the GCR exposure is more severe than in LEO and varies inversely with solar activity. Unpredictable solar storms also present an acute risk to astronauts if adequate shielding is not provided. Near planetary surfaces such as the Earth, moon or Mars, secondary particles are produced when the ambient deep space radiation environment interacts with these surfaces and/or atmospheres. These secondary particles further complicate the local radiation environment and modify the associated health risks. Characterizing the radiation fields in this vast array of scenarios and environments is a challenging task and is currently accomplished with a combination of computational models and dosimetry. The computational tools include models for the ambient space radiation environment, mass shielding geometry, and atomic and nuclear interaction parameters. These models are then coupled to a radiation transport code to describe the radiation field at the location of interest within a vehicle or habitat. Many new advances in these models have been made in the last decade, and the present review article focuses on the progress and contributions made by workers and collaborators at NASA Langley Research Center in the same time frame. Although great progress has been made, and models continue to improve, significant gaps remain and are discussed in the context of planned future missions. Of particular interest is the juxtaposition of various review committee findings regarding the accuracy and gaps of combined space radiation environment, physics, and transport models with the progress achieved over the past decade. While current models are now fully capable of characterizing radiation environments in the broad range of forecasted mission scenarios, it should be remembered that uncertainties still remain and need to be addressed.

Protecting spacecraft crews from energetic space radiations that pose both chronic and acute health risks is a critical issue for future missions beyond low Earth orbit (LEO). Chronic health risks are possible from both galactic cosmic ray and solar energetic particle event (SPE) exposures. However, SPE exposures also can pose significant short term risks including, if dose levels are high enough, acute radiation syndrome effects that can be mission- or life-threatening. In order to address the reduction of short term risks to spaceflight crews from SPEs, we have developed recommendations to NASA for a design-standard SPE to be used as the basis for evaluating the adequacy of proposed radiation shelters for cislunar missions beyond LEO. Four SPE protection requirements for habitats are proposed: (1) a blood-forming-organ limit of 250 mGy-equivalent for the design SPE; (2) a design reference SPE environment equivalent to the sum of the proton spectra during the October 1989 event series; (3) any necessary assembly of the protection system must be completed within 30 min of event onset; and (4) space protection systems must be designed to ensure that astronaut radiation exposures follow the ALARA (As Low As Reasonably Achievable) principle.

Radiation transport codes require accurate nuclear cross sections to compute particle fluences inside shielding materials. The Tripathi semi-empirical reaction cross section, which includes over 60 parameters tuned to nucleon-nucleus (NA) and nucleus-nucleus (AA) data, has been used in many of the world's best-known transport codes. Although this parameterization fits well to reaction cross section data, the predictive capability of any parameterization is questionable when it is used beyond the range of the data to which it was tuned. Using uncertainty analysis, it is shown that a relativistic Three-Dimensional Lippmann-Schwinger (LS3D) equation model based on Multiple Scattering Theory (MST) that uses 5 parameterizations---3 fundamental parameterizations to nucleon-nucleon (NN) data and 2 nuclear charge density parameterizations---predicts NA and AA reaction cross sections as well as the Tripathi cross section parameterization for reactions in which the kinetic energy of the projectile in the laboratory frame ($T_{\rm Lab}$) is greater than 220 MeV/n. The relativistic LS3D model has the additional advantage of being able to predict highly accurate total and elastic cross sections. Consequently, it is recommended that the relativistic LS3D model be used for space radiation applications in which $T_{\rm Lab}>$ 220 MeV/n.

The space radiation environment is composed of energetic particles which can deliver harmful doses of radiation that may lead to acute radiation sickness, cancer, and even death for insufficiently shielded crew members. Spacecraft shielding must provide structural integrity and minimize the risk associated with radiation exposure. The risk of radiation exposure induced death (REID) is a measure of the risk of dying from cancer induced by radiation exposure. Uncertainties in the risk projection model, quality factor, and spectral fluence are folded into the calculation of the REID by sampling from probability distribution functions. Consequently, determining optimal shielding materials that reduce the REID in a statistically significant manner has been found to be difficult. In this work, the difference of the REID distributions for different materials is used to study the effect of composition on shielding effectiveness. It is shown that the use of correlated uncertainties allows for the determination of statistically significant differences between materials despite the large uncertainties in the quality factor. This is in contrast to previous methods where uncertainties have been generally treated as uncorrelated. It is concluded that the use of correlated quality factor uncertainties greatly reduces the uncertainty in the assessment of shielding effectiveness for the mitigation of radiation exposure.

in the second half of the 19 th century (1864, 1878, 1894, 1895, and 1896). The incident proton energy distributions for these solar particle events are assumed to be similar to that of the November 1960 event, one of the most energetic of the modern space era. The crewmembers are assumed to be located at the mean surface elevation on Mars, at the lowest elevation on Mars in the Hellas Impact Basin, and on the summit of Olympus Mons, the highest surface elevation on Mars. The crewmembers are assumed to be shielded by the overlying carbon dioxide atmosphere of Mars, and locally shielded by a space suit, a surface landing spacecraft, or a surface habitat. These estimates are compared with current NASA Permissible Exposure Limits.

Radiation exposure estimates for crew members on the surface of Mars may vary widely because of the large variations in terrain altitude. The maximum altitude difference between the highest (top of Olympus Mons) and the lowest (bottom of the Hellas impact basin) points on Mars is about 32 km. In this work estimates of radiation exposures as a function of altitude, from the Hellas impact basin to Olympus Mons, are made for a solar particle event proton radiation environment comparable to the Carrington event of 1859. We assume that the proton energy distribution for this Carrington-type event is similar to that of the Band Function fit of the February 1956 event. In this work we use the HZETRN 2010 radiation transport code, originally developed at NASA Langley Research Center, and the Computerized Anatomical Male and Female human geometry models to estimate exposures for aluminum shield areal densities similar to those provided by a spacesuit, surface lander, and permanent habitat as a function of altitude in the Mars atmosphere. Comparisons of the predicted organ exposures with current NASA Permissible Exposure Limits (PELs) are made.

Nuclear cross section calculations are often performed by using the partial wave method or the Eikonal method through Glauber theory. The expressions for the total cross section, total elastic cross section, and total reaction cross section in the partial wave method involve infinite sums and do not utilize simplifying approximations. Conversely, the Eikonal method gives these expressions in terms of integrals but utilizes the high energy and small angle approximations. In this paper, by using the fact that the l th partial wave component of the T-matrix can be very accurately approximated by its Born term, the infinite sums in each of the expressions for the differential cross section, total elastic cross section, total cross section, and total reaction cross section are re-written in terms of finite sums plus closed form expressions. The differential cross sections are compared to the Eikonal results for 16 O + 16 O , 12 C + 12 C , and p + 12 C elastic scattering. Total cross sections, total reaction cross sections, and total elastic cross sections are compared to the Eikonal results for 12 C + 12 C scattering.

It is well known that multiple scattering theories are very useful in the study of nucleon–nucleus and nucleus–nucleus scattering processes. The derivation of a nonrelativistic multiple scattering theory (NRMST) is well-established and clear. A key component to the formulation of an NRMST is the ability to separate the unperturbed Hamiltonian from the residual interaction. For the relativistic problem, it is not clear how to perform this separation starting from a field theoretical Lagrangian. Instead, one starts from an infinite set of Feynman diagrams, which play the role of the kernel in the Bethe–Salpeter equation for nucleus–nucleus scattering. Once the kernel is defined, it is straightforward to develop a relativistic multiple scattering theory (RMST). To be more complete than previous studies, delta degrees of freedom are included, which is a minimum requirement to explain pion production. It is demonstrated that an RMST can be formulated by expressing the kernel in a form that is similar to the re...

The space radiation environment consists of energetic particles that originate from the Sun and from sources outside the solar system. It is necessary to understand how these particles interact with materials to design effective radiation shielding. The transport of radiation through materials can be described by the Boltzmann equation. Efficient space radiation transport codes often require parameterized energy-dependent spectral distributions. A recent study showed that pions may contribute considerably to the total dose in galactic cosmic ray environments. Consequently, accurate parameterized pion spectral distributions are needed. In other studies, the Badhwar parameterization has been used for inclusive pion production in high energy nucleon–nucleon and nucleon–nucleus collisions, whereas a thermal model has been used to describe pion production in low energy nuclear collisions. In this paper, the thermal model is parameterized in terms of projectile energy, projectile nucleon number, and target nucleon number. Thermal and Badhwar model predictions of pion spectra from nucleon–nucleus and nucleus–nucleus collisions are compared for projectile energies ranging from 0.3 to 158 A GeV. It is recommended that the thermal model be used for projectile energies between 0.4 and 5 A GeV and the Badhwar model be used for higher projectile energies.

A numerical Gram–Schmidt orthonormalization procedure is presented for constructing an orthonormal basis function set from a non-orthonormal set, when the number of basis functions is large. This method will provide a pedagogical illustration of the Gram–Schmidt procedure and can be presented in classes on numerical methods or computational physics.

The effects of relativistic kinematics are studied for nuclear collisions of equal mass nuclei. It is found that the relativistic and non-relativistic elastic scattering amplitudes are nearly indistinguishable, and, hence, the relativistic and non-relativistic differential cross sections become indistinguishable. These results are explained by analyzing the Lippmann–Schwinger equation with the first order optical potential that was employed in the calculation.

1864, 1878, 1894, 1895, and 1896), are made for male and female crew members located at the mean surface elevation and at an altitude of 8 km in the Martian atmosphere. The incident solar particle event proton energy distributions for these events are assumed to be similar to that of the Band function t of the February 1956 event. Radiation exposure estimates were performed using NASA’s On-Line Tool for the Assessment of Radiation in Space (OLTARIS). The HZETRN (High charge (Z) and Energy TRaNsport) space radiation transport code, which is incorporated into OLTARIS, was used to describe the transport of incident protons and any secondary particles generated by their interactions with the atmosphere of Mars, through spacesuit, surface lander, or permanent habitat shielding, and body organ self-shielding. Estimates of eective dose and organ dose are made using the Computerized Anatomical Male (CAM), Computerized Anatomical Female (CAF), Male Adult voXel (MAX), and Female Adult voXel (FAX) human geometry models. The predicted exposures are compared with current NASA Permissible Exposure Limits (PELs).