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.     

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.     

空间飞行器碎片防护结构的简化设计

给出一种基于实验和理论分析的航天器碎片防护结构简化设计方法 ,该方法可用于进行大型空间飞行器碎片防护结构的方案选择和初步结构设计。利用空间碎片的工程环境模型和防护结构几何经验公式 ,采用“设计碎片”的概念 ,对防护结构进行几何结构设计和质量估算 ,并采用改进的防护性能验证算法进行空间碎片的风险评估。通过对惠式防护结构的计算 ,得到的计算结果基本符合实际要求。     

On the validity of the aluminum equivalent approximation in space radiation shielding applications

The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range 1 ? Z ? 28 (H–Ni) and secondary neutrons through selected target materials. The coupling of the GCR extremes to HZETRN allows for the examination of the induced environment within the interior of an idealized spacecraft as approximated by a spherical shell shield, and the effects of the aluminum equivalent approximation for a good polymeric shield material such as generic polyethylene (PE). The shield thickness is represented by a 25 g/cm² spherical shell. Although, one could imagine the progression to greater thickness, the current range will be sufficient to evaluate the qualitative usefulness of the aluminum equivalent approximation. Upon establishing the inaccuracies of the aluminum equivalent approximation through numerical simulations of the GCR radiation field attenuation for PE and aluminum equivalent PE spherical shells, we further present results for a limited set of commercially available, hydrogen rich, multifunctional polymeric constituents to assess the effect of the aluminum equivalent approximation on their radiation attenuation response as compared to the generic PE.     

Proton lateral broadening distribution comparisons between GRNTRN,MCNPX, and laboratory beam measurements

Recent developments in NASA’s deterministic High charge (Z) and Energy TRaNsport (HZETRN) code have included lateral broadening of primary ion beams due to small-angle multiple Coulomb scattering, and coupling of the ion-nuclear scattering interactions with energy loss and straggling. This new version of HZETRN is based on Green function methods, called GRNTRN, and is suitable for modeling transport with both space environment and laboratory boundary conditions. Multiple scattering processes are a necessary extension to GRNTRN in order to accurately model ion beam experiments, to simulate the physical and biological-effective radiation dose, and to develop new methods and strategies for light-ion radiation therapy. In this paper we compare GRNTRN simulations of proton lateral broadening distributions with beam measurements taken at Loma Linda University Proton Therapy Facility. The simulated and measured lateral broadening distributions are compared for a 250 MeV proton beam on aluminum, polyethylene, polystyrene, bone substitute, iron, and lead target materials. The GRNTRN results are also compared to simulations from the Monte Carlo MCNPX code for the same projectile-target combinations described above.     

Analytical-HZETRN model for rapid assessment of active magnetic radiation shielding

The use of active radiation shielding designs has the potential to reduce the radiation exposure received by astronauts on deep-space missions at a significantly lower mass penalty than designs utilizing only passive shielding. Unfortunately, the determination of the radiation exposure inside these shielded environments often involves lengthy and computationally intensive Monte Carlo analysis. In order to evaluate the large trade space of design parameters associated with a magnetic radiation shield design, an analytical model was developed for the determination of flux inside a solenoid magnetic field due to the Galactic Cosmic Radiation (GCR) radiation environment. This analytical model was then coupled with NASA’s radiation transport code, HZETRN, to account for the effects of passive/structural shielding mass. The resulting model can rapidly obtain results for a given configuration and can therefore be used to analyze an entire trade space of potential variables in less time than is required for even a single Monte Carlo run. Analyzing this trade space for a solenoid magnetic shield design indicates that active shield bending powers greater than ∼15 Tm and passive/structural shielding thicknesses greater than 40 g/cm² have a limited impact on reducing dose equivalent values. Also, it is shown that higher magnetic field strengths are more effective than thicker magnetic fields at reducing dose equivalent.     

Satellite collision probability estimation using polynomial chaos expansions

This paper presents the application of polynomial chaos (PC) to estimating the probability of collision between two spacecraft. Common methods of quantifying this probability for conjunction assessment use either Monte Carlo analyses or include simplifying assumptions to improve tractability. A PC expansion, or PCE, provides a means for approximating the solution to a large set of stochastic ordinary differential equations, which includes orbit propagation. When compared to Monte Carlo methods, non-intrusive, i.e., sampling-based, PCE generation techniques may greatly reduce the number of orbit propagations required to approximate the possibly non-Gaussian, a posteriori probability density function. The presented PC-based method of computing collision probability requires no fundamental simplifying assumptions, and reduces the computation time compared to Monte Carlo. This paper considers two cases where the common conjunction assessment assumptions are no longer valid. The results indeed demonstrate a reduction in computation time when compared to Monte Carlo, and improved accuracy when compared to simplified techniques.     

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.     

航天器热模型蒙特卡罗法参数分析及健壮度评估研究

针对传统航天器热模型的参数分析及温度余量选择存在的缺陷,提出了基于蒙特卡罗法的参数分析及健壮度评估方法。文章首先以航天器设备温度为因变量,以各不确定参数为自变量,应用蒙特卡罗法模拟取样,得到动态参数样本;通过样本的统计式推导,给出了参数分析及健壮度评估的求解方法。结合某星热模型进行了仿真应用,结果表明:与传统方法相比,蒙特卡罗法不但可以提高参数分析的效率,而且量化了各不确定参数敏感性以及设备温度分布概率,为设计人员判断设备温度余量提供数值依据。     

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.     

屏蔽材料对木星轨道卫星内部介质充电效应的影响研究

在木星轨道的空间辐射环境中,占主导地位的粒子是能量大于1MeV（甚至高于100MeV）的高能电子,这可能会产生卫星内部介质充电效应。在卫星的防辐射设计中,通常需要一定厚度的材料来屏蔽这些电子,使得进入卫星内部的电子通量达到安全的水平。利用所建立的GEANT4-RIC（radiation induced conductivity）方法,研究了运行于木星轨道的卫星对高能电子的最佳屏蔽材料设计。研究了铝、钛、铁、铜、钽和铅作为卫星屏蔽材料的可能性。研究结果表明,在木星探测任务中,为了减轻卫星内部介质充电效应,高原子序数材料比低原子序数材料在相同质量下提供的屏蔽效果更好。因此,用钛、铁、铜、钽或铅代替地球轨道卫星上常用的屏蔽材料铝,可以节省屏蔽质量。     

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.     

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.     

Method for the prediction of the effective dose equivalent to the crew of the International Space Station

This paper describes a methodology for assessing the pre-mission exposure of space crew aboard the International Space Station (ISS) in terms of an effective dose equivalent. In this approach, the PHITS Monte Carlo code was used to assess the particle transport of galactic cosmic radiation (GCR) and trapped radiation for solar maximum and minimum conditions through an aluminum shield thickness. From these predicted spectra, and using fluence-to-dose conversion factors, a scaling ratio of the effective dose equivalent rate to the ICRU ambient dose equivalent rate at a 10 mm depth was determined. Only contributions from secondary neutrons, protons, and alpha particles were considered in this analysis.     

基于线性协方差方法的交会对接误差分析

将线性协方差分析方法和蒙特卡罗仿真相结合,按交会任务和飞行特征把交会过程分为变轨飞行、自由飞行和中途速度修正三种特征段,研究了状态误差的传播规律和交会过程中各种误差对交会对接精度的影响。在变轨飞行段,分析了追踪航天器的姿态误差、控制系统性能状态估计误差,以及目标航天器轨道摄动对状态误差传播的影响。在自由飞行段,分析了追踪航天器估计状态误差的先验值和测轨误差对状态误差传播的影响。在中途速度修正段,分析了追踪航天器姿态误差和控制系统性能误差对状态误差传播的影响。仿真结果表明,误差分析方法设计合理,可以指导交会对接的轨道设计工作,能对已经设计好的交会策略进行误差分析和设计验证。     

New equivalent sphere approximation for BFO dose estimation: Solar particle events

The use of a 5 cm tissue equivalent sphere model to obtain dose estimates for the blood-forming organs from energetic space radiations has been widespread for some time. Recent studies have noted that calculated doses obtained using the 5 cm equivalent sphere model were very conservatively overestimated when compared to those obtained with a detailed body geometry. Such conservatism may introduce significant shield weight penalties if used in spacecraft design studies. The use of detailed human geometry models will yield more accurate estimates of blood-forming organ doses and dose equivalents, but with a concomitant reduction in computational ease. In this work we propose a preliminary, yet new blood-forming organ equivalent sphere approximation for use in estimating SPE exposure and in shield design studies that is more realistic than the existing 5-cm approximation.     

Monte Carlo simulations of CASSINI/LEMMS

In an effort to characterize the response of the low energy magnetospheric measurements system (LEMMS) on the CASSINI spacecraft to energetic ions and electrons we have taken advantage of the excellent pre-launch beam calibrations in comparison to an extensive series of electron and ion Monte Carlo simulations. We selected the geometry and tracking toolkit to provide the framework for the instrument modeling and simulation environment. The results from these simulations match very well with the data collected during the instrument calibration. This gives us confidence that this simulation toolkit handles both electron and ion interactions in a reasonable fashion and that we can successfully apply this tool to regions of the spectrum where calibration data is not available.     

航天器与短期空间碎片云碰撞概率算法

讨论了航天器与碎片云碰撞概率的提法,介绍了不同碰撞概率间的转换方法。在航天器轨道和碎片云中心轨道都确定情况下,研究了碰撞概率的一般算法;并根据C-W方程推导了只在短时间内有效的简化碰撞概率算法。最后通过蒙特卡洛法验证了简化算法的正确性。     

反向蒙特卡罗方法在卫星辐射分析中的研究与应用

反向蒙特卡罗方法(AMC/RMC)是Geant4中一个强有力的偏置技术. 粒子产生于包含灵敏体的反向界面并在几何体中被反向追踪直至外界面或溢出能量阈值, 其计算时间只集中于对结果有贡献的粒子径迹. 与正向蒙特卡罗方法(FMC)相比, RMC更高效, 特别是当灵敏体远小于几何体其他部分和外界面时, 其优势更明显. 通过RMC与FMC的比较, 验证了RMC应用于卫星辐射剂量分析的准确性. RMC与SHIELDOSE2和SSAT的比较说明了RMC是高精度卫星辐射剂量的优选方法.      

空间任意形状凸面的轨道空间外热流计算方法

采用蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法，进行了平板、半球面、抛物面的地球反照角系数和地球红外角系数计算，通过与文献数据的比较，证明了由此方法所编程序的可靠性和实用性。利用这种方法，可以计算空间任意形状凸表面的轨道空间外热流。