Elsevier

Advances in Space Research

Volume 47, Issue 3, 1 February 2011, Pages 533-544
Advances in Space Research

Validation of a multi-layer Green’s function code for ion beam transport

https://doi.org/10.1016/j.asr.2010.09.012Get rights and content

Abstract

To meet the challenge of future deep space programs, an accurate and efficient engineering code for analyzing the shielding requirements against high-energy galactic heavy ion radiation is needed. In consequence, a new version of the HZETRN code capable of simulating high charge and energy (HZE) ions with either laboratory or space boundary conditions is currently under development. This code, GRNTRN, is based on a Green’s function approach to the solution of the one-dimensional Boltzmann transport equation and like its predecessor is deterministic in nature. The computational model consists of the lowest order asymptotic approximation followed by a Neumann series expansion with non-perturbative corrections. The physical description includes energy loss with straggling, nuclear attenuation, nuclear fragmentation with energy dispersion and down shift. Code validation in the laboratory environment is addressed by showing that GRNTRN accurately predicts energy loss spectra as measured by solid-state detectors in ion beam experiments with multi-layer targets. In order to verify and benchmark the code with space boundary conditions, measured particle fluxes are propagated through several thicknesses of shielding using both GRNTRN and the current version of HZETRN. The favorable agreement obtained indicates that GRNTRN accurately models the propagation of HZE ions in laboratory settings. It also compares very well with the extensively validated space environment HZETRN code and thus provides verification of the HZETRN propagator.

Introduction

As part of its human space exploration program, NASA envisions a number of long duration space missions on which astronauts risk exposure to radiation originating from the Sun and galactic sources. Since it has long been recognized that such radiation can have a detrimental effect on the health of humans and on the performance of mission critical equipment, radiation shielding has become a topic of ever-increasing importance as the space program proceeds into an era of extended human space operations (Space Studies Board, 1996). The shielding and exposure of space travelers is controlled by the transport properties of the radiation through the spacecraft, its onboard systems and the bodies of the individuals themselves. Meeting the challenge of future space programs will therefore require accurate and efficient methods for performing radiation transport calculations to analyze and predict shielding requirements. According to a recent National Research Council Report (Committee on the Evaluation of Radiation Shielding for Space Exploration, 2008), predictions derived from radiation transport calculations need to be tested using a common code for laboratory and space measurements that have been validated with accelerator results. However, as noted by Wilson et al. (1990), numerical solution methods for the Boltzmann transport equation are best suited to space radiations where the energy spectra are smooth over large energy intervals, and less suited to the simulation of laboratory beams which exhibit large spectral variation over a very limited energy domain and large energy derivative. As a result, codes based on these methods are not readily validated by comparison with laboratory experiment. Only analytical procedures are able to simulate both space radiations and laboratory beam transport with equal ability and a common procedure when using deterministic methods. Green’s function techniques have therefore been identified as the likely means of generating efficient high charge and energy (HZE) shielding codes for space engineering that are capable of being validated in laboratory experiments (Wilson et al., 1989). In consequence, a laboratory code designed to simulate the transport of heavy ions through a single layer of material was developed (Wilson et al., 1990, Wilson et al., 1993). It was based on a Green’s function model as a perturbation series with non-perturbative corrections. The code was validated for single layer targets and then extended to handle multi-layer targets (Wilson et al., 1991, Shinn et al., 1994, Shinn et al., 1995). This early code used a scale factor to equate range-energy relations of one material thickness into an equivalent amount of another material, and proceeded to perform calculations of nuclear factors in the specific material (Shinn et al., 1997). While this method has proven to be acceptable using low-resolution detectors (Shinn et al., 1994, Walker et al., 2005), it is not the most accurate reflection of different material properties and is unsuited for high-resolution measurements. Lacking from the prior solutions were range and energy straggling and energy downshift and dispersion associated with nuclear events. In a recent publication (Tweed et al., 2004), it was shown how these effects could be incorporated into the multiple fragmentation perturbation series leading to the development of a new Green’s function code GRNTRN (a GReeN’s function code for ion beam TRaNsport). The current version of GRNTRN has proven to be accurate in modeling ion beams for a single layer of material (Walker et al., 2005, Tweed et al., 2007), and has now been extended to handle multiple layers. Unlike the earlier Green’s function code of Shinn et al., 1994, Shinn et al., 1997 the new code does not homogenize the target by replacing each layer by an equivalent amount of another material. Instead it transports ions through the target, layer by layer, while making use of the actual material properties of each target layer.

Section snippets

The Boltzmann equation

The transport of high charge and energy ions through matter is governed by the linear Boltzmann equation (Wilson, 1977, Wilson et al., 1991)xϕj(x,E)=kjRσjk(E,E)ϕk(x,E)dE-σj(E)ϕj(x,E),xx,j=1,2,3,N,where N is the number of ions in the model, ϕj(x, E) is the flux of ions of type j moving along the x-axis at energy E in units of MeV/amu, and σj(E) and σjk (E, E′) are the media macroscopic cross sections. The σjk(E, E′) represent all those processes by which type k particles moving in the x

General

It will now be shown that the single layer Green’s function described above can be used to generate the Green’s function for a multi-layer target. The target is assumed to consist of M layersLm={x:xm-1xxm},m=1,2,3,,M,some or all of which may be comprised of distinct, homogeneous materials. The single layer Green’s function for the layer Lm will be denoted by the symbol Gjk(x, xm−1, E, Em−1;m) and the multi-layer Green’s function by the symbol Gjk(x, x0, E, E0). Conceptually, the procedure is quite

The experiments

In recent years, 1 GeV/nucleon 56Fe beams from the Brookhaven National Laboratory Alternating Gradient Synchrotron (BNL AGS) have been used to study fragmentation in several types and thicknesses of prospective shielding materials. Silicon detector measurements taken during these experiments provide a ready source of data with which to validate GRNTRN in the laboratory setting.

The detector configuration for the fragmentation experiments was of the type shown schematically in Fig. 2 and typical

Code verification for the space environment

In order to verify the GRNTRN code with space boundary conditions, measured particle fluxes for the 56Fe ions associated with the 1977 solar minimum(Wilson et al., 1995a) were propagated through a multi-layer target using both GRNTRN and the current version of HZETRN (Wilson et al., 2005) and a comparison made between the corresponding results. The target chosen for this study consisted of 10 g/cm2 Al followed by 10 g/cm2CH2 and 30 g/cm2 H2O.

When the only particles striking the boundary of the

Conclusion

A Green’s function solution of the Boltzmann equation has been used to construct a new computer code (GRNTRN) that is capable of simulating the transport of HZE ions through multi-layer shields with space or laboratory boundary conditions. The code has been validated in the laboratory environment by showing that it predicts energy loss spectra as measured by solid-state detectors in ion beam experiments with multi-layer targets with reasonable accuracy. In order to benchmark the code with space

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