A study of the generation of linear energy transfer spectra for space radiations

The conversion of particle-energy spectra into a linear energy transfer (LET) distribution is a guide in assessing biologically significant components. The mapping of LET to energy is triple valued and can be defined only on open subintervals. A well-defined numerical procedure is found to allow generation of LET spectra on the open subintervals that are integrable in spite of their singular nature

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 (ray) events. At any designated (ray traced) target point within the vehicle, the model accepts the differential flux spectrum of Galactic Cosmic Rays (GCR) 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 seconds/ion. The ionizing radiation environment at LEO is represented by O'Neill fs GCR model (2004), covering charged particles in the 1 less than or equal to Z less than or equal to 28. 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

Shielding from Space Radiations

This Final Progress Report for NCC-1-178 presents the details of the engineering development of an analytical/computational solution to the heavy ion transport equation in terms of a multi-layer Green's function formalism as applied to the Small Spacecraft Technology Initiative (SSTI) program. The mathematical developments are recasted into a series of efficient computer codes for space applications. The efficiency of applied algorithms is accomplished by a nonperturbative technique of extending the Green's function over the solution domain. The codes may also be applied to the accelerator boundary conditions to allow code validation in laboratory experiments. Correlations with experiments for the isotopic version of the code with 59 and 80 isotopes present for a two layers target material in water has been verified

Green's function methods in heavy ion shielding

An analytic solution to the heavy ion transport in terms of Green's function is used to generate a highly efficient computer code for space applications. The efficiency of the computer code is accomplished by a nonperturbative technique extending Green's function over the solution domain. The computer code can also be applied to accelerator boundary conditions to allow code validation in laboratory experiments

Extension of the BRYNTRN code to monoenergetic light ion beams

A monoenergetic version of the BRYNTRN transport code is extended to beam transport of light ions (H-2, H-3, He-3, and He-4) in shielding materials (thick targets). The redistribution of energy in nuclear reactions is included in transport solutions that use nuclear fragmentation models. We also consider an equilibrium target-fragment spectrum for nuclei with mass number greater than four to include target fragmentation effects in the linear energy transfer (LET) spectrum. Illustrative results for water and aluminum shielding, including energy and LET spectra, are discussed for high-energy beams of H-2 and He-4

3DHZETRN: Inhomogeneous Geometry Issues

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here

Standardized Radiation Shield Design Methods: 2005 HZETRN

Research committed by the Langley Research Center through 1995 resulting in the HZETRN code provides the current basis for shield design methods according to NASA STD-3000 (2005). With this new prominence, the database, basic numerical procedures, and algorithms are being re-examined with new methods of verification and validation being implemented to capture a well defined algorithm for engineering design processes to be used in this early development phase of the Bush initiative. This process provides the methodology to transform the 1995 HZETRN research code into the 2005 HZETRN engineering code to be available for these early design processes. In this paper, we will review the basic derivations including new corrections to the codes to insure improved numerical stability and provide benchmarks for code verification

Faster and More Accurate Transport Procedures for HZETRN

Several aspects of code verification are examined for HZETRN. First, a detailed derivation of the numerical marching algorithms is given. Next, a new numerical method for light particle transport is presented, and improvements to the heavy ion transport algorithm are discussed. A summary of various coding errors is also given, and the impact of these errors on exposure quantities is shown. Finally, a coupled convergence study is conducted. From this study, it is shown that past efforts in quantifying the numerical error in HZETRN were hindered by single precision calculations and computational resources. It is also determined that almost all of the discretization error in HZETRN is caused by charged target fragments below 50 AMeV. Total discretization errors are given for the old and new algorithms, and the improved accuracy of the new numerical methods is demonstrated. Run time comparisons are given for three applications in which HZETRN is commonly used. The new algorithms are found to be almost 100 times faster for solar particle event simulations and almost 10 times faster for galactic cosmic ray simulations

Semiempirical fragmentation models on galactic cosmic ray transport calculations with hydrogen target

Nuclear fragmentation cross sections of Silberberg and Tsao that are more accurate for a hydrogen target were implemented in the data base to replace those of Rudstam for a galactic cosmic ray transport code (HZETRN). Sample calculations were made for the transported galactic cosmic ray flux through a liquid hydrogen shield at solar minimum condition to determine the effect of such a change. The transported flux based on the Silberberg-Tsao semiempirical formalism contains fewer high-LET (linear energy transfer) components but more low-LET components than the results based on Rudstam's formalism: and this disparity deepens as the shield thickness increases. A comparison of the results obtained from using both energy-dependent and energy-independent cross sections of Silberberg and Tsao indicates that the energy-independent assumption results in an underestimation of high-LET flux above 100 keV/micron by approximately 40 percent for a 15-g/cm(sup 2) thickness of liquid hydrogen. Similar results were obtained in a previous study when both energy-dependent and energy-independent cross sections of Rudstam were considered. Nonetheless, the present study found that an energy-independent calculation would be best accomplished by using Rudstam's cross sections as done in the past for various engineering applications

Coulomb effects in low-energy nuclear fragmentation

Early versions of the Langley nuclear fragmentation code NUCFRAG (and a publicly released version called HZEFRG1) assumed straight-line trajectories throughout the interaction. As a consequence, NUCFRAG and HZEFRG1 give unrealistic cross sections for large mass removal from the projectile and target at low energies. A correction for the distortion of the trajectory by the nuclear Coulomb fields is used to derive fragmentation cross sections. A simple energy-loss term is applied to estimate the energy downshifts that greatly alter the Coulomb trajectory at low energy. The results, which are far more realistic than prior versions of the code, should provide the data base for future transport calculations. The systematic behavior of charge-removal cross sections compares favorably with results from low-energy experiments