A comparison of total reaction cross section models used in particle and heavy ion transport codes

Understanding the interactions and propagations of high energy protons and heavy ions are essential when trying to estimate the biological effects of Galactic Cosmic Rays (GCR) and Solar Particle Events (SPE) on personnel in space. To be able to calculate the shielding properties of different materials and radiation risks, particle and heavy ion transport codes are needed. In all particle and heavy ion transport codes, the probability function that a projectile particle will collide within a certain distance x in the matter depends on the total reaction cross sections, and the calculated partial fragmentation cross sections scale with the total reaction cross sections. It is therefore crucial that accurate total reaction cross section models are used in the transport calculations. In this paper, different models for calculating nucleon–nucleus and nucleus–nucleus total reaction cross sections are compared with each other and with measurements. The uncertainties in the calculations with the different models are discussed, as well as their overall performances with respect to the available experimental data. Finally, a new compilation of experimental data is briefly presented.     

Nuclear fragmentation of high-energy heavy-ion beams in water.

As a part of the physical-technical program of the heavy-ion therapy project at GSI we have investigated the nuclear fragmentation of high-energy ion beams delivered by the heavy-ion synchrotron SIS, using water as a tissue-equivalent target. For a direct comparison of fragmentation properties, beams of 10B, 12C, 14N, and 16O were produced simultaneously as secondary beams from a primary 18O beam and separated in flight by magnetic beam analysis. The Z-distributions of beam fragments produced in the water target were measured via energy loss in a large ionisation chamber and a scintillator telescope. From these data we obtained both total and partial charge-changing cross sections. In addition we have performed Bragg measurements using two parallel-plate ionization chambers and a water target of variable length. The detailed shape of the measured Bragg curves and the measured cross sections are in good agreement with model calculations based on semi-empirical formulae.     

Simulations of an accelerator-based shielding experiment using the particle and heavy-ion transport code system PHITS.

In order to estimate the biological effects of HZE particles, an accurate knowledge of the physics of interaction of HZE particles is necessary. Since the heavy ion transport problem is a complex one, there is a need for both experimental and theoretical studies to develop accurate transport models. RIST and JAERI (Japan), GSI (Germany) and Chalmers (Sweden) are therefore currently developing and bench marking the General-Purpose Particle and Heavy-Ion Transport code System (PHITS), which is based on the NMTC and MCNP for nucleon/meson and neutron transport respectively, and the JAM hadron cascade model. PHITS uses JAERI Quantum Molecular Dynamics (JQMD) and the Generalized Evaporation Model (GEM) for calculations of fission and evaporation processes, a model developed at NASA Langley for calculation of total reaction cross sections, and the SPAR model for stopping power calculations. The future development of PHITS includes better parameterization in the JQMD model used for the nucleus-nucleus reactions, and improvement of the models used for calculating total reaction cross sections, and addition of routines for calculating elastic scattering of heavy ions, and inclusion of radioactivity and burn up processes. As a part of an extensive bench marking of PHITS, we have compared energy spectra of secondary neutrons created by reactions of HZE particles with different targets, with thicknesses ranging from <1 to 200 cm. We have also compared simulated and measured spatial, fluence and depth-dose distributions from different high energy heavy ion reactions. In this paper, we report simulations of an accelerator-based shielding experiment, in which a beam of 1 GeV/n Fe-ions has passed through thin slabs of polyethylene, Al, and Pb at an acceptance angle up to 4 degrees.     

Liquid drop model considerations in HZE particle fragmentation by hydrogen

The fragmenting of high energy, heavy ions by hydrogen targets is an important physical process in several areas of space radiation protection research. Quantum mechanical, optical model methods for calculating cross sections for particle fragmentation by hydrogen have been developed from a modified abrasion-ablation collision formalism. The abrasion stage is treated as a knockout process which leaves the residual prefragment in an excited state. In the ablation stage the prefragment deexcites to produce the final fragment. The prefragment excitation energies are estimated from a combination of liquid drop model considerations and frictional-spectator interaction processes. Estimates of elemental and isotopic production cross sections are in good agreement with published cross section measurements.     

HZE effects on mammalian cells.

In track segment experiments cell survival and chromosome aberrations of mammalian cells have been measured for various heavy ion beams between helium and uranium in the energy range between 0.5 and 960 MeV/u, corresponding to a velocity range of 0.03 to 0.87 C, and an LET spectrum from 10 to 15 000 keV/micrometers. At low LET, the cross section (sigma) for cell killing increases with increasing LET and shows a common curve for all ions regardless of the atomic number. This indicates that in this region the track structure of the different ions is of only a minor influence, and it is rather the total energy transfer, which is important for cell killing. At higher LET values, deviations from a common sigma-LET curve can be observed which indicate a saturation effect. The saturation of the lighter ions occurs at lower LET values than for the heavier ions. These findings are also confirmed by the chromosome data, where the efficiency for the induction of chromosomal aberrations for high LET particles depends on the track structure and is nearly independent of LET. In the heavier beams (Z > or = 10) individual particles cause multiple chromosome breaks in mitotic cells.     

Cell inactivation, repair and mutation induction in bacteria after heavy ion exposure: results from experiments at accelerators and in space.

To understand the mechanisms of accelerated heavy ions on biological matter, the responses of spores of B. subtilis to this structured high LET radiation was investigated applying two different approaches. 1) By the use of the Biostack concept, the inactivation probability as a function of radial distance to single particles' trajectory (i.e. impact parameter) was determined in space experiments as well as at accelerators using low fluences of heavy ions. It was found that spores can survive even a central hit and that the effective range of inactivation extends far beyond impact parameters where inactivation by delta-ray dose would be effective. Concerning the space experiment, the inactivation cross section exceeds those from comparable accelerator experiments by roughly a factor of 20. 2) From fluence effect curves, cross sections for inactivation and mutation induction, and the efficiency of repair processes were determined. They are influenced by the ions characteristics in a complex manner. According to dependence on LET, at least 3 LET ranges can be differentiated: A low LET range (app. < 200 keV/micrometers), where cross sections for inactivation and mutation induction follow a common curve for different ions and where repair processes are effective; an intermediate LET range of the so-called saturation cross section with negligible mutagenic and repair efficiency; and a high LET range (>1000 keV/micrometers) where the biological endpoints are majorly dependent on atomic mass and energy of the ion under consideration.     

Towards multi-dimensional space weather modeling for energetic oxygen ions in the earth''s inner magnetosphere: Equilibrium configuration

We report the first 3+1 dimensional model development for energetic atomic oxygen ions in the Earth's radiation belts. Energetic Oxygen ions cans be supplied to the Earth's Inner magnetosphere from the sun (as a component of solar wind and solar energetic particles), from anomalous cosmic rays, and from acceleration processes acting on ionospheric atomic oxygen ions. We have built a multi-dimensional oxygen ion model in the following free parameters: geomagnetic L-shell, the magnetic moment, the second adiabatic invariant, and the discrete charge state number. Quiet time, steady state oxygen ion distributions have been obtained numerically from an assumed outer radiation zone boundary condition at L=7, average values of the radial diffusion coefficients, and standard values for the exospheric neutral densities due to the MSIS-86 upper atmosphere and exosphere neutral thermal particle density model. Average distributions of free electrons in the plasmasphere were also assumed with a mean plasmapause location just beyond L=4. We included the six lowest ionic charge states of atomic oxygen (¹⁶O) based on an existing charge exchange cross section compilation by Spjeldvik and Fritz (1978). Computed oxygen ion distributions include the resulting equilibrium structure of energy oxygen ions between 10 KeV and 100 MeV.     

A model of the effects of heavy ion radiation on human tissue

In heavy ion radiotherapy and space travel humans are exposed to energetic heavy ions (C, Si, Fe and others). This type of irradiation often produces more severe biological effects per unit dose than more common X-rays. A new Monte Carlo model generates a physical space with the complex geometry of human tissue or a cell culture based model of tissue, which is affected by the passage of ionizing radiation. For irradiation, the model relies on a physical code for the ion track structure; for tissues, cellular maps are derived from two- or three-dimensional confocal microscopy images using image segmentation algorithm, which defines cells as pixilated volumes. The model is used to study tissue-specific statistics of direct ion hits and the remote ion action on cells. As an application of the technique, we considered the spatial pattern of apoptotic cells after heavy ion irradiation. The pattern of apoptosis is modeled as a stochastic process, which is defined by the action cross section taken from available experimental data. To characterize the degree of apoptosis, an autocorrelation function that describes the spatial correlation of apoptotic cells is introduced. The values of the autocorrelation function demonstrate the effect of the directionality of the radiation track on the spatial arrangements of inactivated cells in tissue. This effect is intrinsic only to high linear-energy-transfer radiation.     

Simulation of depth–dose distributions for various ions in polyethylene medium

Study of depth–dose distributions for intermediate energy ion beams in tissue-like media such as polyethylene (CH₂)_n provides a good platform for further improvements in the fields of hadrontherapy and space radiation shielding. The depth–dose distributions for ¹²C ions at various energies and for light and intermediate ion beams (³He, ¹⁶O, ²⁰Ne and ²⁸Si) as well as for heavy ions ⁵⁶Fe in polyethylene were estimated by using simulation toolkit: Geant4. Calculations were performed mainly by considering two different combinations of standard electromagnetic (EM), binary cascade (BIC), statistical multifragmentation (SMF) and Fermi breakup (FB) models. The energies of the ion beams were selected to achieve the Bragg peaks at predefined position (∼60 mm) and as per their availability. Variations of peak-to-entrance ratio (from 7.44 ± 0.05 to 8.87 ± 0.05), entrance dose (from 2.89 ± 0.01 to 203.71 ± 0.63 MeV/mm) and entrance stopping power (from 3.608 to 208.858 MeV/mm, calculated by SRIM) with atomic number (Z) were presented in a systematic manner. The better peak-to-entrance ratio and less entrance dose in the region Z = 2 to 8 (i.e. ³He to ¹⁶O) may provide the suitability of the ion beams for hadrontherapy.     

The FLUKA code for space applications: recent developments.

The FLUKA Monte Carlo transport code is widely used for fundamental research, radioprotection and dosimetry, hybrid nuclear energy system and cosmic ray calculations. The validity of its physical models has been benchmarked against a variety of experimental data over a wide range of energies, ranging from accelerator data to cosmic ray showers in the earth atmosphere. The code is presently undergoing several developments in order to better fit the needs of space applications. The generation of particle spectra according to up-to-date cosmic ray data as well as the effect of the solar and geomagnetic modulation have been implemented and already successfully applied to a variety of problems. The implementation of suitable models for heavy ion nuclear interactions has reached an operational stage. At medium/high energy FLUKA is using the DPMJET model. The major task of incorporating heavy ion interactions from a few GeV/n down to the threshold for inelastic collisions is also progressing and promising results have been obtained using a modified version of the RQMD-2.4 code. This interim solution is now fully operational, while waiting for the development of new models based on the FLUKA hadron-nucleus interaction code, a newly developed QMD code, and the implementation of the Boltzmann master equation theory for low energy ion interactions.     

Cellular parameters for track structure modeling of radiation hazard in space.

Based on irradiation with 45 MeV/u N and B ions and with Co-60 gamma rays, cellular parameters of Katz's track structure model have been fitted for the survival of V79-379A Chinese hamster lung fibroblasts. Cellular parameters representing neoplastic transformations in C3H10T/1/2 cells after their irradiation with heavy ion beams, taken from earlier work, were also used to model the radiation hazard in deep space, following the system for evaluating, summing and reporting occupational exposures proposed in 1967 by a subcommittee of NCRP. We have performed model calculations of the number of transformations in surviving cells, after a given fluence of heavy charged particles of initial energy 500 MeV/u, penetrating thick layers of cells. We take the product of cell transformation and survival probabilities, calculated along the path lengths of charged particles using cellular survival and transformation parameters, to represent a quantity proportional to the "radiation risk factor" discussed in the NCRP document. The "synergistic" effect of simultaneous charged particle transfers is accounted for by the "track overlap" mode inherent in the model of Katz.     

RBE: mechanisms inferred from cytogenetics.

Cyclotron-accelerated heavy ion beams provide a fine degree of control over the physical parameters of radiation. Cytogenetics affords a view into the irradiated cell at the resolution of chromosomes. Combined they form a powerful means to probe the mechanisms of RBE. Cytogenetic studies with high energy heavy ion beams reveal three LET-dependent trends for 1) level of initial damage, 2) distribution of damage among cells, and 3) lesion severity. The number of initial breaks per unit dose increases from a low-LET plateau to a peak at approximately 180 keV/micrometer and declines thereafter. Overdispersion of breaks is significant above approximately 100 keV/micrometer. Lesion severity, indicated by the level of chromosomal fragments that have not restituted even after long repair times, increases with LET. Similar studies with very low energy 238Pu alpha particles (120 keV/micrometer) reveal higher levels of initial breakage per unit dose, fewer residual fragments and a higher level of misrepair when compared to high energy heavy ions at the same LET. These observations would suggest that track structure is an important factor in genetic damage in addition to LET.     

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.     

极光场线上上行氧离子(O+)束驱动的静电离子迥旋波和离子声波不稳定性

本文研究了由背景热电子、背景冷质子(H+)和强各向异性氧离子(O+)束组成的模型等离子体中静电O+迴旋波和离子声波不稳定性.结果表明,低频(|ω|<σ_p,σ_p表示质子迴旋频率)静电O+迴旋波和离子声波可以由极光场线上上行O+束来激发.上行O+束可能是极光场线上低频静电不稳定性一个重要的自由能源.      

Microdosimetric considerations of effects of heavy ions on E. coli K-12 mutants.

The inactivation cross sections of E. coli K-12 recombination-deficient mutants, JC1553 (recA) and AB2470 (recB), for several MeV/u alpha-particles and N ions have been successfully analyzed by Katz's target theory in which radiosensitivity parameter E0 is assumed to be LET independent and equal to D37 for gamma-rays. For E. coli K-12 wild type, AB1157 (rec+, uvr+), however, it is impossible to interpret the inactivation cross section data by an LET-independent E0-value. In the latter case, as in the case of B. subtilis spore, it is necessary to assume that the radiosensitivity of the target for the core of a heavy ion is higher than that for delta-electrons. As well as Waligorski, Hamm and Katz's dose, the dose around the trajectory of an ion based on Tabata and Ito's energy deposition algorithm for electrons has been used in the course of analysis.     

Depth dependency of neutron density produced by cosmic rays in the lunar subsurface

Depth dependency of neutrons produced by cosmic rays (CRs) in the lunar subsurface was estimated using the three-dimensional Monte Carlo particle and heavy ion transport simulation code, PHITS, incorporating the latest high energy nuclear data, JENDL/HE-2007. The PHITS simulations of equilibrium neutron density profiles in the lunar subsurface were compared with the measurement by Apollo 17 Lunar Neutron Probe Experiment (LNPE). Our calculations reproduced the LNPE data except for the 350–400 mg/cm² region under the improved condition using the CR spectra model based on the latest observations, well-tested nuclear interaction models with systematic cross section data, and JENDL/HE-2007.     

Nuclear fragmentation database for GCR transport code development

A critical need for NASA is the ability to accurately model the transport of heavy ions in the Galactic Cosmic Rays (GCR) through matter, including spacecraft walls, equipment racks, etc. Nuclear interactions are of great importance in the GCR transport problem, as they can cause fragmentation of the incoming ion into lighter ions. Since the radiation dose delivered by a particle is proportional to the square of (charge/velocity), fragmentation reduces the dose delivered by incident ions. The other mechanism by which dose can be reduced is ionization energy loss, which can lead to some particles stopping in the shielding. This is the conventional notion of shielding, but it is not applicable to human spaceflight since the particles in the GCR tend to be too energetic to be stopped in the relatively thin shielding that is possible within payload mass constraints. Our group has measured a large number of fragmentation cross sections, intended to be used as input to, or for validation of, NASA’s radiation transport models. A database containing over 200 charge-changing cross sections and over 2000 fragment production cross sections has been compiled. In this report, we examine in detail the contrast between fragment measurements at large acceptance and small acceptance. We use output from the PHITS Monte Carlo code to test our assumptions using as an example ⁴⁰Ar data (and simulated data) at a beam energy of 650 MeV/nucleon. We also present preliminary analysis in which isotopic resolution was attained for beryllium fragments produced by beams of ¹⁰B and ¹¹B. Future work on the experimental data set will focus on extracting and interpreting production cross sections for light fragments.     

Biological effects of heavy ions from the standpoint of target theory.

The biological effect of heavy ions is best described through the action cross section, as a function of the end-point of interest and the charge and speed of the ion. In track theory this is called the "ion-kill" cross section, for it is the effect produced by a single heavy ion and its delta rays. As with nuclear emulsions the biological track structure passes from the grain count regime to the track width regime to the thindown region with an increase in LET. With biological cells, as with any detector capable of storing sublethal damage, with low LET irradiation the action cross section (in the ion-kill mode) is increasingly obscured by the effect of "gamma-kill", by the influence of overlapping delta rays from neighboring heavy ions. Thus at low LET response is dominated by the gamma-kill mode, so that the RBE approaches 1. The theory requires 4 radiosensitivity parameters for biological detectors, extracted from survival curves at several high LET bombardments passing through the grain count regime, and at high doses. Once these are known the systematic response of biological detectors to all high LET bombardments can be unfolded separating ion kill from gamma kill, predicting the response to a mixed radiation environment, and predicting low dose response even at the level of a single heavy ion. Cell killing parameters are now available for a variety of cell lines. Newly added is a set of parameters for cell transformation.