Charged Particle Transport Research Articles

Microwave air plasmas in capillaries at low pressure I. Self-consistent modeling

This work presents the self-consistent modeling of micro-plasmas generated in dry air using microwaves (2.45 GHz excitation frequency), within capillaries (<1 mm inner radius) at low pressure (300 Pa). The model couples the system of rate balance equations for the most relevant neutral and charged species of the plasma to the homogeneous electron Boltzmann equation. The maintenance electric field is self-consistently calculated adopting a transport theory for low to intermediate pressures, taking into account the presence of O− ions in addition to several positive ions, the dominant species being O, NO+ and O+ . The low-pressure small-radius conditions considered yield very-intense reduced electric fields (∼600–1500 Td), coherent with species losses controlled by transport and wall recombination, and kinetic mechanisms strongly dependent on electron-impact collisions. The charged-particle transport losses are strongly influenced by the presence of the negative ion, despite its low-density (∼10% of the electron density). For electron densities in the range (1– cm−3, the system exhibits high dissociation degrees for O2 (∼20–70%, depending on the working conditions, in contrast with the ∼0.1% dissociation obtained for N2), a high concentration of O2(a) (∼1014 cm−3) and NO(X) ( cm−3) and low ozone production (<).

Solution of a generalized Boltzmann's equation for nonequilibrium charged-particle transport via localized and delocalized states.

We present a general phase-space kinetic model for charged-particle transport through combined localized and delocalized states, capable of describing scattering collisions, trapping, detrapping, and losses. The model is described by a generalized Boltzmann equation, for which an analytical solution is found in Fourier-Laplace space. The velocity of the center of mass and the diffusivity about it are determined analytically, together with the flux transport coefficients. Transient negative values of the free particle center-of-mass transport coefficients can be observed due to the trapping to, and detrapping from, localized states. A Chapman-Enskog-type perturbative solution technique is applied, confirming the analytical results and highlighting the emergence of a density gradient representation in the weak-gradient hydrodynamic regime. A generalized diffusion equation with a unique global time operator is shown to arise, reducing to the standard diffusion equation and a Caputo fractional diffusion equation in the normal and dispersive limits. A subordination transformation is used to solve the generalized diffusion equation by mapping from the solution of a corresponding standard diffusion equation.

Secondary bremsstrahlung and the energy-conservation aspects of kerma in photon-irradiated media

Kerma, collision kerma and absorbed dose in media irradiated by megavoltage photons are analysed with respect to energy conservation. The user-code DOSRZnrc was employed to compute absorbed dose D, kerma K and a special form of kerma, Kncpt, obtained by setting the charged-particle transport energy cut-off very high, thereby preventing the generation of ‘secondary bremsstrahlung’ along the charged-particle paths. The user-code FLURZnrc was employed to compute photon fluence, differential in energy, from which collision kerma, Kcol and K were derived. The ratios K/D, Kncpt/D and Kcol/D have thereby been determined over a very large volumes of water, aluminium and copper irradiated by broad, parallel beams of 0.1 to 25 MeV monoenergetic photons, and 6, 10 and 15 MV ‘clinical’ radiotherapy qualities. Concerning depth-dependence, the ‘area under the kerma, K, curve’ exceeded that under the dose curve, demonstrating that kerma does not conserve energy when computed over a large volume. This is due to the ‘double counting’ of the energy of the secondary bremsstrahlung photons, this energy being (implicitly) included in the kerma ‘liberated’ in the irradiated medium, at the same time as this secondary bremsstrahlung is included in the photon fluence which gives rise to kerma elsewhere in the medium. For 25 MeV photons this ‘violation’ amounts to 8.6%, 14.2% and 25.5% in large volumes of water, aluminium and copper respectively but only 0.6% for a ‘clinical’ 6 MV beam in water. By contrast, Kcol/D and Kncpt/D, also computed over very large phantoms of the same three media, for the same beam qualities, are equal to unity within (very low) statistical uncertainties, demonstrating that collision kerma and the special type of kerma, Kncpt, do conserve energy over a large volume. A comparison of photon fluence spectra for the 25 MeV beam at a depth of ≈51 g cm−2 for both very high and very low charged-particle transport cut-offs reveals the considerable contribution to the total photon fluence by secondary bremsstrahlung in the latter case. Finally, a correction to the ‘kerma integral’ has been formulated to account for the energy transferred to charged particles by photons with initial energies below the Monte-Carlo photon transport cut-off PCUT; for 25 MeV photons this ‘photon track end’ correction is negligible for all PCUT below 10 keV.

Understanding the physical systems from their underlying geometrical and topological properties

As it is well known, a certain lack of theoretical understanding of the mechanisms governing the various phenomena exists in several areas of physics. In particular, it concerns those which involve transport of charged particles in low dimensions. In this work the physics of the 2-dimensional charge transport with parallel (in plane) magnetic field is analyzed from the geometrical and algebraic viewpoint making emphasis of how the physical interpretation arises from a consistent mathematical formulation of the problem. As a new result of this investigation with respect to the current literature we explicitly show that: (i) the specific form of the low dimensional Dirac equation enforces the field solution to fulfil the Majorana condition, (ii) the quantum Hall effect is successfully explained, (iii) a new topological effect (as the described by the Aharonov–Casher theorems) is presented and (iv) the link with supersymmetrical models is briefly commented.

Impact Study on the Methodology used for Photon-Heating Determination in Material-Testing Reactors

Determination of photon heating by calculation is an important issue for the Jules Horowitz Reactor (JHR), the next international Material-Testing Reactor (MTR) under construction at the CEA Cadarache research center in the south of France. Accurate knowledge of photon heating in structure materials and irradiation devices is necessary for JHR design and safety studies. In this paper, we quantify the impact of different photon-heating calculation routes by comparing absorbed dose and Kinetic Energy Released per MAss (KERMA) calculations from two different Monte Carlo codes, TRIPOLI-4.9 and Monte Carlo N-Particle transport code (MCNP). These calculations are carried out in JHR-representative geometries with the nuclear-data library JEFF3.1.1 and the photon-data library EPDL97. Discrepancies amounting to up to 18% between absorbed dose and KERMA are found in JHR irradiation devices and are linked to charged-particle transport effects taking place in heterogeneous materials of small dimensions. In a JHR-assembly cell, discrepancies of about 1% on photon KERMA and of about 3% on absorbed dose are highlighted between the two Monte Carlo codes. These latter discrepancies are small compared to typical sources of uncertainty for Monte Carlo calculation (for instance, nuclear data uncertainty) and are supposed to be due to differences in the processing of gamma-production data by neutron interactions and to differences in electromagnetic-shower models and implementation between the two codes.

PENGEOM—A general-purpose geometry package for Monte Carlo simulation of radiation transport in material systems defined by quadric surfaces

The Fortran subroutine package pengeom provides a complete set of tools to handle quadric geometries in Monte Carlo simulations of radiation transport. The material structure where radiation propagates is assumed to consist of homogeneous bodies limited by quadric surfaces. The pengeom subroutines (a subset of the penelope code) track particles through the material structure, independently of the details of the physics models adopted to describe the interactions. Although these subroutines are designed for detailed simulations of photon and electron transport, where all individual interactions are simulated sequentially, they can also be used in mixed (class II) schemes for simulating the transport of high-energy charged particles, where the effect of soft interactions is described by the random-hinge method. The definition of the geometry and the details of the tracking algorithm are tailored to optimize simulation speed. The use of fuzzy quadric surfaces minimizes the impact of round-off errors. The provided software includes a Java graphical user interface for editing and debugging the geometry definition file and for visualizing the material structure. Images of the structure are generated by using the tracking subroutines and, hence, they describe the geometry actually passed to the simulation code. Program summaryProgram title: PengeomCatalogue identifier: AEYH_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYH_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 89390No. of bytes in distributed program, including test data, etc.: 5062646Distribution format: tar.gzProgramming language: Fortran, Java.Computer: PC with Java Runtime Environment installed.Operating system: Windows, Linux.RAM: 210 MiBClassification: 21.1, 14.Nature of problem: The Fortran subroutines perform all geometry operations in Monte Carlo simulations of radiation transport with arbitrary interaction models. They track particles through material systems consisting of homogeneous bodies limited by quadric surfaces. Particles are moved in steps (free flights) of a given length, which is dictated by the simulation program, and are halted when they cross an interface between media of different compositions or when they enter selected bodies.Solution method: The pengeom subroutines are tailored to optimize simulation speed and accuracy. Fast tracking is accomplished by the use of quadric surfaces, which facilitate the calculation of ray intersections, and of modules (connected volumes limited by quadric surfaces) organized in a hierarchical structure. Optimal accuracy is obtained by considering fuzzy surfaces, with the aid of a simple algorithm that keeps control of multiple intersections of a ray and a surface. The Java GUI PenGeomJar provides a geometry toolbox; it allows building and debugging the geometry definition file, as well as visualizing the resulting geometry in two and three dimensions.Restrictions: By default pengeom can handle systems with up to 5000 bodies and 10,000 surfaces. These numbers can be increased by editing the Fortran source file.Unusual features: All geometrical operations are performed internally. The connection between the steering main program and the tracking routines is through a Fortran module, which contains the state variables of the transported particle, and the input-output arguments of the subroutine step. Rendering of two- and three-dimensional images is performed by using the pengeom subroutines, so that displayed images correspond to the definitions passed to the simulation program.Additional comments: Java editor and viewer (PenGeomJar), geometry examples, translator to POV-Ray™ format, detailed manual. The Fortran subroutine package pengeom is part of the penelope code system [1].Running time: The running time much depends on the complexity of the material system. The most complicated example provided, phantom, an anthropomorphic phantom, has 264 surfaces and 169 bodies and modules, with different levels of grouping; the largest module contains 51 daughters. The rendering of a 3D image of phantom with 1680x1050 pixels takes about 25 s (i.e., about 1.5⋅10−5 seconds per ray) on an Intel Core I7-3520M CPU, with Windows 7 and subroutines compiled with gfortran.

Charged Particle Energization and Transport in Reservoirs throughout the Heliosphere: 1. Solar Energetic Particles

“Reservoirs” of energetic charged particles are regions where the particle population is quasi-trapped in large-scale (relative to the gyroradii) magnetic field structures. Reservoirs are found throughout the heliosphere: the huge heliosheath (90<r<110 AU) between the termination shock and the heliopause; the domain of PUIs and ACRs within the solar wind itself; the inner solar system (inside of r<5AU) when filled with SEPs or CIRs; closed structures dragged out from the solar corona by CMEs; and the ring currents of the larger planets (Earth, Jupiter, Saturn, etc.) when energized by magnetic storms. Energization (or cooling) of the charged particles within these reservoirs is produced by the interaction when the particle magnetic drifts have a component along the large-scale electric fields produced by plasma convection. The appropriate description of this transport is “weak scattering”, in which the particle's first adiabatic invariant (magnetic moment) is approximately conserved while the particle itself moves rather freely along magnetic field lines. Considerable insight into the observed properties of energization processes can be gained from a remarkably simple equation that describes the particle's fractional time-rate-of-change of momentum (dlnp/dt) which depends only upon its pitch angle, the divergence of the plasma velocity (V⊥) transverse to the magnetic field), and the inner product of (V⊥) with the curvature vector of the field lines. The possibilities encompassed in this simple (but general) equation are quite rich, so we restrict our application of it in this paper to the compressive acceleration of SEPs within CMEs.

Numerical computation of discrete differential scattering cross sections for Monte Carlo charged particle transport

We investigate a method for numerically generating discrete scattering cross sections for use in charged particle transport simulations. We describe the cross section generation procedure and compare it to existing methods used to obtain discrete cross sections. The numerical approach presented here is generalized to allow greater flexibility in choosing a cross section model from which to derive discrete values. Cross section data computed with this method compare favorably with discrete data generated with an existing method. Additionally, a charged particle transport capability is demonstrated in the time-dependent Implicit Monte Carlo radiative transfer code, Milagro. We verify the implementation of charged particle transport in Milagro with analytic test problems and we compare calculated electron depth–dose profiles with another particle transport code that has a validated electron transport capability. Finally, we investigate the integration of the new discrete cross section generation method with the charged particle transport capability in Milagro.

A stochastic method of solution of the Parker transport equation

We present the stochastic model of the transport of galactic cosmic ray (GCR) particles in the heliosphere. Based on a solution of the Parker transport equation we developed models of the short-term variation of the GCR intensity, i.e. the Forbush decrease (Fd) and the 27-day variations of the GCR intensity. Parker's transport equation, being the Fokker-Planck type equation, delineates non-stationary transport of charged particles in a turbulent medium. The presented approach of the numerical solution is grounded on solving the set equivalent stochastic differential equations (SDEs). We demonstrate the method of deriving from Parker's transport equation the corresponding SDEs in the heliocentric spherical coordinate system for the backward approach. Features indicative of the preeminence of the backward approach over the forward are stressed. We compare the outcomes of the stochastic models of the Fd and 27- day variation of the GCR intensity with our former models established by the finite difference method. Both models are in agreement with the experimental data.

Studies on heavy charged particle interaction, water equivalence and Monte Carlo simulation in some gel dosimeters, water, human tissues and water phantoms

Some gel dosimeters, water, human tissues and water phantoms were investigated with respect to their radiological properties in the energy region 10keV–10MeV. The effective atomic numbers (Zeff) and electron densities (Ne) for some heavy charged particles such as protons, He ions, B ions and C ions have been calculated for the first time for Fricke, MAGIC, MAGAT, PAGAT, PRESAGE, water, adipose tissue, muscle skeletal (ICRP), muscle striated (ICRU), plastic water, WT1 and RW3 using mass stopping powers from SRIM Monte Carlo software. The ranges and straggling were also calculated for the given materials. Two different set of mass stopping powers were used to calculate Zeff for comparison. The water equivalence of the given materials was also determined based on the results obtained. The Monte Carlo simulation of the charged particle transport was also done using SRIM code. The heavy ion distribution along with its parameters were shown for the given materials for different heavy ions. Also the energy loss and damage events in water when irradiated with 100keV heavy ions were studied in detail.

The role of pyrimidine and water as underlying molecular constituents for describing radiation damage in living tissue: A comparative study

Water is often used as the medium for characterizing the effects of radiation on living tissue. However, in this study, charged-particle track simulations are employed to quantify the induced physicochemical and potential biological implications when a primary ionising particle with energy 10 keV strikes a medium made up entirely of water or pyrimidine. Note that pyrimidine was chosen as the DNA/RNA bases cytosine, thymine, and uracil can be considered pyrimidine derivatives. This study aims to assess the influence of the choice of medium on the charged-particle transport, and identify how appropriate it is to use water as the default medium to describe the effects of ionising radiation on living tissue. Based on the respective electron interaction cross sections, we provide a model, which allows the study of radiation effects not only in terms of energy deposition (absorbed dose and stopping power) but also in terms of the number of induced molecular processes. Results of these parameters for water and pyrimidine are presented and compared.

SU‐E‐T‐499: Initial Developments of An OpenCL‐Based Cross‐Platform Monte Carlo Dose Engine for Carbon Ion Therapy

PurposeDose calculation is of critical importance for carbon ion therapy. Monte Carlo (MC) simulation is considered to be the most accurate method for calculation of absorbed dose and of all the more fundamental physical quantities related to biological effects. The long computation time, however, limits its routine clinical applications. We have recently started developing a fast MC package, gCMC for carbon therapy on a parallel processing platform, e.g. GPU, aiming at achieving sufficient efficiency to enable MC in clinically important tasks. This abstract reports our progress.MethodsgCMC was developed in OpenCL environment. Our initial developments focused on water material. gCMC supported carbon ion transport in the energy range of 1–450 MeV/u. A Class II condensed history algorithm was implemented for charged particle transport simulations with stopping power computed via Bethe‐Bloch equation. Energy straggling and multiple scattering were modeled. Total cross section of nuclear interaction was extracted from Geant4. At present, nuclear interaction events were sampled but transports of secondary particles were not included.ResultsWe tested cases with a homogeneous water phantom and a pencil carbon ion beam with energy of 200–400 MeV/u. When only electro‐magnetic channel was included, dose/fluence difference between gCMC and Geant4 results averaged within 10% isodose line was &lt;0.5% of the maximum dose/fluence. After enabling nuclear interactions without transporting secondary particles, dose and fluence agreed with the corresponding results computed by Geant4 with &lt;1% difference. Due to the support for multiple platforms of OpenCL, gCMC was executable on NVidia and AMD GPUs, and Intel CPUs. It took ∼50 sec to transport 107 200MeV/u source carbon ions on an NVidia Titan GPU card.ConclusionPreliminary studies have demonstrated the accuracy and efficiency of gCMC. With further developments in near future, gCMC will potentially achieve clinically acceptable fast and accurate MC simulations for carbon ion therapy.

SU‐E‐T‐558: Monte Carlo Photon Transport Simulations On GPU with Quadric Geometry

Purpose:Monte Carlo simulation on GPU has experienced rapid advancements over the past a few years and tremendous accelerations have been achieved. Yet existing packages were developed only in voxelized geometry. In some applications, e.g. radioactive seed modeling, simulations in more complicated geometry are needed. This abstract reports our initial efforts towards developing a quadric geometry module aiming at expanding the application scope of GPU‐based MC simulations.Methods:We defined the simulation geometry consisting of a number of homogeneous bodies, each specified by its material composition and limiting surfaces characterized by quadric functions. A tree data structure was utilized to define geometric relationship between different bodies. We modified our GPU‐based photon MC transport package to incorporate this geometry. Specifically, geometry parameters were loaded into GPU's shared memory for fast access. Geometry functions were rewritten to enable the identification of the body that contains the current particle location via a fast searching algorithm based on the tree data structure.Results:We tested our package in an example problem of HDR‐brachytherapy dose calculation for shielded cylinder. The dose under the quadric geometry and that under the voxelized geometry agreed in 94.2% of total voxels within 20% isodose line based on a statistical t‐test (95% confidence level), where the reference dose was defined to be the one at 0.5cm away from the cylinder surface. It took 243sec to transport 100million source photons under this quadric geometry on an NVidia Titan GPU card. Compared with simulation time of 99.6sec in the voxelized geometry, including quadric geometry reduced efficiency due to the complicated geometry‐related computations.Conclusion:Our GPU‐based MC package has been extended to support photon transport simulation in quadric geometry. Satisfactory accuracy was observed with a reduced efficiency. Developments for charged particle transport in this geometry are currently in progress.

IMPLEMENTING TURBULENCE TRANSPORT IN THE CRONOS FRAMEWORK AND APPLICATION TO THE PROPAGATION OF CMEs

We present the implementation of turbulence transport equations in addition to the Reynolds-averaged MHD equations within the Cronos framework. The model is validated by comparisons with earlier findings before it is extended to be applicable to regions in the solar wind that are not highly super-Alfv\'enic. We find that the respective additional terms result in absolute normalized cross-helicity to decline more slowly, while a proper implementation of the mixing terms can even lead to increased cross-helicities in the inner heliosphere. The model extension allows to place the inner boundary of the simulations closer to the Sun, where we choose its location at 0.1 AU for future application to the Wang-Sheeley-Arge model. Here, we concentrate on effects on the turbulence evolution for transient events by injecting a coronal mass ejection (CME). We find that the steep gradients and shocks associated with these structures result in enhanced turbulence levels and reduced cross-helicity. Our results can now be used straightforwardly for studying the transport of charged energetic particles, where the elements of the diffusion tensor can now benefit from the self-consistently computed solar wind turbulence. Furthermore, we find that there is no strong back-reaction of the turbulence on the large-scale flow so that CME studies concentrating on the latter need not be extended to include turbulence transport effects.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

ORGAN AND EFFECTIVE DOSE COEFFICIENTS FOR CRANIAL AND CAUDAL IRRADIATION GEOMETRIES: PHOTONS

With the introduction of new recommendations of the International Commission on Radiological Protection (ICRP) in Publication 103, the methodology for determining the protection quantity, effective dose, has been modified. The modifications include changes to the defined organs and tissues, the associated tissue weighting factors, radiation weighting factors and the introduction of reference sex-specific computational phantoms. Computations of equivalent doses in organs and tissues are now performed in both the male and female phantoms and the sex-averaged values used to determine the effective dose. Dose coefficients based on the ICRP 103 recommendations were reported in ICRP Publication 116, the revision of ICRP Publication 74 and ICRU Publication 57. The coefficients were determined for the following irradiation geometries: anterior-posterior (AP), posterior-anterior (PA), right and left lateral (RLAT and LLAT), rotational (ROT) and isotropic (ISO). In this work, the methodology of ICRP Publication 116 was used to compute dose coefficients for photon irradiation of the body with parallel beams directed upward from below the feet (caudal) and directed downward from above the head (cranial). These geometries may be encountered in the workplace from personnel standing on contaminated surfaces or volumes and from overhead sources. Calculations of organ and tissue kerma and absorbed doses for caudal and cranial exposures to photons ranging in energy from 10 keV to 10 GeV have been performed using the MCNP6.1 radiation transport code and the adult reference phantoms of ICRP Publication 110. As with calculations reported in ICRP 116, the effects of charged-particle transport are evident when compared with values obtained by using the kerma approximation. At lower energies the effective dose per particle fluence for cranial and caudal exposures is less than AP orientations while above ∼30 MeV the cranial and caudal values are greater.

Monte Carlo study of coherent scattering effects of low-energy charged particle transport in Percus-Yevick liquids.

We generalize a simple Monte Carlo (MC) model for dilute gases to consider the transport behavior of positrons and electrons in Percus-Yevick model liquids under highly nonequilibrium conditions, accounting rigorously for coherent scattering processes. The procedure extends an existing technique [Wojcik and Tachiya, Chem. Phys. Lett. 363, 381 (2002)], using the static structure factor to account for the altered anisotropy of coherent scattering in structured material. We identify the effects of the approximation used in the original method, and we develop a modified method that does not require that approximation. We also present an enhanced MC technique that has been designed to improve the accuracy and flexibility of simulations in spatially varying electric fields. All of the results are found to be in excellent agreement with an independent multiterm Boltzmann equation solution, providing benchmarks for future transport models in liquids and structured systems.

Solving Parker’s transport equation with stochastic differential equations on GPUs

The numerical solution of transport equations for energetic charged particles in space is generally very costly in terms of time. Besides the use of multi-core CPUs and computer clusters in order to decrease the computation times, high performance calculations on graphics processing units (GPUs) have become available during the last years. In this work we introduce and describe a GPU-accelerated implementation of Parker’s equation using Stochastic Differential Equations (SDEs) for the simulation of the transport of energetic charged particles with the CUDA toolkit, which is the focus of this work. We briefly discuss the set of SDEs arising from Parker’s transport equation and their application to boundary value problems such as that of the Jovian magnetosphere. We compare the runtimes of the GPU code with a CPU version of the same algorithm. Compared to the CPU implementation (using OpenMP and eight threads) we find a performance increase of about a factor of 10–60, depending on the assumed set of parameters. Furthermore, we benchmark our simulation using the results of an existing SDE implementation of Parker’s transport equation.

EFFECTS OF LATITUDINALLY DEPENDENT SOLAR WIND SPEED ON DIFFUSION COEFFICIENTS OF COSMIC RAYS IN THE PRESENCE OF ADIABATIC FOCUSING

The solar wind is observed to display high speeds in high heliolatitude coronal holes and low speeds near the ecliptic plane. The heliospheric magnetic field associated with the solar wind plays a very important role in the transport and modulation of charged energetic particles, including galactic cosmic rays (GCRs) and solar energetic particles (SEPs), in the three-dimensional heliosphere. In previous studies, a constant solar wind speed, which is independent of heliolatitude, was assumed and commonly used in modulation modeling of cosmic rays. In this work, we investigate the realistic latitudinally dependent solar wind speed and utilize the theoretical models in hyperbolic and piecewise polynomial forms to explore the important effects on the heliospheric magnetic field and the diffusion coefficients (parallel, perpendicular, and drift scale) of cosmic rays in the presence of adiabatic focusing. Comparisons of the diffusion coefficients derived from standard Parker field and modified magnetic fields are presented. Since the structures and properties of different solar wind sources (coronal streamer belt, polar coronal hole, and transition region between them) differ from each other in essence, we suggest that the latitudinally dependent solar wind speed and the corresponding heliospheric magnetic field and diffusion coefficients with adiabatic focusing should be employed in the global modeling studies of GCRs and SEPs in the heliosphere.

Multibody collision contribution to the slowing down of charged particles through metals

Investigating charged particle transport through solid matter is important in those fields, such as particle induced x‐ray emission analysis, where quantifying and identifying the reactions produced in the medium are of fundamental interest. A rigorous approach by solving the transfer equation means to face many difficulties most of which arise from the long range nature of the Coulomb interactions, involving more than one particle simultaneously. The common practice of neglecting the multibody collisions, though correct for rarefied neutral gases, often leads to very poor approximations, when charged particles move through dense matter. Here, we discuss a numerical simulation of the Fokker–Planck equation where the multibody collisions are taken into account. The model allows to calculate point‐wise the distribution of energy and momentum transferred to the target. Copyright © 2015 John Wiley &amp; Sons, Ltd.