Transport Cross Sections Research Articles

Transport cross sections relevant to cool hydrogen plasmas bounded by graphite

Atomic collision quantities relevant to transport in hydrogen plasmas bounded by graphite walls are considered. Fully quantal, ab initio calculations of the differential and integral elastic scattering cross sections for H+, D+, and T+ colliding with C at center of mass energies between 0.1 and 200 eV are described. The computed elastic cross section and its transport moments, the momentum transfer, and viscosity cross sections, are compared with those from a simple analytical model (the Massey–Mohr approximation) and with a three-body classical scattering approach in order to extend the data to higher collision energies. For energies typical of the edge plasma, the elastic scattering cross section is found to be as much as 10 times larger than that estimated from the widely used analytical approximation. The highly accurate quantal results are also tabulated and made available to the plasma science community through the world wide web.

Effective potential energies and transport cross sections for atom-molecule interactions of nitrogen and oxygen

The potential energy surfaces for ${\mathrm{H}}_{2}\ensuremath{-}\mathrm{N}$ and ${\mathrm{N}}_{2}\ensuremath{-}\mathrm{N}$ interactions are calculated by accurate ab initio methods and applied to determine transport data. The results confirm that an effective potential energy for accurately determining transport properties can be calculated using a single predetermined orientation. A simple method is developed to determine the dispersion coefficients of effective potential energies. Effective potential energies required for ${\mathrm{O}}_{2}\ensuremath{-}\mathrm{O}$ collisions are determined. The ${\mathrm{H}}_{2}\ensuremath{-}\mathrm{N},$ ${\mathrm{N}}_{2}\ensuremath{-}\mathrm{N},$ ${\mathrm{O}}_{2}\ensuremath{-}\mathrm{H},$ and ${\mathrm{O}}_{2}\ensuremath{-}\mathrm{O}$ collision integrals are calculated and tabulated for a broad range of temperatures. The theoretical values of the ${\mathrm{N}}_{2}\ensuremath{-}\mathrm{N}$ and ${\mathrm{O}}_{2}\ensuremath{-}\mathrm{O}$ diffusion coefficients compare well with measured data available at room temperature.

Sound interaction with moving vortices

This report is devoted to the nonlinear acoustic pressure of sound waves propagating in the vicinity of a rather general class of localized flows induced by the motion of spherically symmetric structures of the type of vortices in the liquid, say, biological, atmosphere, or ocean inhomogeneous environment. As a result expressions for cyclic and mean forces exerted on a vortex are derived. Conventional general expression for transport cross section derived in nonlinear theory of interaction of sound with rigid particles is proven to be incorrect for the vortex-sound interaction case. The absence of mean force is demonstrated for specific case of Hills vortex both in the traveling and standing sound wave fields. It is underlined, however, that the force could be observable if the distribution of mean sound energy in the incident sound field in the frames of vortex dimensions could be characterized by a nonzero spatial gradient. Instead of the previously used expression for mean radiation force exerted on a moving inhomogeneity valid for a solid particle based on its transport cross section, the correct generalized expression for force exerted on vortex structure is derived.

Conductivity of Nonideal Zinc and Carbon Plasmas - Experiments and Theoretical Results

In recent years it has become possible to produce and analyze dense, strongly coupled plasmas. In particular it was possible to determine transport properties. In this contribution we report on measurements of the electrical conductivity of nonideal zinc and carbon plasmas, which are produced by evaporating a wire placed in a capillary (exploding wire) within some hundred nanoseconds. The particle density is in the range of 10 22 cm −3 . The plasma temperature, which is obtained by fitting a Planck function to the measured spectrum, is between 8000 and 20000 K. We compare the measured electrical conductivies with theoretical results using quantum kinetic theory for partially ionized plasmas. Here, the transport cross sections are calculated in T-matrix approximation and the plasma composition of the nonideal plasma is determined by the solution of coupled mass action laws.

Differences in the energy loss of protons and positive muons in solids

We evaluate the magnitude of the difference in the electronic energy loss of positive muons and protons in solids in the low-energy range using both the dielectric formalism and the non-linear transport cross-section (TCS) method. The effects of mass increase at low energies, showing stopping differences between 5% and 1% for velocities in the range 0.2< v<1 a.u. We find that nuclear stopping effects must also be taken into account for a consistent analysis in the low-energy range.

Background subtraction III: The application of REELS data to background removal in AES and XPS

An analysis is provided of the use of reflected electron energy loss spectroscopy (REELS) data for the removal, by deconvolution, of the inelastically scattered electron background in Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) measurements in order to deduce the peak area intensities. Traditionally, the REELS data have either been used directly or the background intensity in the REELS data have been scaled by dividing by a factor A with respect to the elastic peak intensities, prior to the deconvolution. The scaling leads to an increase in the measured peak area approximately proportional to A. Measurements of the angular variation of the REELS data for scattering angles θ in the range 133°⩽ θ⩽153° show for the first time that the inelastically scattered intensity can vary by a factor of 2.5, for an angular change of 16°, with respect to the elastic peak background intensity. This angular variation has structure which relates directly to that of the differential elastic scattering cross-section. A simple relation for A, for losses greater than 80 eV, is thus found involving the differential elastic scattering cross-section and the transport cross-section. This leads to a result for A, for our instrument, which has a minimum of 0.9 at Rb (37) and a maximum of 1.6 at Ta (73), consistent with experimental data. For losses less than 80 eV, the scaling changes exponentially with energy from 1/ A at high values of energy loss to 1 at zero energy loss with a characteristic decay energy of around 26 eV. Using these results, an angle-averaged set of REELS data may be generated for spectral deconvolution in AES and XPS.

Improved elastic collision modeling in DEGAS 2 for low-temperature plasmas

Recent emphasis on low-temperature divertor operations has focused attention on proper treatment of neutral-elastic collisions in low-temperature environments. For like species collisions, as in D++D, quantum mechanical indistinguishability precludes differentiation of small-angle elastic scattering from resonant charge exchange for collision energies &amp;lt;2 eV. The current work improves the low-temperature simulation capabilities of the DEGAS 2 Monte Carlo neutral transport code [D. P. Stotler and C. F. F. Karney, Contrib. Plasma Phys. 34, 392–397 (1994)] by employing a set of quantum mechanical collision cross sections produced by Oak Ridge National Laboratory to provide a comprehensive treatment of ion-neutral elastic collisions. Ion-molecular collisions in the form of D++D2 are included for the first time. An integration technique is utilized that reduces the total collision cross section while keeping the other transport cross sections invariant. The inclusion of ion-molecular elastic collisions results in significant increases in energy exchange between background ions and neutral test species.

Effective potential energies and transport cross sections for interactions of hydrogen and nitrogen

The interaction energies for ${\mathrm{N}}_{2}\ensuremath{-}\mathrm{He}$ and ${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{H}}_{2}$ are calculated by accurate ab initio methods. The virial coefficient and differential scattering cross section for ${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{H}}_{2}$ are calculated; the theoretical results are compared with experimental data. The transport collision integrals for ${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}\ensuremath{-}{\mathrm{N}}_{2}$ interactions are calculated and tabulated; the results yield transport coefficients that compare well with measured data. Transport coefficients are found to be determined accurately from the interaction energies for a specific configuration of the molecule formed from the interaction partners. Comparisons with results of measurement and accurate calculations demonstrate that the transport properties of complex molecular interactions can be determined rapidly and fairly accurately from the interaction energies of simpler systems using combination rules for the short-range parameters of effective interaction energies and the coefficients for the long-range forces. The coefficients for a two-parameter temperature expansion of diffusion and viscosity are tabulated for a realistic universal potential-energy that is based primarily on the results of very accurate calculations of the He-He interaction energy.

Neutron streaming experiment at FNG: results and analysis

The experimental validation of the available codes and nuclear data to calculate correctly the effects of streaming paths in the shield of a fusion reactor was provided by a streaming experiment carried out at the 14 MeV Frascati Neutron Generator (FNG). The experiment consisted in the irradiation of a mock-up of the shielding blanket (stainless steel and water equivalent material, 1 m thick) and of the toroidal field coil. A void channel with high aspect ratio and a cavity at the end of the channel were realised in the bulk shield. Some nuclear quantities were measured in the cavity at the end of the channel and behind it up to the simulated superconducting magnet. The neutron flux was measured using the activation foil technique while the nuclear heating was measured using thermoluminescent detectors. The experimental data were compared with the results of calculations performed by the Monte Carlo code MCNP-4B, using the Fusion Evaluated Nuclear Data Library (FENDL, version 1.0, 2.0) and the European Fusion File (EFF, versions 3.0, 3.1). The comparison shows that all the used libraries reproduce the neutron flux generally within ±20% total uncertainty both in the void penetration and in the bulk shield behind it. The trend to underestimate the high energy flux ( E>8 MeV) with increasing penetration depth is found again as in previous bulk shield experiment, showing that the relevant transport cross sections at around 14 MeV need further investigation. The comparison between experimental and calculated nuclear heating shows an agreement within ±30% for all tested nuclear data libraries and in all experimental positions. The comparison with the case of bulk shield without penetration is also discussed.

Potential Energies and Collision Integrals for Interactions of Carbon and Nitrogen Atoms

Potential energies for C 2 and CN are calculated by a configuration interaction method for those states for which the molecule dissociates into ground state atoms. The potential energy curves are shown graphically; parameters determined from the potential energy wells are tabulated and compared with the corresponding data available from measurements. The potential energies of the 7Σu+ and A' 5 Σ g + states of N 2 are computed from very accurate state-of-the-art molecular structure calculations and improved using the results of spectroscopic measurements, respectively. Transport cross sections are tabulated for a broad range of collision energies. Collision integrals are determined from the cross sections; the C-C and C-N results are tabulated for temperatures in the range 300-30,000 K. The improved collision integrals for N-N interactions differ from the corresponding results of an existing tabulation by a small insignificant amount. The scattering results are used to validate simple methods for estimating collision integrals and to examine the diffusion, viscosity, and thermal diffusion in a gas composed of carbon and nitrogen atoms.

Effects of interaction potential on elastic-electron-scattering parameters in surface-sensitive electron spectroscopies

The interaction potential for elastic-scattering of electrons by atoms influences the magnitudes of calculated elastic-scattering cross sections. We have investigated the influence of two choices of interaction potential, the Thomas–Fermi–Dirac (TFD) potential and the Dirac–Hartree–Fock–Slater (DHFS) potential, on the differential elastic-scattering cross sections and the total elastic-scattering cross sections for the elastic-scattering of 1000 eV electrons by six representative elements (Be, C, Al, Cu, Ag, and Au). The differential cross sections for the two potentials varied by up to a factor of three for scattering angles less than 30°, while total cross sections varied between 15 and 61%. In contrast, transport cross sections (which emphasize large-angle scattering events) calculated from the two potentials differed by between 1 and 8.5% for the six elements. We compared results of Monte Carlo calculations of elastic backscattering probabilities of normally incident 1000 eV electrons on Be, C, Al, Cu, Ag, and Au with the two potentials, and found percentage differences in these probabilities varying between 1.2 and 9.4% for emission angles of 45±10°. Monte Carlo calculations were also made of signal intensities in X-ray photoelectron spectroscopy (XPS), emission depth distribution functions (EDDFs) in XPS, and mean escape depths (MEDs) in XPS for selected photoelectron lines from Be, C, Al, Cu, Ag, and Au using the TFD and DHFS potentials and a common XPS configuration. The percentage deviations in the results for the two potentials did not exceed 2% for the signal intensities, were generally less than 10% for the emission depth distribution functions, and less than 2.5% for the mean escape depths. The lack of sensitivity of the Monte Carlo results to interaction potential is due to the fact that small-angle elastic-scattering events are not significant in the transport of signal electrons in XPS and Auger electron spectroscopy (AES). We point out that XPS signal intensities and EDDFs and MEDs for both XPS and AES can be calculated from a solution of the Boltzmann equation within the transport approximation. This approach is useful for the correction of elastic-scattering effects in quantitative AES and XPS because the only parameter used to describe elastic-scattering effects is the transport cross section (which is relatively insensitive to the choice of interaction potential).

Reflection coefficient of low-energy ions as a universal function of the scaled transport cross section

Multiple collision theory of heavy ion ranges in an infinite medium has been used to calculate the reflection coefficient from the penetration profile, by a method first described by Bottiger et al. Interaction with target electrons has been neglected and nuclear collisions have been described by the power cross sections. Calculations are restricted to low reduced ion energies e0≤0.1 and to target/ion mass ratios μ≤10, when electronic stopping is much less than the nuclear stopping. The Gaussian approximation of the penetration profile and the reflection coefficient are found in a form of simple analytic formulas. Furthermore, the penetration profile was constructed by using Edgeworth expansion and moments of the distribution up to the fourth order, and the reflection coefficient was determined from the profile. Good agreement between the analytical results and the reflection coefficient obtained from Edgeworth expansion was found, for target atom/ion mass ratios μ≥1.3. It is shown that the reflection coefficient is a universal function of the scaled transport cross section. The scaling is fulfilled for v≥2, when ion reflection is determined by large-angle multiple collisions, and breaks down for v<1 i.e. μ<1, when scattering angles are small. Results are compared with TRIM computer simulation data.

Absorbed dose calculations for the Ignitor tokamak magnet coils insulator

The Ignitor experiment is an advanced compact high magnetic field tokamak with cryogenically cooled (30 K) normal conductor magnets. Its main purpose is to produce deuterium–tritium plasma regimes where ignition can take place. From the neutronics point of view, the routine operations with 50% of tritium will lead to a very short (4 s) but intense emission of 14 MeV neutrons (up to 3×10 19 n/s). The capability of the boron-free glass reinforced epoxy resin presently adopted for the insulation of the coils conductor to withstand the severe irradiation condition could be a key issue in the performance, reliability and lifespan of Ignitor. In order to better know the radiation environment in which the insulators will operate, calculations of the absorbed dose are performed using the parallelized version of MCNP-4B Monte Carlo code. A detailed 3D geometry description of the tokamak, an accurate representation of the neutron source distribution together with the more recent version of transport cross-section libraries EFF (European Fusion File) are used in this work. The variation of calculated dose depending on the insulator position inside the device, on the neutron energy spectra and on the total number of neutrons produced over the scheduled machine lifetime are discussed in the present paper.

Transport properties of boron and aluminum

Transport cross sections and collision integrals are tabulated for a wide range of energies and temperatures for the interactions B–B and Al–Al. For aluminum, a semiclassical approximation was used to determine the scattering phase shifts from which the transport cross sections were calculated. For boron, the smaller reduced mass and the deep potential wells required the phase shifts at lower energies to be determined from a numerical solution of the time-independent Schroedinger equation; the semiclassical approximation was used at higher energies where the two methods agree. The variations of the collision integrals for viscosity and diffusion are presented graphically as a function of temperature. The results are applied to estimate the transport properties of gallium.

Collision Integrals of High-Temperature Air Species

Collision integrals (transport cross sections ) of air species in the temperature range 50 ‐100,000 K have been calculated by using experimental and theoretical informations on potential energy curves and cross sections. The results for the different interactions (neutral‐neutral, neutral ‐parent ion, electron ‐neutral) have been compared with old and recent calculations obtaining, in general, a satisfactory agreement. Finally analytical forms for e tting and interpolating the present numerical results are reported.

Energy-averaged electron–ion momentum transport cross section in the Born approximation and Debye–Hückel potential: Comparison with the cut-off theory

An exact analytical expression for the energy-averaged electron–ion momentum transport cross section in the Born approximation and Debye–Hückel exponentially screened potential has been derived and compared with the formulae given by other authors. A quantitative comparison between cut-off theory and quantum mechanical perturbation theory has been presented. Based on results from the Born approximation and Spitzer's formula, a new approximate formula for the quantum Coulomb logarithm has been derived and shown to be more accurate than previous expressions.

Investigation of the effect of high order Z1 terms in electronic stopping powers on the ranges of heavy ions with energies of about 1 GeV/amu

This work is a contribution to the multifaceted study of non-Z12 behaviour of electronic stopping powers and total ranges of heavy ions passing through a homogeneous medium with energies of about 1 GeV/amu. Previously, systematic deviations of total ion range calculations based on first-order perturbation theory, from corresponding experimental values were observed. In the present work this effect is confirmed on an extended data set, including both new experimental measurements of the ranges of some nuclei from Ar to U in the BR2 nuclear photoemulsion and others related data. The discrepancy increases with the atomic number of the projectile nucleus and is observable especially for ions with atomic numbers Z1>50. It is demonstrated that incorporation of a high order correction in electronic stopping powers makes possible to eliminate the systematic discrepancy between computed and experimental values of the total ions ranges. Two forms of corrections are analysed: the simple analytical form of a relativistic second Born approximation proposed by Jackson and McCarthy and a more sophisticated form developed by Lindhard and Sorensen using a quantum transport cross-section method. Herewith, the close relativistic collisions between a projectile ion and an atomic electron make the decisive contribution to the observed effect at an ion energy of about 1 GeV/amu. The effect of the projectile charge and atomic number on the integral characteristics of stopping is also analysed.

NEA Organised Validation of Multi-Dimensional Transport Codes and Cross-Section Sets Used Presently in Reactor Shielding

A Task Force of the OECD/NEA Nuclear Science Committee performed benchmark calculations to validate two- and three-dimensional transport codes and cross-section sets used for radiation shielding. Based on careful measurements from the VENUS critical facility of SCK/CEN-Mol/Belgium, the Task Force started with two-dimensional benchmark calculations representing the arrangement of VENUS-1, which is a mock-up of the Westinghouse three loop reactor. About 20 different calculations were presented. Several 2D-SN-codes were used including some in-house codes and the Monte Carlo program MCNP-4A. The transport cross-sections were taken from ENDF/B-VI or JEF 2.2 and the dosimetry data mainly from IRDF-90v2. The most challenging task was the validation of the latest versions of three-dimensional transport codes with the complex arrangement of VENUS-3. Approximately 14 independent benchmark calculations were contributed world-wide. Several versions of 3D-SN-codes and the Monte Carlo code MCNP were applied. In conclusion the results of the three-dimensional benchmark (VENUS-3) are in general much closer to the experimental values than for the two-dimensional benchmark (VENUS-1). This shows the inherent deficiencies of two-dimensional transport calculations, due to approximations such as diffusion based axial buckling corrections and improper averaging of source and shielding materials, since real configurations are always three-dimensional.

Energy-averaged electron–ion momentum transport cross section in the Born Approximation and Debye–Hückel potential: Comparison with the cut-off theory

An exact analytical expression for the energy-averaged electron–ion momentum transport cross section in the Born approximation and Debye–Hückel exponentially screened potential has been derived and compared with the formulae given by other authors. A quantitative comparison between cut-off theory and quantum mechanical perturbation theory has been presented. Based on results from the Born approximation and Spitzer's formula, a new approximate formula for the quantum Coulomb logarithm has been derived and shown to be more accurate than previous expressions.

The mobility of He+ ions in helium gas

Recent values for the X 2u+ and A 2g+ He2+ potentials have been used to determine quantal phase shifts. These phase shifts have been used to compute transport cross sections that are highly accurate over a wide range of energy. A Gram-Charlier treatment of the Boltzmann kinetic equation has been used to calculate from the cross sections the mobility of He+ ions in He gas at temperatures of 2, 4.35, 5, 6, 77, 85 and 300 K for E/N values up to 40 Td, where E is the electric field strength and N is the gas number density. Excellent agreement is obtained with experimental values at 77 and 300 K. Differences of up to 4% are obtained with experiment at 4.35 K, supporting a suggestion that there may be additional uncertainties in the pressure measurements employed in this experiment. The 85 K observations are between 4% and 6% below our calculations, a somewhat larger difference than the quoted experimental uncertainty. Excellent agreement is obtained with the transverse diffusion coefficient measurements at 294 K.