Electron Transport In Matter Research Articles

Validation of the single-event method for low-energy electron transport via stopping power calculations with MCNP

Monte Carlo simulations of low-energy (<50 keV) electron transport in matter are essential for a broad range of application fields. Several Monte Carlo codes have developed specialized treatments for this case, but a comprehensive validation of low-energy electron transport for general-purpose simulations remains lacking in the literature. One approach to accomplish this validation is calculation of stopping power using low-energy electron transport physics, as stopping power is a fundamental radiation transport quantity which must be simulated accurately for nearly any application. In this work, we use the Monte Carlo N-Particle (MCNP) radiation transport code with the single-event method for electron transport to calculate stopping powers of low-energy electrons (50 eV to 30 keV) in 41 elemental solids, 14 compound solids, and five rare gas solids, comparing simulation results to published semi-empirical stopping power calculations from optical measurements. In general, the simulations give good agreement (typically within ±10%) with semi-empirical stopping power values at higher energies: 300 eV and above for most elemental solids, 1 keV and above for compound solids, and 400 eV and above for rare gas solids. Agreement between MCNP and semi-empirical values is worse below these energies. The most significant source of error is the EPRDATA14 cross section data, which does not account for changes in electronic structure due to solid-state bonding, particularly in compound materials. The simplistic model of atomic excitation used to generate the EPRDATA14 cross sections is another key source of error. Additionally, the breakdown of the continuous slowing-down approximation introduces significant uncertainty at low energies, although this is a limitation of the calculation method and not of the simulation procedure. Accounting for these and other uncertainty sources, the single event method in MCNP is robust and able to give good accuracy for a variety of low-energy electron transport problems through diverse kinds of materials.

Characterization of induced nanoplasmonic fields in time-resolved photoemission: A classical trajectory approach applied to gold nanospheres

Attosecond time-resolved spectroscopy has been shown to be a powerful method for examining the electronic dynamics in atoms, and this technique is now being transferred to the investigation of elastic and inelastic scattering during electron transport and collective electronic (plasmonic) effects in solids. By sampling over classical photoelectron trajectories, we simulated streaked photoelectron energy spectra as a function of the time delay between ionizing isolated attosecond extreme ultraviolet (XUV) pulses and assisting infrared or visible streaking laser pulses. Our calculations comprise a sequence of four steps: XUV excitation, electron transport in matter, escape from the surface, and propagation to the photoelectron detector. Based on numerical applications to gold nanospheres of 5- and 50-nm radius, we investigate streaked photoemission spectra with regard to (i) the nanoparticle's dielectric response to the electric field of the streaking laser pulse, (ii) relative contributions to photoelectron release from different locations on the surface and inside the nanoparticle, (iii) contributions of photoemission from the Fermi level only versus emission from the entire occupied conduction band, and (iv) their fidelity in imaging the spatiotemporal distribution of the induced plasmonic field near the particle's surface.

Collisional and collective effects in two dimensional model for fast-electron transport in refluxing regime

The relativistic laser-driven electron transport in partially or fully ionized matter has been investigated in many recent experiments. The high laser intensity achievable today (up to 1020 W/cm2) allows to generate electron current density above 1011 A/cm2. In this regime, electromagnetic effects start to be dominant over collisional ones. In this context, we have developed a simple 2D model for the fast electron transport accounting for (1) electric effects on the electron penetration range and (2) the electron refluxing in thin foils. We compare our model with those existing in literature and with some recent experimental results on fast electron transport in matter. The model predicts a maximum value for the electron penetration range in the region where the collisional and the resistive effects are comparable.

Model of individual collisions for description of electron transport in matter

Distributions of electron characteristics are constructed with the use of data of elastic and nonelastic processes of interaction between electrons and matter. The data are taken from the National Nuclear Data Center, http://www.nndc.bnl.gov/. These characteristics are used for developing the technique of modeling the electron transport in matter. The developed model does not use the well-known slowdown approximation and multiple scattering theories. The comparison of some moments of the distributions with the NIST data is carried out. The satisfactory fit of some results computed by using the developed model and MCNP results is obtained.

Testing Monte Carlo computer codes for simulations of electron transport in matter

In this paper, three Monte Carlo codes were tested for electron transport in various materials. MCNPX (version 2.4.0), Penelope (version 2003) and EGSnrc codes were used for modeling simple problems. These problems were focused on bremsstrahlung, energy deposition in matter, electron ranges and production of secondary electrons by gamma radiation. The electrons were primary particles, except in the last exercise, where photons were used. Various materials, e.g., water, lead and tungsten were used. The energy of the primary particles was within the energy range from 20 to 450 keV. The simulation results were compared with each other.

The role of absorption in large-angle elastic scattering

The measurements of energy loss distributions obtained in electron scattering experiments at high momentum transfer are presented for Xe, Ar and methane. The spectra show a large variety of intensity distributions, clearly different from those obtained in measurements at the dipole limit. The fraction of the intensity present in the energy loss distribution compared to the elastic peak is significant, but is in line with the reduction of the elastic cross section due to absorption. It is argued that, if similar effects are present in the condensed phase, they should be dealt with in any quantitative analysis of electron transport in matter, as is often done using Monte Carlo simulations. This argument is worked out in some detail for Reflection Electron Energy Loss Spectroscopy.

Electron scattering from argon: Data evaluation and consistency

The demand for coherent scattering data for modeling electron transport in matter has increased in recent years. While much effort has been devoted to the improvement of models describing electron transport and scattering, the updating of fundamental data sets on the basis of recent experimental results has often been neglected. The use of a well-validated set of electron cross sections ensures accurate calculations of transport parameters and ionization yields, with typical applications in material analysis, detector response studies, plasma diagnostics, physics of the atmosphere, and radiotherapy. Data consistency can be verified on the basis of various theoretical requirements, and systematic errors can be minimized by cross-checking results obtained from independent experiments. For example, the oscillator strength distribution of an atom can be obtained both from photoabsorption experiments and from zero-angle electron-atom collisions at high energy, on the basis of the Bethe theory. A considerable number of all electron-scattering experiments are concerned with light noble gases, in particular with argon. This gas is a dominant constituent of noble-gas discharge plasmas and plays an important role in rare-gas halide lasers and proportional scintillator counters. This work reviews electron-scattering cross sections and optical data for the argon atom, discusses the progress made in the field of electron scattering and photoabsorption, and focuses on the most appropriate criteria for verifying data consistency.

Transport of intense laser-produced electron beams in matter

Fast electron transport in matter is a key issue for assessing the feasibility of fast ignition; however several important points are not clear yet. Therefore we realized an experiment with ultra-intense lasers (⩽ 6 1019 W cm−2) studying transport in metallic (Al) and insulating (CH) foil targets. The dynamics of fast electron propagation versus target thickness was investigated by optical self-emission from targets rear side. In Al targets we distinguished two-components in the fast electron population: moderately relativistic electrons and a highly collimated micro-bunched relativistic tail. A large ohmic heating at the rear of the thinner targets was observed due to the background return current. In CH, optical emission is mainly due to the Cherenkov effect and is much larger than in Al. We also observed that in insulators the fast-electron beam undergoes strong filamentation and the number of filaments increases with thickness. This behaviour was attributed to an ionization front instability.

Cross sections for electron interactions in condensed matter

AbstractThe fundamental components of Monte Carlo algorithms for the simulation of electron transport in matter are the differential and total cross sections for the relevant interaction mechanisms. We present different theoretical models and approximations to compute these cross sections for elastic scattering, inelastic collisions and bremsstrahlung emission of electrons with kinetic energies larger than about 100 eV. We limit our considerations to those models that are broadly applicable and suited for efficient random sampling. The approximations underlying the various models and their range of applicability are discussed. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Monte Carlo Simulation of Electron Transport and X-Ray Generation. I. Electron Elastic and Inelastic Scattering

We present different theoretical approaches to determine differential cross sections for elastic and inelastic interactions of electrons. These cross sections are the basic ingredients for accurate Monte Carlo simulation of electron transport in matter. The considered models range from simple analytical approximations employed in early calculations to purely numerical differential cross sections described by large databases calculated with state-of-the-art theory.

Numerical solution of the equation of electron transport in matter

A numerical method is suggested for solving the equation of transport of fast electrons in matter in plane and spherical geometry, with due regard for the fluctuations of energy loss and for the formation of secondary electrons. It is demonstrated that the calculation results are in good agreement with experimental data. A comparison is made between the suggested method and the method of moments.

Electron transport in solids and liquids

We review our recent experimental studies of the excess electron states in insulating solids and liquids. We use a muon spin relaxation technique to explore the phenomenon of delayed muonium formation: excess electrons liberated in the μ+ ionization track converge upon the positive muons and form Mu (μ+e−) atoms in which the μ+ polarization is partially lost. The spatial distribution of such electrons with respect to the muon is shown to be highly anisotropic: the μ+ thermalizes well “downstream” from the center of the electron distribution. Measurements in electric fields up to 30 kV/cm allow one to estimate the characteristic muon-electron distance in different insulators: the results range from 10−6 to 10−4 cm. Such a microscopic length scale enables the electron to sometimes spend its entire free lifetime in a state which may not be detected by conventional macroscopic techniques. This circumstance illustrates the potential of μ+SR techniques in studies of electron transport in matter. The muonium formation process in condensed matter is shown to depend critically upon whether the excess electron forms a polaron or remains in a delocalized state. Different mechanisms of electron transport in insulators are discussed.

Target-thickness-dependent electron emission from carbon foils bombarded with swift highly charged heavy ions

We have measured electron yields from the beam entrance and exit surfaces of thin carbon foils (d\ensuremath{\approxeq}4--700 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) bombarded with swift (13.6 MeV/u) highly charged (q=16--18) argon ions. The dependence of the electron yields on target thickness and charge state of the ions is analyzed within the framework of an extended semiempirical model. Due to the high velocity of the ions, it is possible to distinguish electron production in primary ionization (related to the stopping power and the effective charge of the ions) from secondary electron production due to the transport of so-called \ensuremath{\delta} electrons (cascade multiplication). By combining the experimental results with numerical simulations of electron transport in matter by a Monte Carlo method, we have obtained electron transport lengths of high energy (E\ensuremath{\gg}100 eV) \ensuremath{\delta} electrons parallel and perpendicular to the ion trajectory, as well as diffusion lengths of slow electrons (E\ensuremath{\ll}100 eV). In order to study the velocity dependence of these transport lengths, we have not only investigated 13.6 MeV/u Ar ions, but also 1 MeV/u C and 3.9 MeV/u S, for which experimental results are available [Koschar et al., Phys. Rev. A 40, 3632 (1989)]. We discuss the origin of electron yield reductions (compared to a simple scaling with the square of the nuclear charge) with heavy ions and present measurements of double differential energy and angular electron distributions of 13.6 MeV/u ${\mathrm{Ar}}^{17+}$ ions.

Analytical expression describing the attenuation of Auger electrons and photoelectrons in solids

AbstractThe attenuation of Auger electrons and photoelectrons in solids as described by the so‐called depth distribution function (DDF), has been studied by means of a Monte Carlo simulation of electron transport in matter. Elastic scattering plays a significant role in the model. Based on the results of a large number of simulations, an empirically derived analytical expression for the DDF is proposed that includes the effects of elastic scattering. As part of this analytical DDF, a new attenuation parameter (AP) is introduced, which being a material constant independent of emission angle and layer thickness, can assume a central role in quantitative AES and XPS. The proposed AP as well as the general validity of the results is discussed. Most importantly, a simple relationship between the most significant quantities governing the transport of electrons in transport of electrons in solids, i.e. the inelastic mean free path (IMFP), the total mean free path (TEMP) and the attenuation parameter, was derived from the results. By a single Monte Carlo simulation, the AP can be determined. The DDF for different experimental geometries, film thicknesses, etc. can then be determined analytically.

Monte Carlo techniques in medical radiation physics

The author's main purpose is to review the techniques and applications of the Monte Carlo method in medical radiation physics since Raeside's review article in 1976. Emphasis is given to applications where proton and/or electron transport in matter is simulated. Some practical aspects of Monte Carlo practice, mainly related to random numbers and other computational details, are discussed in connection with common computing facilities available in hospital environments. Basic aspects of electron and photon transport are reviewed, followed by the presentation of the Monte Carlo codes widely available in the public domain. Applications in different areas of medical radiation physics, such as nuclear medicine, diagnostic X-rays, radiotherapy physics (including dosimetry), and radiation protection, and also microdosimetry and electron microscopy, are presented. Actual and future trends in the field, like Inverse Monte Carlo methods, vectorization of codes and parallel processors calculations are also discussed.

Comparison of various Monte Carlo schemes for simulation of low-energy electron transport in matter

A detailed comparison of various characteristics obtained in an electron transport calculation by Monte Carlo methods with experimental data is given. Some restrictions on the use of the condensed random-walk scheme and the continuous slowing-down approximation are demonstrated. The individual collision scheme proposed provides the best agreement with the experiments for electron energies E 0 less than 50 keV.

Determination of W Values and Backscatter Coefficients for Slow Electrons in Air

Measurements are reported to determine the average energy W expended to form an ion pair in air for incident electrons in the energy range from 30 eV to 5 keV. For energies T greater than or equal to 60 eV the standard deviations are lower than 1%. In addition, backscatter coefficients R/sub i/ with respect to the spatial ionization distribution have been determined. R/sub i/ is an important quantity describing the electron transport in matter and is needed to correct W values. The experimental data are compared with the results of other authors.

Calculation of the dissipated-energy distribution in the theory of electron transport in matter

A method is proposed for calculating the spatial distribution of the dissipated energy from a unidirectional point source of monoenergetic electrons in an infinite homogeneous medium. The distribution is found by a moment-method solution of the corresponding kinetic equations, formulated in the approximation of continuous electron deceleration; the distribution function from the calculated moment system is subsequently reconstructed along the spatial coordinates.