Energy Loss Of Fast Electrons Research Articles

Diagnosis of fast electron transport by coherent transition radiation

Transport of fast electrons in overdense plasmas is of key importance in high energy density physics. However, it is challenging to diagnose the fast electron transport in experiments. In this article, we study coherent transition radiation (CTR) generated by fast electrons on the back surface of the target by using 2D and 3D first-principle particle-in-cell (PIC) simulations. In our simulations, aluminum targets of 2.7 g cc−1 are simulated in two different situations by using a newly developed high order implicit PIC code. Comparing realistic simulations containing collision and ionization effects, artificial simulations without taking collision and ionization effects into account significantly underestimate the energy loss of electron beams when transporting in the target, which fail to describe the complete characteristics of CTR produced by electron beams on the back surface of the target. Realistic simulations indicate the diameter of CTR increases when the thickness of the target is increased. This is attributed to synergetic energy losses of high flux fast electrons due to Ohm heating and colliding drags, which appear quite significant even when the thickness of the solid target only differs by micrometers. Especially, when the diagnosing position is fixed, we find that the intensity distribution of the CTR is also a function of time, with the diameter increased with time. As the diameter of CTR is related to the speed of electrons passing through the back surface of the target, our finding may be used as a new tool to diagnose the electron energy spectra near the surface of solid density plasmas.

X-ray emission reduction and photon dose lowering by energy loss of fast electrons induced by return current during the interaction of a short-pulse high-intensity laser on a metal solid target

During the interaction of a short-pulse high-intensity laser with the preplasma produced by the pulse's pedestal in front of a high-Z metal solid target, high-energy electrons are produced, which in turn create an X-ray source by interacting with the atoms of the converter target. The current brought by the hot electrons is almost completely neutralized by a return current j→ driven by the background electrons of the conductive target, and the force exerted on the hot electrons by the electric field E→ which induces Ohmic heating j→.E→, produced by the background electrons, reduces the energy of the hot electrons and thus lowers the X-ray emission and photon dose. This effect is analyzed here by means of a simple 1-D temperature model which contains the most significant terms of the relativistic Fokker-Planck equation with electron multiple scattering, and the energy equations of ions, hot, and cold electrons are then solved numerically. This Ohmic heating energy loss fraction τOh is introduced as a corrective term in an improved photon dose model. For instance, for a ps laser pulse with 10 μm spot size, the dose obtained with a tantalum target is reduced by less than about 10% to 40% by the Ohmic heating, depending upon the plasma scale length, target thickness, laser parameters, and in particular its spot size. The laser and plasma parameters may be optimized to limit the effect of Ohmic heating, for instance at a small plasma scale length or small laser spot size. Conversely, others regimes not suitable for dose production are identified. For instance, the resistive heating is enhanced in a foam target or at a long plasma scale length and high laser spot size and intensity, as the mean emission angle θ0 of the incident hot electron bunch given by the ponderomotive force is small; thus, the dose produced by a laser interacting in a gas jet may be inhibited under these circumstances. The resistive heating may also be maximized in order to reduce the X-ray emission to lower the radiation level for instance in a safety radiological goal.

Analytical modeling of electron energy loss spectroscopy of graphene: Ab initio study versus extended hydrodynamic model

We present an analytical modeling of the electron energy loss (EEL) spectroscopy data for free-standing graphene obtained by scanning transmission electron microscope. The probability density for energy loss of fast electrons traversing graphene under normal incidence is evaluated using an optical approximation based on the conductivity of graphene given in the local, i.e., frequency-dependent form derived by both a two-dimensional, two-fluid extended hydrodynamic (eHD) model and an ab initio method. We compare the results for the real and imaginary parts of the optical conductivity in graphene obtained by these two methods. The calculated probability density is directly compared with the EEL spectra from three independent experiments and we find very good agreement, especially in the case of the eHD model. Furthermore, we point out that the subtraction of the zero-loss peak from the experimental EEL spectra has a strong influence on the analytical model for the EEL spectroscopy data.

Energy loss of charged particles traversing multilayer graphene

We derive a dielectric response model for dynamic polarization of freestanding multilayer graphene induced by an external charged particle moving at an arbitrary angle of incidence. Using a two-dimensional, two-fluid hydrodynamic model for the single-layer polarizability, we evaluate the probability density for energy loss and the total energy loss of fast electrons traversing graphene under normal incidence for a broad range of the incident electron kinetic energies. Numerical results are obtained in the cases of one, two, and three layers of graphene. When the incident electron kinetic energy T increases, both the probability density and the total energy loss strongly decrease. It is also found that when the kinetic energy T decreases, the π and σ+π plasmon peak positions move to higher energies ω. In addition, the total energy loss approximately scales with the number of graphene layers N for all observed incident electron kinetic energies.

Energy loss of fast electrons impinging upon polymethylmethacrylate

This paper deals with the calculation of the differential inverse inelastic mean free path, the inelastic mean free path, the stopping power, the range of penetration, and the distribution function for inelastic collisions causing energy losses less than or equal to given values, for fast electrons impinging upon polymethylmethacrylate. Numerical tables are provided along with the comparison with computations of other investigators.

Energy loss and online directional track visualization of fast electrons with the pixel detector Timepix

The spectral-, position- and tracking-response of Timepix to energetic electrons has been tested and characterized with well-defined low-intensity parallel beams of monoenergetic electrons in the 7–21 MeV range. The per-pixel energy sensitivity of Timepix serves as a position-sensitive dE/dx detector to determine the energy loss over along the particle track. The sampling path pitch can be set to 55 μm (pixel-size) and arbitrary values between 300 μm (sensor thickness) and nearly 2 mm. Timepix can register and visualize not only the position and trajectories but also the direction of trajectories and the rate of directional scattering of single fast electrons across the semiconductor sensor. The technique serves to measure the spatial distribution of a parallel beam, the beam size spread, transversal beam flux homogeneity and lateral straggling at the pixel-size scale. The mean scattering path along the beam axis and the mean path for lateral beam straggling in silicon can be determined. Measured energy loss distributions were compared with model and previous data as well as with dedicated Monte Carlo MCNPX simulations performed for this work. Tracking distributions were also simulated.

High-energy-density plasmas generation on GEKKO-LFEX laser facility for fast-ignition laser fusion studies and laboratory astrophysics

The world's largest peta watt (PW) laser LFEX, which delivers energy up to 2 kJ in a 1.5 ps pulse, has been constructed beside the GEKKO XII laser at the Institute of Laser Engineering, Osaka University. The GEKKO-LFEX laser facility enables the creation of materials having high-energy-density which do not exist naturally on the Earth and have an energy density comparable to that of stars. High-energy-density plasma is a source of safe, secure, environmentally sustainable fusion energy. Direct-drive fast-ignition laser fusion has been intensively studied at this facility under the auspices of the Fast Ignition Realization Experiment (FIREX) project.In this paper, we describe improvement of the LFEX laser and investigations of advanced target design to increase the energy coupling efficiency of the fast-ignition scheme. The pedestal of the LFEX pulse, which produces a long preformed plasma and results in the generation of electrons too energetic to heat the fuel core, was reduced by introducing an amplified optical parametric fluorescence quencher and saturable absorbers in the front-end system of the LFEX laser. Since fast electrons are scattered and stopped by the strong electric field of highly ionized high-Z (i.e. gold) ions, a low-Z cone was studied for reducing the energy loss of fast electrons in the cone tip region. A diamond-like carbon cone was fabricated for the fast-ignition experiment. An external magnetic field, which is demonstrated to be generated by a laser-driven capacitor-coil target, will be applied to the compression of the fuel capsule to form a strong magnetic field to guide the fast electrons to the fuel core. In addition, the facility offers a powerful means to test and validate astronomical models and computations in the laboratory. As well as demonstrating the ability to recreate extreme astronomical conditions by the facilities, our theoretical description of the laboratory experiment was compared with the generally accepted explanation for astronomical observations.

Monte Carlo method for simulating γ-ray interaction with materials: A case study on Si

In the present work, a Monte Carlo (MC) method has been developed to simulate various quantum mechanical processes for the energy loss of photons and fast electrons. The MC model is demonstrated by application to the interaction of photons with silicon over the energy range from 50 eV to 2 MeV and the subsequent electron cascades. The electron cascade process is commonly represented by two macroscopic parameters, the mean energy required to create an electron–hole pair, W, and the Fano factor, F, describing the electron yield and its variance. At energies lower than 5 keV, W generally decreases with increasing photon energy (from 3.96 to 3.58 eV), and it exhibits a sawtooth variation, as observed previously. However, discontinuities at the shell edges follow the photoionization cross-section, in contrast to previous results. The function, F( E p), initially increases with increasing photon energy, E p, to a maximum value of 0.187 around 155 eV, and then decreases at higher energies. Above the K shell edge, F has a value of 0.135. These results are consistent with experimental observations. The simulated distribution indicates that the interband transition and plasmon excitation are the most important mechanisms of electron–hole pair creation, while core shell ionization appears to be significant only at high energies.

Gamma-ray interaction in Ge: A Monte Carlo simulation

The interactions of X-ray and gamma-ray photons with materials are of fundamental interest to many fields. The interactions of these primary photons with atoms result in the creation of fast electrons. The subsequent electron–solid interactions involve the partitioning of energy loss into different quantum mechanical processes that are important to determining the mean energy required to create an electron–hole pair, W, and the intrinsic variance (or Fano factor, F) for radiation detectors. In the present work, a Monte Carlo method previously developed has been employed to simulate the interaction of photons with Ge over the energy range from 50 eV to ∼2 MeV and the subsequent electron cascades. Various quantum mechanical processes for energy loss of fast electrons, which control the broadening of variance, are investigated in detail. At energies lower than 1 keV, W generally decreases with increasing photon energy from 2.95 to 2.75 eV in Ge, whereas it has a constant value of 2.64 eV for higher energies. Also, the function, F, decreases with increasing photon energy. Above the L shell edge, F has a value of 0.11 that is smaller than that in Si (0.14). However, F exhibits a sawtooth variation, and discontinuities at the shell edges that follow the photoelectric cross sections. These results are in good agreement with experimental measurements. The simulated distribution indicates that the interband transition and plasmon excitation are the most important mechanisms of electron–hole pair creation in Ge, while core shell ionization appears to be significant only at high energies.

Straggling of fast electrons

AbstractThe energy losses of fast electrons vary because of the stochastic nature of the interactions. In order to describe these processes and calculate the spectra of the total energy loss (straggling spectra), Monte Carlo simulations of fast electrons traversing a thin silicon absorber have been used. The distribution functions needed are described by the electronic energy losses in single collision calculated by Bichsel. Comparison between straggling spectra calculated on the basis of the single collision spectrum and that from its first moment (very often ‘stopping power’ in the literature), shows that the latter, the so‐called ‘Continuous Slowing Down Approximation (CSDA),’ is a poor approximation in its description of the individual energy deposition. Copyright © 2006 John Wiley & Sons, Ltd.

Two-dimensional relativistic Fokker-Planck model for core plasma heating in fast ignition targets

One of the key issues in the fast ignition scheme is a clarification of the imploded dense core heating by laser-produced fast electrons. To investigate the core heating process, a two-dimensional relativistic Fokker-Planck code “RFP-2D” for fast electron behavior in dense core plasmas has been developed. Energy loss of fast electrons due to Coulomb interactions is treated through not only usual short-range binary collisions but also long-range binary collisions, including a collective shielding effect. After describing the physics model, an examination is made of the energy deposition of fast electrons injected into a highly compressed D-T cylindrical plasma. The relative importance of the long-range Coulomb interaction and the influence of a self-generated electromagnetic field on the energy deposition profile are demonstrated.

Energy loss of 18 keV electrons in gaseous T and quench condensed D films

Measurements of the energy loss of fast electrons at an energy of 18 keV have been performed on molecules of hydrogen isotopes, gaseous T 2 and frozen D 2 . Whereas in the case of gaseous T 2 the values of total inelastic cross-section ( cm2 for E = 18.6 keV), average energy loss ( eV) and peak position of the energy loss spectra ( eV) agree well with the expectations, the corresponding values for quench condensed D 2 differ significantly from the ones for gaseous T 2 . We observe a significant lower total inelastic cross-section ( cm2, for E = 18.6 keV) larger average energy loss ( eV) and higher peak position ( eV). These differences may be interpreted in terms of changes of the final state spectrum. A CI calculation for a D 2 cluster shows indeed a clear shift of the excited states in agreement with the observation.

Local-Field Effects at Crystalline Surfaces: Electron Energy Loss from Ordered Arrays of Spheres

Local-field effects at crystalline surfaces are analyzed on a classical system consistent of ordered arrays of polarizable spheres. A theory for the energy loss of fast electrons traveling parallel to these arrays is presented. A spectral representation of the surface response function is used to calculate this energy loss. The poles and weights in this representation are determined through the eigenvalues and eigenvectors of an interaction matrix which takes into account the quasi-static electromagnetic fields to an arbitrary multipolar order. We apply the theory to calculate the energy-loss spectra for cubic arrays of aluminum spheres embedded in vacuum and compare the results with those obtained using a dielectric continuum model.

Ionization phenomenon in high-density gaseous and liquid argon in corona discharge experiments

Experimental investigations of corona discharge in Ar for a wide region of fluid density from a rare gas up to a liquid have been carried out. Corona current has been observed for a point cathode voltage above the threshold value . Values of have been measured for a wide range of fluid density N and for different cathode radii . The obtained dependences of on N and have been analysed using the Townsend - Meek breakdown criterion. For low-density gas the calculations of have been carried out by using universal data on ionization coefficient . The data of for low-density gas are in good agreement with these calculations. Deviation from the `gaseous' dependence has been obtained in measurements carried out with a continuous increasing of the fluid density. The onset corona voltage in dense supercritical gas and in liquid is appreciably smaller than the values calculated from the gaseous Paschen curve. To explain this disagreement a model of impact ionization in liquid was developed. An assumption was made that inelastic energy losses of fast electrons by excitation of atoms without their ionization are absent in liquid. The expression for the ionization coefficient in liquid Ar has been obtained and it was used for calculation of in liquid. The calculated values are in agreement with the experimental data obtained in liquid Ar.

Semiempirical cross sections for the simulation of the energy loss of electrons and positrons in matter

Differential cross sections (DCS) suitable for Monte Carlo simulation of the energy loss of fast electrons and positrons in matter are proposed. These DCSs are based on high-energy approximations, complemented with semiempirical ingredients which make them accurate for a wide energy range. The DCS for collision losses, including Fermi's density effect correction, is obtained from the Born approximation and a simple generalized oscillator strength model. Collision stopping powers, and also mean free paths and energy straggling parameters, can be evaluated in a purely analytical way. The DCS for bremsstrahlung emission is given in the form of the Bethe-Heitler DCS with exponential screening including a Coulomb correction. The described DCSs have moderately simple analytical expressions which allow random sampling of the energy loss in detailed Monte Carlo simulations by using purely analytical methods. Suitable sampling algorithms are also described.

An analytical expression for the energy loss of fast electrons travelling parallel to the axis of a cylindrical interface

Abstract An expression for the probability of energy loss of electrons travelling at relativistic speeds parallel to the axis of an infinite cylindrical interface is obtained by solving Maxwell's eauations to find the electric field acting on the electron. This expression is evaluated for the case of an electron travelling through a hole in aluminium and through a hole in amorphous aluminium fiuoride and a comparison is made with the equivalent non-relativistic expression obtained from Poisson's eauation. The non-relativistic solution is shown to underestimate the magnitude and overestimate the energy of the surface plasmon modes. Some calculations are also made to demonstrate the effect of a spatially distributed electron probe on the spectra.

Energy loss of fast electrons moving near plane boundaries with dispersive media

The energy loss per unit length experienced by swift electrons in STEM is calculated for trajectories parallel to plane boundaries with dispersive media. Dispersion corrects the logarithmic divergence of the local energy loss probability at the interface given by the local approach. The effect of damping is also studied, and results are related to the spatial resolution in EELS experiments.

Energy loss in spheres by penetrating electrons

A classical dielectric theory is developed to provide an expression for the energy loss of fast electrons passing through a metallic sphere at a fixed impact parameter, in the case of spheres coated by a thin oxide layer. The expressions for energy loss are valid for any dielectric function e(ω). A high number of terms of the multipole expansion is required in order to take into account the effects of the oxide layer. Results are compared with experimental measurements of energy loss obtained by STEM techniques.

Reciprocity in electron energy-loss spectra from non-centrosymmetric crystals

The energy losses of fast electrons propagating through a thin crystal show a strong effect associated with the interference term between Bloch-wave eigenstates. Reversing the direction of the electrons gives the same spectrum, and reciprocity is observed in the interference term between eigenstates in inelastic electron scattering. The reciprocity principle may be used to advantage to observe for GaAs a very large difference in the characteristic energy-loss spectra for pairs of experimental arrangements related by a mirror operation around the polar (111) planes. This provides a sensitive way of determining the polarity of a crystal based on simple two-beam arguments, and may also be used to obtain direct structure-factor phase information.

Enhancement of energy loss of fast electrons in a ferroelectric medium near the Curie temperature.

The temperature dependence of the energy loss of 624-keV electrons in ferroelectric barium titanate (${\mathrm{BaTiO}}_{3}$) and triglycine sulfate [(${\mathrm{CH}}_{2}$${\mathrm{NH}}_{2}$COOH${)}_{3}$ ${\mathrm{H}}_{2}$${\mathrm{SO}}_{4}$] has been studied with the use of a single-gap magnetic spectrometer. The present measurements confirm the anomalous increase in energy loss of electrons near the Curie temperature ${T}_{C}$ and indicate its dependence on (a) the magnitude of the dielectric anomaly at ${T}_{C}$, (b) the effect of a dc electric field larger than the coercive field, and (c) the application of an alternating electric field. Probable mechanisms for the origin of the observed phenomenon are discussed.