Angular Distribution Of Electrons Research Articles

Scattering of ultrashort electron wave packets: optical theorem, differential phase contrast and angular asymmetries

Recent advances in electron microscopy allowed the generation of high-energy electron wave packets of ultrashort duration. Here we present a non-perturbative S-matrix theory for scattering of ultrashort electron wave packets by atomic targets. We apply the formalism to a case of elastic scattering and derive a generalized optical theorem for ultrashort wave-packet scattering. By numerical simulations with 1 fs wave packets, we find in angular distributions of electrons on a detector one-fold and anomalous two-fold azimuthal asymmetries. We discuss how the asymmetries relate to the coherence properties of the electron beam, and to the magnitude and phase of the scattering amplitude. The essential role of the phase of the exact scattering amplitude is revealed by comparison with results obtained using the first-Born approximation. Our work paves a way for controlling electron-matter interaction by the lateral and transversal coherence properties of pulsed electron beams.

A Modeling Investigation for Solar Flare X-Ray Stereoscopy with Solar Orbiter/STIX and Earth-orbiting Missions

The Spectrometer/Telescope for Imaging X-rays (STIX) on board Solar Orbiter (SolO) provides a unique opportunity to systematically perform stereoscopic X-ray observations of solar flares with current and upcoming X-ray missions at Earth. These observations will produce the first reliable measurements of hard X-ray (HXR) directivity in decades, providing a new diagnostic of the flare-accelerated electron angular distribution and helping to constrain the processes that accelerate electrons in flares. However, such observations must be compared to modeling, taking into account electron and X-ray transport effects and realistic plasma conditions, all of which can change the properties of the measured HXR directivity. Here, we show how HXR directivity, defined as the ratio of X-ray spectra at different spacecraft viewing angles, varies with different electron and flare properties (e.g., electron angular distribution, highest-energy electrons, and magnetic configuration), and how modeling can be used to extract these typically unknown properties from the data. Finally, we present a preliminary HXR directivity analysis of two flares, observed by the Fermi Gamma-ray Burst Monitor and SolO/STIX, demonstrating the feasibility and challenges associated with such observations, and how HXR directivity can be extracted by comparison with the modeling presented here.

Probing the angular distribution of terrestrial cosmic-ray nuclei

Understanding how atmospheric cosmic-rays are distributed on Earth is crucial for simulating cosmic-ray setups and detectors for rare-event detection. The accuracy and reliability of such simulations and experiments depend on obtaining this information. This study focuses on analyzing the impact of key parameters in the PARMA model on the angular distributions of terrestrial cosmic-ray nuclei. These parameters include geomagnetic cut-off rigidity, atmospheric depth and solar activity. Moreover, angular distributions of various particles, including protons, electrons, neutrons, and muons, were systematically calculated over relevant rigidities, solar modulations, and altitudes. For this purpose, the latest version of the Excel-based Program for calculating Atmospheric Cosmic-ray Spectrum EXPACS (v.4.13), which relies on updated experimental data, was used. The results of the calculations showed clear trends in the angular distributions of all cosmic-ray species as a function of the model parameters. These findings provide valuable insights into the dynamics of cosmic rays in our solar system. Moreover, they can contribute to developing more accurate models for predicting the distribution of cosmic rays on the Earth's surface.

Voltage waveform tailoring for high aspect ratio plasma etching of SiO2 using Ar/CF4/O2 mixtures: Consequences of low fundamental frequency biases

The use of non-sinusoidal waveforms in low pressure capacitively coupled plasmas intended for microelectronics fabrication has the goal of customizing ion and electron energy and angular distributions to the wafer. One such non-sinusoidal waveform uses the sum of consecutive harmonics of a fundamental sinusoidal frequency, f0, having a variable phase offset between the fundamental and even harmonics. In this paper, we discuss results from a computational investigation of the relation between ion energy and DC self-bias when varying the fundamental frequency f0 for capacitively coupled plasmas sustained in Ar/CF4/O2 and how those trends translate to a high aspect ratio etching of trenches in SiO2. The fundamental frequency, f0, was varied from 1 to 10 MHz and the relative phase from 0° to 180°. Two distinct regimes were identified. Average ion energy onto the wafer is strongly correlated with the DC self-bias at high f0, with there being a maximum at φ = 0° and minimum at φ = 180°. In the low frequency regime, this correlation is weak. Average ion energy onto the wafer is instead dominated by dynamic transients in the applied voltage waveforms, with a maximum at φ = 180° and minimum at φ = 0°. The trends in ion energy translate to etch properties. In both, the high and low frequency regimes, higher ion energies translate to higher etch rates and generally preferable final features, though behaving differently with phase angle.

Collimated hot electron generation from sub-wavelength grating target irradiated by a femtosecond laser pulse of relativistic intensity

We investigate the production of hot electrons from the interaction of relativistically intense (I>1018 W/cm2) ultrashort (25 fs) laser pulses with sub-wavelength grating target. We measure the hot electron angular distribution and energy spectra for grating target and compare them with those from a planar mirror target. We observe that hot electrons are emitted in a collimated beam along the specular direction of the grating target. From the measurements, we see fast electron temperature and flux for grating are higher than those for mirror due to a stronger coupling with the laser. We performed numerical simulations, which are in good agreement with experimental results, and offer insights into the acceleration mechanism by resulting electric and magnetic fields. Such collimated fast electron beams have a wide range of applications in applied and fundamental science.

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization (NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5π and 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization (RII) channel. This is attributed to the shorter delay time in the RII channel.

Ionization of CH[formula omitted] under fast He-like Si-ion impact

We have studied the absolute double differential cross section (DDCS) of electrons ejected from the methane molecule (CH4) under the impact of highly charged fast projectile ions. The energy and angular distributions of electrons have been measured in interactions with 70 MeV Si12+ ions. These DDCS data together with the derived single differential cross sections and the total cross section (TCS) have been compared with predictions of the continuum distorted wave-eikonal initial state model using different approaches for the molecular orbitals. It has been found that the theories overestimate the measured DDCS values at low ejection energies, which may indicate shortcomings of the model in the case of strong perturbation. At the same time, applying the model to a previous measurement using fast C ions having a lower perturbation strength, excellent agreements have been obtained with the experimental data. Considering the scaling properties, the available TCS data have been plotted with a scaled parameter, namely the perturbation strength, q/v (where q= charge state, v=velocity of the projectile). The KLL Auger e-emission as well as the KLL hyper-satellite peaks are analyzed for different emission angles. The double K-vacancy production shows a considerable enhancement i.e. 37% of the single production cross section which is consistent with some of the recent experiments on K-ionization using x-ray techniques.

Monte Carlo simulation of electron emission from aluminum after low energy protons impact

A Monte Carlo (MC) simulation approach is developed to describe the proton-induced secondary electron emission in solids. First, we calculate the double differential cross-section (DDCS) of excited electrons for different charge fractions of the projectile resulting from electron screening. The DDCS parameter is used in MC calculations to describe electron transport in the medium. This parameter is calculated for electrons excited in the 1 eV − 100 eV energy range. The theoretical electron transport modeling is based on Mott’s elastic scattering cross-section and Lindhard’s dielectric function for inelastic scattering. The results obtained for aluminum describe the angular and energy distributions of backscattered electrons for incident protons with energy below 25 keV at normal incidence. Additionally, the total electron emission yield is also calculated, showing a good agreement with available measurements. Our predictions for energy and angular distributions could not be compared with experimental results due to a lack of data.

Imaging electron angular distributions to assess a full-power petawatt-class laser focus

Imaging electron angular distributions to assess a full-power petawatt-class laser focus

Complex diagnostic and numerical study of x-ray and particle emissions under relativistic ultra-short laser-solid interaction

In this report, we present the experimental results on the generation of x-ray emission and particle acceleration using high temporal contrast (∼10–9 at picosecond time scale), ultrashort (), relativistic () near-IR laser pulses interacting with Titanium foils. Complex diagnostics, including the energy spectra of accelerated electrons from both front and rear target sides, electron angular distribution and x-ray spectroscopy of the plasma emission were employed. Analysis of the characteristic radiation produced by highly charged Ti+20 ions led to the conclusion that laser-plasma interaction, which leads to the generation of keV hot plasma, occurs at plasma densities 10x higher than relativistic critical electron density. Numerical simulations, including hydrodynamic calculations to model pre-plasma, generated on nanosecond-picosecond time scale under our experimental conditions and relativistic particle-in-cell simulations for main pulse interaction with the plasma reproduce well electron energy and angular distributions. They show the onset of hole boring effect under near normal incidence that leads to plasma density steepening and enables penetration of high intensity laser radiation into the overcritical plasma to much higher densities (up to 30 ), what is in a good agreement with the results of x-ray spectroscopy.

Calculation of Energy and Angular Distributions of Electrons Produced in Intermediate-Energy p + H2 Collisions

We extend the two-centre wave-packet convergent close-coupling approach to doubly differential ionisation in proton collisions with H2 to intermediate projectile energies. The results for the doubly differential cross section at projectile energies from 48 to 200 keV are presented as a function of the energy and angle of emitted electrons. We consider a wide range of emission angles from 10 to 160∘, and compare our results to experimental data, where available. Excellent agreement between the presented results and the experimental data was found, especially for emission angles less than 130∘. For very large backward emission angles our calculations tended to slightly overestimate the experimental data when energetic electrons are ejected and the doubly differential cross section is very small. This discrepancy may be due to the large uncertainties in the experimental data in this region and the model target description. Overall, the present results show significant improvement upon currently available theoretical results and provide a consistently accurate description of this process across a wide range of incident energies.

Doubly differential cross sections for ionisation in proton–helium collisions at intermediate energies: energy and angular distribution of emitted electrons

Using the two-centre wave-packet convergent close-coupling approach, we continue our study of the proton–helium collision system. This method uses a correlated two-electron wave function to describe the helium target and discretises the continuum using wave-packet pseudostates. The cross section differential in the electron-emission energy and emission angle is calculated for incident-projectile energies in the intermediate range from 70 to 300 keV, where coupling between various channels and electron–electron correlation effects are important. We also apply an alternative, simpler approach that reduces the target to an effective single-electron system. Overall, the present results from both methods agree well with the available experimental data. This positions both implementations of the two-centre wave-packet convergent close-coupling approach well to further study other doubly differential, as well as fully differential, cross sections of single ionisation in proton–helium collisions.Graphical abstract

MP-CITDSE: A set of ab-initio programs for the simulation of hydrogenic and helium-like atom-laser interactions

MP-CITDSE is a package of programs which solves the time-dependent Schrödinger equation for hydrogenic and helium-like atomic systems interacting with an ultra-short laser pulse (of attosecond or femtosecond duration). The output of the computations – with some minimal processing – may be used to calculate excited populations, single and double ionisation yields, kinetic, angular and radial electron distributions, and harmonic yields. For the Helium atom, a full account of the inter-electronic correlation effects is included via a configuration interaction approach; for the time propagation of the wavefunction a spectral basis expansion on the eigenstates of the field-free Hamiltonian is used; for this reason post-processing of the expansion coefficients just after the pulse lead to simple formulas for quantities of experimental interest. Program summaryProgram Title: MP-CITDSECPC Library link to program files:https://doi.org/10.17632/gv4zxmfdx3.1Developer's repository link:https://github.com/aforembs/MP-CITDSELicensing provisions: GPLv3Programming language: C++Nature of problem: The ultra-fast high-intensity laser pulses of modern experimental sources require an ab-initio theoretical treatment, as the characteristics of such pulses are generally incompatible with the established Lowest-order Perturbation Theory (LOPT) approximation. Such a treatment can be quite cumbersome to not only implement, but also describe in a clear, intuitive manner. Its inherent complexity ensures that even in its simplest form, an ab-initio TDSE solver can easily consist of several thousand lines of code. As with any project of such scope a significant amount of effort is required to keep the code up to date, running on several platforms, compilers and operating systems. As such, while the numerical problem tackled by MP-CITDSE is that of the simulation of hydrogenic and helium-like atom-laser interactions on a single node computer/workstation; its main challenges are longevity and expandability. By doing away with unnecessary abstractions within the code, using a modern standard of a widely used and performant language (C++ 17) and hosting the source code on a publicly available GitHub repository we hope that the programs provided herein prove themselves useful to many current and future AMO Physicists.Solution method: The atomic systems are considered confined in a spherical box of finite size. In the one-electron case (hydrogen) the eigenstates are calculated in a spherical coordinate system by the direct diagonalisation of the field-free Hamiltonian matrix representation on a B-splines piecewise polynomial basis expansion of the radial part of the eigenfunctions; for the two-electron case (helium) the numerically calculated one-electron eigenstates are angularly coupled to form a zero-order (uncorrelated) two-electron numerical basis; then the latter basis is further coupled via a configuration-interaction approach to eventually calculate the helium's two-electron eigenstates.Following these steps, for both systems (hydrogen and helium) the computation proceeds by expanding the time-dependent wavefunction on the corresponding field-free eigenstate basis; thus, we end up to a system of first-order ordinary differential equations (ODEs) in time for the expansion (time-dependent) coefficients; the dynamical parameters for the ODEs time propagation, namely the eigenenergies and dipole matrix elements are calculated only once prior to the ODEs propagation [2]. The structure of the propagating matrix is block tridiagonal.Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the MP-CITDSE code. In this version we solve the ODEs using a Runge-Kutta-Felnberg (RKF) algorithm. Also we have restricted the code to treat hydrogen and helium but with very little effort (non-relativistic) hydrogenic and helium-like atomic systems can also be simulated. The programs are supplied with two methods of compilation, via make and cmake to ensure greater portability.

Robust Local Thickness Estimation of Sub-Micrometer Specimen by 4D-STEM.

A quantitative four-dimensional scanning transmission electron microscopy (4D-STEM) imaging technique (q4STEM) for local thickness estimation across amorphous specimen such as obtained by focused ion beam (FIB)-milling of lamellae for (cryo-)TEM analysis is presented. This study is based on measuring spatially resolved diffraction patterns to obtain the angular distribution of electron scattering, or the ratio of integrated virtual dark and bright field STEM signals, and their quantitative evaluation using Monte Carlo simulations. The method is independent of signal intensity calibrations and only requires knowledge of the detector geometry, which is invariant for a given instrument. This study demonstrates that the method yields robust thickness estimates for sub-micrometer amorphous specimen using both direct detection and light conversion 2D-STEM detectors in a coincident FIB-SEM and a conventional SEM. Due to its facile implementation and minimal dose reauirements, it is anticipated that this method will find applications for in situ thickness monitoring during lamella fabrication of beam-sensitive materials.

Molecular Anions Perspective.

This Perspective attempts to shed light on developments in the theoretical and experimental study of molecular anions highlighting more recent workers in the field. The species I discuss include (i) valence-bound (singly and multiply charged) anions including atmospheric, catalytic, superhalogen, interfacial, and more; (ii) dipole- and correlation-bound anions including their role as doorways to other states and their appearance "in space", and (iii) metastable anions focusing on tools needed for their theoretical treatment. I also briefly discuss angular distributions of photodetached electrons and their growing utilization in experiments and theory. A recurring theme is the dependence of electron binding energies (EBEs) on the surrounding environment. Some anions that are nonexistent as isolated species evolve to be stable but with small EBEs when weakly solvated (e.g., as in a cluster or at an air-solvent interface). Others existing in isolation only as metastable species become stable when the underlying molecular framework contains one or more positively charged group (e.g., protonated side chains in a peptide) that generates a stabilizing Coulomb potential. On the other hand, a destabilizing Coulomb potential between/among negative sites in a multiply charged anion decreases the EBEs of each such site and generates a repulsive Coulomb barrier that can affect stability.

Prediction of Betavoltaic Battery Parameters

The approaches for predicting output parameters of betavoltaic batteries are reviewed. The need to develop a strategy for predicting these parameters with sufficient accuracy for the optimization of betavoltaic cell design without using the simple trial and error approach is discussed. The strengths and weaknesses of previously proposed approaches for the prediction are considered. Possible reasons for the difference between the calculated and measured parameters are analyzed. The depth dependencies of beta particles deposited energy for Si, SiC, GaN, and Ga2O3 and 20% purity 63Ni and titanium tritide as radioisotope sources are simulated using the Monte Carlo algorithm taking into account the full beta energy spectrum, the isotropic angular distribution of emitted electrons and the self-absorption inside the radioisotope source for homogeneously distributed emitting points. The maximum short circuit current densities for the same semiconductors and radioisotope sources are calculated. The methodology allowing the prediction of betavoltaic cell output parameters with accuracy no worse than 30% is described. The results of experimental and theoretical investigations of the temperature dependence of betavoltaic cell output parameters are briefly discussed. The radiation damage by electrons with the subthreshold energy and the need to develop models for its prediction is considered.

Electron-neutral collision cross sections for H2O: II. Anisotropic scattering and assessment of the validity of the two-term approximation

This work proposes a complete and consistent set of cross sections (CS) for electron collisions with water gas molecules to be published in the IST-Lisbon database on LXCat. The set is validated by the electron swarm analysis technique. The anisotropic angular distribution of electrons in rotational collisions is considered by means of the Born approximation in a two-term Boltzmann solver (LisbOn KInetics two-term Boltzmann solver (LoKI-B)) and a Monte Carlo simulations code (LoKI-MC), both freely available as open-source codes. The inclusion of electron anisotropic scattering in rotational collisions significantly improves the agreement between calculations and measurements of the electron drift velocity, reduced mobility, characteristic energy, reduced Townsend ionisation coefficient, reduced effective Townsend coefficient and reduced attachment coefficient. The MC simulations are deemed more accurate and shown to yield similar results as LoKI-B with the proposed set. The use of LoKI-MC also validates the set of CSs against parameters that cannot be obtained by LoKI-B, such as the longitudinal diffusion coefficient or the bulk transport coefficients.

Hot electron scaling for two-plasmon decay in ICF plasmas

We present a parametric scaling of hot electron (HE) generation at quarter critical density from the two-plasmon decay process. The study is conducted with the laser plasma simulation environment code, considering Langmuir decay instabilities (LDI) and laser pump depletion in 2D. The parameter scan is conducted as a function of electron temperature, ion–electron temperature ratio, drive strength, and density scale length. The scaling shows an hot electron (HE) conversion fraction up to 40%, HE fluxes up to 6 × 10 14 W / cm 2, and average temperatures in the range of 30 to 100 keV. The electron angular distributions exhibit two main regions: the plasma “bulk,” characterized by homogeneous emission, up to energies of 30 − 60 keV depending on the individual laser–plasma conditions, and a HE tail after ≃ 50 − 60 keV. The mid-energy electrons are homogeneously emitted toward the end of the plasma bulk and acquire energy through electron plasma wave (EPW) Landau damping from Langmuir wave collapse and LDI cascade. The HE tail has electrons emitted in the forward direction and at low divergence, due to turbulence and EPW Landau damping from multi-staged acceleration. Finally, the laser power transmitted through the quarter critical region reaches values from ∼ 80 % down to ∼ 35 % for increasing HE generation, with absorption due to EPW collisional damping in the range of ∼ 10 % − 35 %.

Energy and angular distributions of electrons emitted in proton collisions with molecular hydrogen

The description of experimental data on energy and angular distributions of electrons produced in intermediate-energy proton collisions with ${\mathrm{H}}_{2}$ has remained an insurmountable problem for over five decades. A coupled-channel method is developed that provides an accurate solution to the problem. The doubly differential cross section as a function of the energy and angle of the ejected electron is calculated. Excellent agreement between the present results and the experimental data is found. This breakthrough in theoretical modeling of differential ionization in $p+{\mathrm{H}}_{2}$ collisions paves the way to accurate description of the recent kinematically complete experiments.

Investigation of photoelectron elliptical dichroism for chiral analysis.

This paper describes a compact new instrument, conceived specifically for measurements of Photo Electron Elliptical Dichroism (PEELD) and designed for simplicity of use as a prototype for a practical analytical device. PEELD is an asymmetry in the electron angular distribution obtained from resonantly enhanced multi-photon ionisation of a chiral molecule, where there is also a non-linear dependence on the polarization ellipticity. Despite the fact that PEELD can provide a unique signature of molecular structure and dynamics it has only been investigated in a few molecules to date. This is addressed in the present study in a range of measurements of several terpenes and phenyl-alcohols. These show that the PEELD signatures in structural isomers can be dramatically different and can also be influenced by the intensity of the light. A systematic study in phenyl-alcohols containing the same chromophore and chiral centre configuration shows consistent PEELD behaviour across the molecules except that the magnitude reduces as the distance from the chromophore to the chiral centre increases. These achievements demonstrate that this relatively simple set up can be used for scientific studies as well as providing a blueprint for a practical chiral analysis instrument.