Electron Trajectories Research Articles

Radiation by an electron in an electromagnetic plane wave: The quasiclassical formula and other domains of applications

The semiclassical Ba\{\i}er-Katkov (BK) formula is an approximation to the spectrum of the radiation by an ultrarelativistic electron in a nonuniform field, taking into account the recoil and spin effects. The question why it involves only the initial electron trajectory is addressed. When the field is an electromagnetic plane wave, the exact helicity amplitudes in the null-plane frame are derived using Volkov solutions of the Dirac equation and a modified form of the BK formula is obtained. In passing, the application to Compton scattering is outlined and interesting spin properties are noted. For a general field, two conditions of validity of the BK formula are proposed: (1) the field is approximately uniform in the transverse directions, (2) the relative velocity between the field and the electron is close to $c$. The applications to bremsstrahlung, coherent bremsstrahlung and channeling radiation are discussed.

Trajectory control of electron beams using high intensity permanent magnests for linac-adaptable convergent beam radiotherapy

Convergent beam radiotherapy, or CBRT, currently under development is based on the adaptation of a linear accelerator (linac) to a device which allows to dynamically curve the original trajectory of the electron beam so that it impacts upon a target. This produces a photon beam via Bremsstrahlung which converges on a predetermined focus point (isocenter). Adaptation of the RTHC device is only possible if it is sufficiently compact, as the device must be placed between the linac head exit and the gurney. This requires that new magnetic deflection devices be developed. This paper describes the theoretical and experimental development of controlled-deflection electron beam systems (at energies in MeV ranges) generated in a dual linear accelerator waveguide. A device which follows RTHC geometry is adapted for the system, using new magnetic deflector designs based on permanent neodymium magnets which reach magnetic field intensities in the order of Tesla. The methodology that was developed includes calculations of the radii of curvature with relativistic considerations for mono- and poly-energetic electrons. Deflection angles were calculated based on this theoretical foundation, using a program developed in MatLab® which shows the trajectory of electrons both under ideal conditions (uniform magnetic field) and real conditions (magnetic field defined through intensity distribution). Monte Carlo simulation subroutines were implemented in order to estimate the spectrum of electrons issuing from the linac as well as to directly determine the electron beam trajectory with magnetic deflectors present. Theoretical and simulated results were compared to experiments performed with a clinical linear accelerator, demonstrating correspondence between different methodologies and confirming the ability to achieve electron beam deflection levels necessary for implementation of convergent beam radiotherapy device.

Stochastic mechanics for ponderomotive effect of a spin-less electron interacting with a high-intensity plane wave laser field

We discuss the relativistically covariant ponderomotive effect of a spin-less electron by a high-intensity laser field of a plane wave in the quantum regime. At first we recall the relativistic ponderomotive effect in classical mechanics. Then against that, we will investigate quantum mechanical expression of the ponderomotive effect by relativistic stochastic mechanics, where, we also propose relativistic stochastic mechanics to draw a trajectory of a spin-less electron. After giving a strict solution of stochastic mechanics, its slowly varying motion is examined as its ponderomotive effect in the quantum regime. Finally, we will see the universality of the ponderomotive effect acting on a spin-less electron interacting with a present high-intensity femtosecond laser, via the dressed (effective) mass of a spin-less electron bridging between classical and quantum mechanics.

Chemical dynamics characteristics of Kapton polyimide damaged by electron beam irradiation

Polyimides, particularly poly-(pyromellitic dianhydride-4,40-oxydianiline) or PMDA-ODA (Kapton-H®), are ubiquitous in the aircraft and aerospace industries, flexible printed circuits, and many other high-performance applications. For many of these applications, the polymer's stability during and after radiation damage is a serious concern. The effect of electron irradiation on the breaking of inter-molecular bonds and creation of free radicals in Kapton polyimide were studied using reactive molecular dynamics simulation with the polarizable ReaxFF method and experimentally on pristine and electron irradiated polyimide by vibrational spectroscopy, electron paramagnetic resonance, nuclear magnetic resonance, wide angle x-ray diffraction, small angle x-ray scattering, and dynamic mechanical analysis. In our simulations, the electron beam is approximated by a dense column of negatively charged particles, which is inserted at random positions in the polyimide matrix. In order to observe inter-molecular bond breaking during the time frame of the molecular simulations, each electron beam is switched on for 2 fs, causing an average energy of 21 eV per electron trajectory to be transferred to the polyimide through Coulomb interactions during the simulation. Experimentally, polyimide is aged in vacuum with a 90 keV electron beam with a maximum penetration depth greater than the material's thickness.Throughout the simulations, modifications in the chemical structure of the polyimide during and after the electron beam irradiations are monitored. During electron beam irradiation, hydrogen atoms separate from different parts of the polyimide through C–H bond cleavage. After turning off the electron beams and running a microcanonical molecular dynamics simulation for 0.5 ns, several chemical and structural rearrangements are observed in the polyimide structure. The chemical modifications mostly include ring opening and other changes to the imide rings. The computations are compared to infrared spectroscopy, electron paramagnetic resonance, nuclear magnetic resonance, x-ray scattering, and mechanical measurements on aged and pristine polyimide to both guide and validate the conclusions from the computational study. Apart from these changes in chemistry we also evaluate temperature evolution and change in mechanical response of the polyimide slab caused by electron beam exposure. Taken together, the direct measurements of the electronic, chemical, and mechanical properties of the irradiated Kapton films validate the key results of the model.

Numerical simulations of magnetic electron-impact ion source

An electron impact ion source equipped with a magnet has been designed for enhancing the ionization efficiency of such ion sources with potential applications in Knudsen effusion mass spectrometry or electron impact sources used in gas mass spectrometry. This modernized device utilizes the trapping of electrons in parallel electrical and magnetic fields with the goal of maximizing the probability of impact between an electron and an atom or molecule to be ionized. The influence of magnetic and electrical fields on ions and electron trajectories inside the ion source was studied with numerical simulations. Based on the electron and ion trajectories we have modified the classical Nier-type ion source and found the optimal geometrical and potential parameters to provide better electron ionization and higher ion extraction efficiency. This design has the potential to enhance ionization efficiency by a factor of ∼15–20 compared with existing designs.

Leveraging radiation reaction via laser-driven plasma fields

We investigated the effect of a plasma charge separation field on radiation reaction (RR) in laser–plasma interactions. By implementing the plasma field equation developed in one-dimension into the classical Landau–Lifshitz formula, our numerical test-particle modeling revealed distinctive plasma electron dynamics in three regimes: the low density underdense regime, the near-critical density (NCD) regime and the highly overdense one. It is discovered from the electron trajectories and gamma-ray emission that the RR effect is mostly significant at near-critical plasma densities. The underlying mechanism is well interpreted by the theoretical analysis from the perspective of the potential contained in the charge separation field and demonstrated in two dimensional particle-in-cell simulations using the quantum electro-dynamic photon emission approach. Our findings indicate that the NCD plasma is the most efficient medium to leverage RR and generate high-energy and low-divergence gamma-photons.

On Simulation of Sheet Electron Beams with Regard to the Initial Transverse Thermal Velocities of Electrons

A technique to take into account the initial transverse electron thermal velocities in converged sheet electron beams has been developed. This determines the main integral characteristics of a thermal beam in a gun and transportation region of the paraxial approximation via chosen characteristic electron trajectories. We have equations of characteristic electrons motion, initial conditions to solve equations, and formulas for the current density distribution in the thermal beam cross-section and current fraction in conventional boundary. The derived equations and formulas may be used in modeling electron-optical systems and choosing parameters in which the effect of heat electron motion on beam characteristics will lie within tolerable limits.

Research of mini steak tube with planar image plane for laser three-dimensional scanning Lidar

Aiming at satisfying the requirement of laser three-dimensional imaging technology for miniaturization and large detection area streak tube, and also to resolve the potential problems of using spherical screen in existing streak tube, a mini streak tube with planar fluorescent screen was designed by using MATLAB software. After electronic trajectory tracking and image quality evaluation, the effective working diameter of the bellows cathode is 30 mm, the static limit spatial resolution of the edge is better than 42 lp/mm, the magnification is slightly greater than 1, the diameter of the tube is 50 mm, and the length is 126 mm.

A predictive model for two-surface multipactor stability and growth based on chaos theory

In this paper, a novel theoretical approach on multipactor discharge based on principles from nonlinear dynamics and chaos theory is extended to a parallel-plate geometry with radio-frequency (RF) and DC electric-fields. Maps that relate the RF emission phase to the RF arrival phase are developed with no a priori assumptions on the electron trajectories (neglecting space-charge effects). A wide range of system parameters are scanned in the theory, resulting in bifurcation diagrams that recover a plethora of resonant and nonresonant modes. This new approach agrees well with conventional resonance theory where applicable but also provides insight on parameter regions where the former theory is limited. Further, it is found that the attractor form manifests in the exponential growth rate, where higher-periodicity and chaotic modes dilute multipactor growth. These theoretical predictions are validated against particle-in-cell simulations.

The influence of the driving-bicircular-field component intensities on the helicities of emitted high-order harmonics

High-order harmonics generated by a linearly polarized laser field are also linearly polarized. Having in mind that for various application, such as the exploration of magnetic materials, chiral molecules etc., we need circularly polarized high harmonics which serve as coherent soft x-rays, we explore high-order harmonic generation by the so-called bicircular laser field. This field consists of two coplanar counter-rotating circularly polarized fields of different frequencies equal to integer multiples of a fundamental frequency ω. High harmonics generated by such field are circularly polarized with helicity alternating between +1 and −1. Combining a group of such harmonics, instead of obtaining a circularly polarized attosecond pulse train, one obtains a pulse with unusual polarization properties. But, if the harmonics of particular helicity are stronger, i.e., if we have helicity asymmetry in a high-harmonic energy interval, then it is possible to generate an elliptical or even circular pulse train. We theoretically investigated a wide range of bicircular field-component intensities (I1 and I2) and found regions where both the harmonic intensity is high and the helicity asymmetry is large. Particular attention is devoted to the ω−2ω and ω−3ω bicircular fields and atoms having the s and p ground states. In our calculations we use strong-field approximation and quantum-orbit theory. We show that, even in the extreme case of I2 = 8I1, for an ω−3ω bicircular field, high-order harmonic generation is more efficient than in the I2 = I1 case. The obtained results are explained analyzing the relevant electron trajectories and velocities, which follow from the quantum-orbit theory. For the atoms having p ground state the helicity asymmetry parameter is large for a wide range of high-harmonic photon energies, while for the atoms having s ground state the helicity asymmetry parameter can be large only for low harmonics. We confirm this by averaging the obtained results over the intensity distribution in the laser focus.

A Multiobjective Optimization Design Tool for Traveling-Wave Tubes’ Electron Optics System

The nondominated sorting genetic algorithm II and the electron optics simulator were combined to form a multiobjective optimization design tool for electron optics systems of traveling-wave tubes. After determining the objective functions that vary with the macroscopic electrical parameters that need to optimize the electron optics system, the optimization tool is capable of obtaining the optimal solution set automatically. Then, the microscopic electron trajectories of the individuals in the optimal solution set are analyzed to get the final scheme. In the collector optimization, the maximum collector efficiency and the minimum back-streaming current are used as optimization goals. While for the demonstrated electron gun, the maximum waist position is set to be the optimization goal, together with constraints of emitting current and beam waist radius. After analyzing the energy density distribution on the collector inner surface or the laminar flow of the electron gun, the final scheme is determined from the optimal solution set.

Suppressed short-trajectory near-threshold harmonics as a sign of tunnel exit

We study high-order harmonic generation (HHG) from atoms with different ionization potentials by solving numerically the time-dependent Schrödinger equation. A numerical scheme is used which allows us to resolve the contributions of only the short electron trajectory to HHG. With increasing laser wavelengths and reducing laser intensities, the calculated short-trajectory HHG spectra show an energy region near the threshold, where the HHG yields are suppressed strikingly. The width of the region depends on the ionization potential of the target. We show that this suppression can be attributed to the effect of tunnel exit, by providing a distinct HHG feature for studying tunneling. It also provides a chance for exploring other HHG mechanisms beyond tunneling.

3D-Simulation of a Bayard Alpert ionisation gauge using SIMION program

Numerical simulation of a Bayard-Alpert ionisation gauge using SIMION 8.1 software is presented. Gauge sensitivity, being the most important parameter of an ionisation gauge, has been derived using two different approaches. In the first one, SIMION is used to determine mean length of electron trajectories, and ion collection efficiency. From these values, known ionisation cross sections and the gas temperature, the sensitivity can be readily calculated. In the second and more detailed approach, a Monte Carlo method was implemented in the Lua programming language to simulate electron impact ionisation of the gas. The Lua code is incorporated in the SIMION trajectory simulations, in which the ionisation event is modelled by transforming a primary electron into an ion. This approach evaluates the contribution of each trajectory to the gas ionisation. It considers energy dependence of the ionisation probability and the contribution of the electrons backscattered from the grid to the sensitivity. The simulation approaches were tested on the gauge geometry, recently modelled by the CERN group. Very good quantitative agreement with the CERN simulations was obtained using both approaches. Monte Carlo simulations reveal that the relative contribution of electrons backscattered from molybdenum grid to the sensitivity is about 14%.

Imaging the source of high-harmonics generated in atomic gas media.

We report the application of the time gated ion microscopy technique in accessing online the position of the source of harmonics generated in atomic gas media. This is achieved by mapping the spatial extreme-ultraviolet (XUV)-intensity distribution of the harmonic source onto a spatial ion distribution, produced in a separate focal volume of the generated XUV beam through single photon ionization of atoms. It is found that the position of the harmonic source depends on the relative position of the harmonic generation gas medium and the focus of the driving infrared (IR) beam. In particular, by translating the gas medium with respect to the IR beam focus different "virtual" source positions are obtained online. Access to such online source positioning allows better control and provides increased possibilities in experiments where selection of electron trajectory is important. The present study gives also access to quantitative information which is connected to the divergence, the coherence properties and the photon flux of the harmonics. Finally, it constitutes a precise direct method for providing complementary experimental info to different attosecond metrology techniques.

Mechanism of vacuum flashover on surface roughness

An investigation is conducted regarding the influence of surface roughness on the flashover strength of an insulator in vacuum. A series of experiments is first presented, showing the relationship between surface roughness and flashover voltage, combined with measurement of surface potential distribution. It is found that surface charging on a roughened dielectric is suppressed remarkably; also the flashover voltage threshold depicts a rise-and-fall trend with roughness increasing, exhibiting a voltage summit at a certain roughness value. In addition, optical observation is implemented to draw a parallel with an electron trajectory in vacuum. A proposal can therefore be made that multipactor expansion tends to be mitigated as electron bombardment on a dielectric occurs with a lower secondary electron yield. Then a theoretical model considering the microscopic physical process is established to explain the above phenomena, consisting of an internal charge migration layer, an interfacial electron absorption layer and an external electron obstruction layer. The validity of this theoretical model can be confirmed by obtaining the surface trap distribution, microscopic morphology and net secondary electron yield.

Dynamical stability of electron trajectories in a free-electron laser with quadrupole wiggler

The dynamical stability of electron trajectories of a free-electron laser with a quadrupole wiggler is studied. For this purpose, the numerical computation of Kolmogorov entropy is used. Self-electric and self-magnetic fields are taken into account, and the focusing of the beam is enhanced by an axial magnetic field. A considerable decrease in the dynamical stability of electron trajectories was found when self-fields are considered. Also, it was found that an axial magnetic field can significantly alter the regular trajectories of the electrons.

Emergence of Novel Multipactor Modes Under Standing Wave Conditions in a Coaxial Line With an RF Window

The multipactor (MP) phenomenon can generate exponentially increasing electron populations in RF vacuum systems, leading to components becoming damaged. This paper uses numerical methods to analyze an RF vacuum window in a coaxial line under various standing wave conditions. Our methods are first benchmarked against the analytic and experimental results for the traveling wave and the numerical results for standing waves that were found in previous work. Second, the effect of standing waves on electron motion in the axial direction is discussed and related to electron trajectories in the presence of an RF window. It is found that standing waves with the magnetic maximum located behind the RF window lead to window collisions that can affect MP depending on the power, frequency, and conductor radii. For a low number of window collisions, MP was highly predictable by earlier work, but as the percentage of collisions occurring on the window surpassed approximately 50%, a novel mode of MP emerged to dominate the phenomenon.

Efficiency of radiation friction losses in laser-driven ‘hole boring’ of dense targets

In the interaction of laser pulses of extreme intensity (>1023 Wcm−2) with high-density, thick plasma targets, simulations show significant radiation friction losses, in contrast to thin targets for which such losses are negligible. We present an analytical calculation, based on classical radiation friction modeling, of the conversion efficiency of the laser energy into incoherent radiation in the case when a circularly polarized pulse interacts with a thick plasma slab of overcritical initial density. By accounting for three effects including the influence of radiation losses on the single electron trajectory, the global ‘hole boring’ motion of the laser-plasma interaction region under the action of radiation pressure, and the inhomogeneity of the laser field in both longitudinal and transverse direction, we find a good agreement with the results of three-dimensional particle-in-cell simulations. Overall, the collective effects greatly reduce radiation losses with respect to electrons driven by the same laser pulse in vacuum, which also shift the reliability of classical calculations up to higher intensities.

Modelling of electron trajectories inside SEM chamber concerning mirror effect phenomenon

A computational investigation is carried out to describe the behaviour of reflected electrons upon a charged insulator sample and producing mirror effect images. A theoretical expression for the scanning electron path equation is derived concerning Rutherford scattering and some electrostatic aspects. The importance of the derived formula come from its correlation among some of the most important parameters that controls the mirror effect phenomena. These parameters, in fact, are the trapped charges, incident angle and the scanning potential which investigated by considering its influences on the incident electrons. A pervious experimental operation requirements are adopted for operating the introduced expression. However, the obtained results are almost encouraged for using the presented expression to simulate the electron trajectory in sense of mirror effect.

Targeted DNA oxidation and trajectory of radical DNA using DFT based QM/MM dynamics.

Molecular insight into electronic rearrangements and structural trajectories arising from oxidative damages to DNA backbone is of crucial importance in understanding the effect of ionizing radiation, developing DNA biosensors and designing effective DNA cleaving molecules. Employing a Density Functional Theory based multi-scale Quantum-Mechanical-Molecular-Mechanical (QM/MM) simulation and a suitable partitioning of the Hamiltonian on solvated nucleotide, and single-, and double-stranded DNA, we mimic hydrogen transfer reactions from the backbone by OH radicals and report structural trajectories arising from on-the-fly electronic charge- and spin-density redistribution in these three different structural topologies of DNA. Trajectories reveal that H4′ abstraction can disrupt the deoxyribose moiety through the formation of C4′=O4′ ketone and a π-bond with base at C1′-N9 in a nucleotide versus only partial ketone formation in single- and double-stranded DNA, where the orientation of the base is topologically restrained. However, H5′ abstraction can lead DNA cleavage at 5′ end through the formation of C5′=O5′ ketone and breakage of P-O5′ bond. Results demonstrate that structural damages from oxidative reactions are restrained by base stacking and base-pair hydrogen bonding. The methodology can be suitably used to study targeted DNA and RNA damages from radicals and radiomimetic drugs to design DNA cleaving molecules for chemotherapy.