Calculation Of Electron Trajectories Research Articles

Properties of electron lenses produced by ponderomotive potential with Bessel and Laguerre–Gaussian beams

The properties of electron round lenses produced by the ponderomotive potential are investigated in geometrical optics. The potential proportional to the intensity distribution of a focused first-order Bessel or Laguerre–Gaussian (LG) beam is exploited to produce an electron round lens and a third-order spherical aberration (SA) corrector. Several formulas for the focal length and SA coefficients in the thin-lens approximation are derived to set the lens properties and associated light beam parameters. When the mode field of the optical beam is small, the electron trajectory calculation results show properties similar to those obtained using the formulas. Alternatively, large higher-order aberrations are introduced because of the annular distribution of the potential. The second- and higher-order Bessel and LG beams produce no focusing power and no negative third-order SA; however, they can still be used as circularly symmetric higher-order aberration correctors. Results show that the ponderomotive potential–based electron lens or phase plate forms a refractive index medium with a shape that is considerably more flexible than that achieved in the case of conventional electrostatic and magnetic electron optics. The formulas presented herein can serve as guidelines for designing preferred light fields, thus promoting the advancement of a novel technology in electron optics that exploits the electron–light interaction.

Generation of even and odd harmonics in the XUV region with controlling the relative delay and polarization of two-color fields

Abstract We report high harmonic generation in the extreme ultraviolet (XUV) region by using two-color laser fields at the wavelengths of 800 nm and 400 nm. With a Ti: sapphire femtosecond laser at a 10 Hz repetition rate efficient high harmonic generation was obtained in an argon gas medium with the IR field (ω) and its second harmonic (2ω) with parallel and perpendicular polarizations. The relative delay between the pulses is controlled via a Michelson interferometer arrangement. In addition to the odd high harmonic spectrum with frequencies (2n+1)ω, where n - integer number, also even spectral components 2nω are obtained, when the fields of the two colors are temporally overlapped and interact with the argon gas. Due to this overlap, the yield of odd harmonics can be increased as well. The calculations of electron trajectories within the semi-classical approach show differences in the action of the fields with parallel and perpendicular polarizations. For the former, there exist broad time intervals for returning electrons, and in the latter case there are only narrow intervals for possible solutions for each of the electron returns to the parent ion for a fixed phase difference between the ω and 2ω fields. By varying the relative delay between the two laser fields it is possible to spectrally enrich and enhance the produced XUV radiation or suppress it. The conclusions of the semi-classical approach were confirmed by calculations of the harmonic intensities within the strong field dipole approximation.

ELMAG 3.01: A three-dimensional Monte Carlo simulation of electromagnetic cascades on the extragalactic background light and in magnetic fields

The version 3.01 of ELMAG, a Monte Carlo program for the simulation of electromagnetic cascades initiated by high-energy photons and electrons interacting with extragalactic background light (EBL), is presented. Pair production and inverse Compton scattering on EBL photons as well as synchrotron losses are implemented using weighted sampling of the cascade development. New features include, among others, the implementation of turbulent extragalactic magnetic fields and the calculation of three-dimensional electron and positron trajectories, solving the Lorentz force equation. As final result of the three-dimensional simulations, the program provides two-dimensional source images as function of the energy and the time delay of secondary cascade particles. Program summaryProgram Title:ELMAG 3.01Program Files doi:http://dx.doi.org/10.17632/gsr7dfnyx6.1Licensing provisions: CC by NC 3.0.Programming language: Fortran 90Supplementary material: See http://elmag.sourceforge.net/Nature of problem: Calculation of secondaries produced by electromagnetic cascades on the extragalactic background light (EBL), including deflections in magnetic fields.Solution method: Monte Carlo simulation of pair production and inverse Compton scattering on EBL photons; weighted sampling of the cascading secondaries; recording of energy, observation angle and time delay of secondary particles at the present epoch in a 1.5-dimensional approximation or of sky-maps in a three-dimensional approach.Restrictions: Using the three-dimensional approach, the energies of cascade photons should be above 1 GeV for Brms≲10−10 G.

Design and implementation of electron diverters for lobster eye space-based X-ray optics.

Micropore optics have recently been implemented in a lobster eye geometry as a compact X-ray telescope. Fields generated by rare-earth magnets are used to reduce the flux of energetic electrons incident upon the focal plane detector in such a setup. We present the design and implementation of the electron diverters for X-ray telescopes of two upcoming missions: the microchannel X-ray telescope onboard the space-based multiband astronomical variable objects monitor and the soft X-ray instrument onboard the solar wind magnetosphere ionosphere link explorer. Electron diverters must be configured to conform to stringent limits on their total magnetic dipole moment and be compensated for any net moment arising from manufacturing errors. The two missions have differing designs, which are presented and evaluated in terms of the fractions of electrons reaching the detector, as determined by relativistic calculations of electron trajectories. The differential flux of electrons to the detector is calculated, and the integrated electron background is determined for both designs.

Electron Motion in the Three-Dimensional Field of Undulator

In this paper we consider the motion of relativistic electrons in an ideal three-dimensional magnetic field of an undulator. The ideality of the magnetic field means that, on the undulator axis, the field is directed strictly vertically upward and has a strictly sinusoidal shape. In the overwhelming majority of cases, only this leading component of the field is taken into account in calculating the electron trajectory. In this paper, in the equations of motion of an electron in the magnetic field of an undulator, all three components of the field are taken into account, so that the undulator field under consideration satisfies the stationary Maxwell equations. In this case, the differential equations of motion of the electron are solved analytically with the help of perturbation theory, and not by the method of averaging over fast oscillations of the electron, as was done in a number of previous papers. These analytic expressions for trajectories describe the behavior of particles in the focusing magnetic field of an undulator much more completely. An analysis of these expressions shows that the behavior of electrons in such a three-dimensional field of the undulator is much more complicated than what follows from the equations obtained by the averaging method. In particular, there is a cross effect when changes in the initial vertical parameters of the electron trajectory cause changes in the horizontal component of its trajectory and vice versa. A comparison of the solutions obtained analytically with the results of numerical calculations of electron trajectories using the Runge–Kutta method demonstrates their high accuracy.

Theoretical and numerical analysis of electron motion in a three-dimensional undulator field

The results of numerical calculations of electron trajectories in the three-dimensional ideal magnetic field of an undulator are given. These trajectories can be regarded as exact results in our case. It is shown that, in a series of cases, results of the calculation of trajectories using approximate analytical formulas significantly differ from those obtained using numerical methods. The obtained numerical results show that the influence of the undulator on the dynamics of the electron beam is very complicated and cannot be reduced only to the focusing properties of the undulator magnetic field or wiggler.

Contribution of multiple electron rescatterings on high-order harmonic generation in the mid-infrared wavelength regime

We theoretically investigate multiple electron rescatterings in high-order harmonic generation with a wide range of driving laser wavelengths. In order to obtain a clear and intuitive insight, the time-frequency analysis of the dipole acceleration calculated by the numerical solution of the time-dependent Schrodinger equation is performed and compared with the classical electron trajectory calculation. The result shows that in the mid-infrared regime, the high-order electron trajectory associated with multiple rescatterings plays a more important role than the usually referred-to “long and “short” electron trajectories. To provide quantitative evidence, the strong-field approximation is used to calculate the yield ratio of the high-order harmonic generation from the first rescattering and the multiple rescatterings.

Voltage optimization of a 4-element injection lens on a hemispherical spectrograph with virtual entry aperture

We present simulation results for a biased paracentric hemispherical deflector analyzer equipped with a 4-element input lens and a position sensitive detector used in our zero-degree Auger projectile spectroscopy apparatus. Calculations of electron trajectories traversing the lens and analyzer fields were performed and cross checked using both boundary-element and finite-difference methods. The two middle lens electrode voltages were varied as free parameters, while various criteria were used to select their optimal values in an effort to obtain improved energy resolution.

Detection of electron energy distribution function anisotropy in a magnetized electron cyclotron resonance plasma by using a directional Langmuir probe

Anisotropy in the electron energy distribution function (EEDF) in an electron cyclotron resonance plasma with magnetized electrons and weakly magnetized ions is experimentally investigated using a directional Langmuir probe. Under an assumption of independent EEDFs in the directions parallel and perpendicular to the magnetic field, the directional variation of the EEDF is evaluated. In the measured EEDFs, a significantly large population density of electrons with energies larger than 30 eV is found in one of the cross-field directions depending on the magnetic field direction. With the aid of an electron trajectory calculation, it is suggested that the observed anisotropic electrons originate from the EEDF anisotropy and the cross-field electron drift.

Improvement of uniformity of the negative ion beams by tent-shaped magnetic field in the JT-60 negative ion source

Non-uniformity of the negative ion beams in the JT-60 negative ion source with the world-largest ion extraction area was improved by modifying the magnetic filter in the source from the plasma grid (PG) filter to a tent-shaped filter. The magnetic design via electron trajectory calculation showed that the tent-shaped filter was expected to suppress the localization of the primary electrons emitted from the filaments and created uniform plasma with positive ions and atoms of the parent particles for the negative ions. By modifying the magnetic filter to the tent-shaped filter, the uniformity defined as the deviation from the averaged beam intensity was reduced from 14% of the PG filter to ∼10% without a reduction of the negative ion production.

Attostreaking with metallic nano-objects

The application of atto-second streaking spectroscopy (ASS) to direct time-domain studies of the plasmonic excitations in metallic nano-objects is addressed theoretically. The streaking spectrograms for a rectangular gold nano-antenna and spherical gold clusters are obtained within strong field approximation using classical electron trajectory calculations. The results reported here for spherical clusters are also representative of spherical nano-shells. This study demonstrates that ASS allows for detailed characterization of plasmonic modes, including near-field enhancement, frequency and decay rate. The role of the inhomogeneity of the induced electric fields is also demonstrated.

Image instability during the electrical measurement in scanning electron microscope

AbstractDuring electrical measurements in a scanning electron microscope (SEM), secondary electron (SE) images often become dark or the image contrast becomes weaker. We have revealed that this phenomenon originates in the negative charging of the insulating part in an electric circuit. This charging can be caused by stray electrons, even if the insulator is not directly irradiated. The electrostatic field owing to this charge deflects SEs and reduces the intensity of detected electrons. We have demonstrated this effect by observing systematic shifts of the field of view of SE detector, which appears in SE images. This explanation is supported by a calculation of electron trajectories in the electrostatic field in the SEM chamber. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Single particle simulations of electron transport in the near-field of Hall thrusters

The results of 3D, single particle electron trajectory calculations are presented for the near-field of a laboratory E × B Hall plasma thruster. For a prescribed static magnetic and electric field distribution, single electrons are launched and tracked from a simulated cathode. Collisions with external thruster surfaces are accounted for; however, field fluctuations are disregarded. Bulk statistics including the channel to beam electron current ratio, electron lifetimes and spatial distributions of the number density, mean energy, energy distributions, velocity distributions and velocity component ratios are catalogued. For conditions typical of a moderate power Hall thruster, the mean lifetime of electrons in the domain of axial scale length, L = 0.3 m, is approximately 120 ns. Electrons which eventually enter the channel are found to strike the thruster ∼103 times as frequently as electrons which exit the domain in the plume. For the static E and B field distributions used in this study, the channel to beam current ratio is found to be on the order of 0.1 and the velocity ratio, VE/VE×B, over the channel has a mean of ∼0.5, with higher values driven largely by collisions with the thruster indicating the importance of such events in driving transport into the channel.

Effects of Elliptical Polarization on Strong-Field Short-Pulse Double Ionization

We predict new end-of-pulse behavior in high-field atomic double ionization. Calculations of atomic electron trajectories in short intense laser pulses confirm our analysis of elliptical polarization. We exhibit a four-band structure in ion momentum distributions under various ellipticities, and predict that sequential and nonsequential double ionization can be cleanly distinguished under elliptical polarization.

Numerical simulation of a trochoidal electron monochromator

The trochoidal electron monochromator (TEM) has been investigated in numerical simulation using the SIMION 8.0 package. Electron trajectory calculations have been carried out for a large number of initial electrons. The electron energy distribution functions (EEDFs) of the TEM have been obtained from the simulations as functions of various monochromator parameters (magnetic field, electric field, geometry, acceleration potential). The influence of the parameters on the performance of the TEM has been discussed. Simulations have been compared with experimental results.

Monte Carlo electron-trajectory simulations in bright-field and dark-field STEM: Implications for tomography of thick biological sections

A Monte Carlo electron-trajectory calculation has been implemented to assess the optimal detector configuration for scanning transmission electron microscopy (STEM) tomography of thick biological sections. By modeling specimens containing 2 and 3 at% osmium in a carbon matrix, it was found that for 1-μm-thick samples the bright-field (BF) and annular dark-field (ADF) signals give similar contrast and signal-to-noise ratio provided the ADF inner angle and BF outer angle are chosen optimally. Spatial resolution in STEM imaging of thick sections is compromised by multiple elastic scattering which results in a spread of scattering angles and thus a spread in lateral distances of the electrons leaving the bottom surface. However, the simulations reveal that a large fraction of these multiply scattered electrons are excluded from the BF detector, which results in higher spatial resolution in BF than in high-angle ADF images for objects situated towards the bottom of the sample. The calculations imply that STEM electron tomography of thick sections should be performed using a BF rather than an ADF detector. This advantage was verified by recording simultaneous BF and high-angle ADF STEM tomographic tilt series from a stained 600-nm-thick section of C. elegans. It was found that loss of spatial resolution occurred markedly at the bottom surface of the specimen in the ADF STEM but significantly less in the BF STEM tomographic reconstruction. Our results indicate that it might be feasible to use BF STEM tomography to determine the 3D structure of whole eukaryotic microorganisms prepared by freeze-substitution, embedding, and sectioning.

Kinetics of ultrashort relativistic electron pulses emitted from solid targets

Interaction of ultrashort high-intensity laser pulses with solid targets generates relativistic electrons which escape from the target. The kinetics of these ultrashort electron pulses is governed by self-fields generated by the charge of the electron cloud. In this paper an analytical theory is developed which allows calculation of electron trajectories, electron fluxes, and electron spectra at any distance from the target. The theory is exact for two limiting cases: (a) a monoenergetic electron pulse with an arbitrary temporal shape; (b) an infinitely short electron pulse with an arbitrary energy spectrum. These results have applications in high-intensity irradiation experiments, e.g., in experiments irradiating samples with ultrashort electron or x-ray pulses, in developing optics for fourth-generation light sources, and in work relating to x-ray lasers.

A novel spectrometer for spin-polarized electron energy-loss spectroscopy

By making use of advanced methods for the calculation of electron trajectories in the presence of space charge fields we have designed and built a novel electron energy-loss spectrometer for the purpose of measuring spin flip excitations at surfaces. The measurement of the spin asymmetry requires a deflection angle between the photocathode and the sample position which amounts to 90° in total. That deflection angle is not provided by standard electron deflectors, or by a combination of those. We show that a 90° deflection angle can be realized by a combination of two novel deflectors with 90° and 180° deflection angles each. The performance of the new spectrometer matches the performance of the best electron spectrometers developed for surface vibration spectroscopy.

Modeling of life deterioration by ion bombardment of a dispenser cathode coated with an Ir/W film

We have developed the calculation method for ion bombardment traces. When an M type dispenser cathode is operated in a cathode ray tube (CRT), the surface coating film is subjected to ion bombardment due to ionized residual gas. With long-time use, the coating film is dissipated and a change to an S type occurs. This occurrence of an S type causes a deterioration of emission and focus characteristics. A method for calculating the life time dependency of the shape of ion bombardment traces using the degree of vacuum in the tube, the grid voltage, and the cathode current was studied. The calculated results and measured results were in close agreement. As a result, it was confirmed that modeling is possible using (1) an electron and ion beam trajectory calculation program, and (2) formulas for calculating the ionization cross-section and sputtering yield.

Extraction of scattered low-energy electrons in field emission conditions

Recently we demonstrated a prototype instrument that employs a new technique for determining surface structures. The instrument consists of a scanning tunneling microscope tip as a field emission gun and a detector for projecting electron scattering patterns. Previous results showed a low efficiency in detecting scattered electrons, because the potential between the tip and the sample drew the electrons back toward the sample. To improve the efficiency, we attempted detection using a tip-shield that can extract the scattered electrons toward a vacuum region effectively. Our results confirmed that the tip-shield improves detection efficiency. Consequently, we observed an extra beam that might be scattered toward the surface-parallel direction. The results of our electron trajectory calculations agreed qualitatively with the experimental data. We have tentatively designated the two spots we obtained as (0 0) and (1 0) diffraction beams of the graphite surface.