Electron Velocity Vector Research Articles

Trajectories and radiation of charged particles in the pulsar magnetosphere

ABSTRACT Trajectories and radiation of the accelerating electrons are studied in the pulsar magnetosphere approximated as the electromagnetic field of the Deutsch’s solutions. Because the electrons are accelerated rapidly to ultra-relativistic velocity near the neutron star surface, the electron velocity vector (and then its trajectory) is derived from the balance between Lorentz force and radiation reaction force, which makes the pitch angle between electron trajectories and magnetic field lines non-zero in most part of the magnetosphere. In such a case, the spectral energy distributions (SEDs) of synchro-curvature radiation for the accelerating electrons with a mono-energetic form are calculated. Our results indicate that: (i) the pitch angle is the function of electron position (r, θ, ϕ) in the open field line regions, and increases with increasing r and θ as well as increasing the inclination angle; (ii) the radius of curvature becomes large along the particle trajectory, and (iii) the SED appears a double peak structure depending on the emission position, where the synchrotron radiation plays an important role in X-ray band and curvature radiation mainly works in GeV band, which is only determined by parameters α and ζ.

Coherent X-Ray Radiation Generated Near the Axis of the Beam of Relativistic Electrons in an Artificial Periodic Structure

A theory of the coherent X-ray radiation produced by a beam of relativistic electrons in an artificial periodic structure and propagating along the electron-beam axis is developed. Expressions describing the spectral-angular densities of parametric X-ray radiation in the direction close to the electron velocity vector (FPXR) and of transition radiation (TR) and their interference are obtained in the Bragg scattering geometry. An analysis based on the obtained expressions for the spectral-angular density shows possibilities of their use to determine the optimal parameters of the experiment recording the FPXR. The advantages of the experiment recording the FPXR at low electron energies ( $${{E}_{e}} \leqslant $$ 50 MeV) are shown.

Derivation of the electron drift velocity vector in gas under crossed ac electric and dc magnetic fields assuming constant-collision-frequency models

The periodic variation of the average electron velocity vector under crossed ac electric and dc magnetic fields is formulated analytically on the basis of kinetic equations for single-electron motion assuming constant-collision-frequency models with and without ionization. The velocity vector draws elliptic loci with the alternation of the electric field, and this is verified by Monte Carlo simulations. The amplitude and the mean deflection angle of the velocity vector, which represent basic features of electron transport in magnetized plasmas, are explicitly described with the collision frequency, the ac angular frequency, and the intensities of the fields.

Configuration of propagator method for calculation of electron velocity distribution function in gas under crossed electric and magnetic fields

This paper presents a self-contained description on the configuration of propagator method (PM) to calculate the electron velocity distribution function (EVDF) of electron swarms in gases under DC electric and magnetic fields crossed at a right angle. Velocity space is divided into cells with respect to three polar coordinates v, θ and ϕ. The number of electrons in each cell is stored in three-dimensional arrays. The changes of electron velocity due to acceleration by the electric and magnetic fields and scattering by gas molecules are treated as intercellular electron transfers on the basis of the Boltzmann equation and are represented using operators called the propagators or Green’s functions. The collision propagator, assuming isotropic scattering, is basically unchanged from conventional PMs performed under electric fields without magnetic fields. On the other hand, the acceleration propagator is customized for rotational acceleration under the action of the Lorentz force. The acceleration propagator specific to the present cell configuration is analytically derived. The mean electron energy and average electron velocity vector in a model gas and SF6 were derived from the EVDF as a demonstration of the PM under the Hall deflection and they were in a fine agreement with those obtained by Monte Carlo simulations. A strategy for fast relaxation is discussed, and extension of the PM for the EVDF under AC electric and DC/AC magnetic fields is outlined as well.

Electrons acceleration in a TE113 cylindrical cavity affected by a static inhomogeneous magnetic field

The relativistic dynamics of an electron accelerated in a cylindrical cavity mode TE113 in the presence of a static inhomogeneous magnetic field is studied. This type of acceleration is known as Spatial AutoResonance Acceleration (SARA). The magnetic field profile is such that it keeps the phase difference between the electric microwave field and the electron velocity vector within the acceleration phase band. We study the dynamic of the electron through simulations of the relativistic Newton-Lorentz equation. Numerical experiments with TE113 cylindrical microwave fields of a frequency of 2.45GHz and an amplitude of the order of 7kV/cm show that it is possible accelerate the electrons up to energies of the order of 300keV. This energy is about of 30% higher than those obtained in previous studies by using the TE112 mode.

The effect of the mechanism of electron surface scattering on high-frequency conductivity of a thin metal film

The problem of high-frequency conductivity of a thin cylindrical metal film is solved using the kinetic method. The kinetic boundary conditions taking into account the dependence of the reflectivity coefficient on the angle of incidence θ between the electron velocity vector and a normal to the metal surface are used. The obtained results are compared with the theoretical calculations for the Fuchs diffusion-reflection boundary conditions.

Modeling of electron cyclotron resonance acceleration in a stationary inhomogeneous magnetic field

In this paper, the cyclotron autoresonance acceleration of electrons in a stationary inhomogeneous magnetic field is studied. The trajectory and energy of electrons are found through a numerical solution of the relativistic Newton-Lorentz equation by a finite difference method. The electrons move along a ${\mathrm{TE}}_{112}$ cylinder cavity in a steady-state magnetic field whose axis coincides with the cavity axis. The magnetic field profile is such that it keeps the phase difference between the electric microwave field and the electron velocity vector within the acceleration phase band. The microwaves amplitude of $6\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$ is used for numerical calculations. It is shown that an electron with an initial longitudinal energy of 8 keV can be accelerated up to 260 keV by 2.45 GHz microwaves at a distance of 17 cm.

On the possibility of using parametric X-ray radiation to study anisotropy of a crystal mosaic structure

Parametric X-ray radiation (PXR) of relativistic electrons moving in a mosaic crystal is considered. A strong dependence of the PXR angular spectral distribution on the mosaic structure is shown. The effect of mosaic structure on the PXR spectrum strongly increases in the longitudinal plane specified by the radiating electron velocity vector and the averaged reciprocal lattice vector and decreases in the transverse plane with a decrease in the angle of incidence of the radiating electron onto a crystal plane, which allows one to study the anisotropy of mosaic structure of crystal planes.

Tethys and Dione as sources of outward-flowing plasma in Saturn’s magnetosphere

Rotating at over twice the angular speed of Earth, Saturn imposes a rapid spin on its magnetosphere. As a result, cold, dense plasma is believed to be flung outward from the inner magnetosphere by centrifugal force and replaced by hotter, more tenuous plasma from the outer magnetosphere. The centrifugal interchange of plasmas in rotating magnetospheres was predicted many years ago and was conclusively demonstrated by observations in Jupiter's magnetosphere, which--like that of Saturn (but unlike that of Earth)--is rotationally dominated. Recent observations in Saturn's magnetosphere have revealed narrow injections of hot, tenuous plasma believed to be the inward-moving portion of the centrifugal interchange cycle. Here we report observations of the distribution of the angle between the electron velocity vector and the magnetic field vector ('pitch angle') obtained in the cold, dense plasma adjacent to these inward injection regions. The observed pitch-angle distributions are indicative of outward plasma flow and consistent with centrifugal interchange in Saturn's magnetosphere. Further, we conclude that the observed double-peaked ('butterfly') pitch-angle distributions result from the transport of plasma from regions near the orbits of Dione and Tethys, supporting the idea of distinct plasma tori associated with these moons.

Dissociative photoionization of N(2)O in the region of the N(2)O(+)(B (2)Pi) state studied by ion-electron velocity vector correlation.

Dissociative direct photoionization of the N2O(X 1Sigma+) linear molecule via the N2O+(B 2Pi) ionic state induced by linearly polarized synchrotron radiation P in the 18-22 eV photon energy range is investigated using the (VA+,Ve,P) vector correlation method, where VA+ is the nascent velocity vector of the NO+, N2+, or O+ ionic fragment and Ve that of the photoelectron. The DPI processes are identified by the ion-electron kinetic energy correlation, and the IchiA+(thetae,phie) molecular frame photoelectron angular distributions (MFPADs) are reported for the dominant reaction leading to NO+ (X 1Sigma+,v) + N(2D)+ e. The measured MFPADs are found in satisfactory agreement with the reported multichannel Schwinger configuration interaction calculations, when bending of the N2O+(B 2Pi) molecular ion prior to dissociation is taken into account. A significant evolution of the electron scattering anisotropies is observed, in particular in the azimuthal dependence of the MFPADs, characteristic of a photoionization transition between a neutral state of Sigma symmetry and an ionic state of Pi symmetry. This interpretation is supported by a simple model describing the photoionization transition by the coherent superposition of two ssigma and ddelta partial waves and the associated Coulomb phases.

Dissociative photoionization of N2O in the region of the N2O+(C 2Σ+) state, studied by ion–electron velocity vector correlation

Imaging and time-of-flight-resolved coincidence techniques are combined to extend the (VA+,Ve,P) vector correlation method to the study of dissociative photoionization of small polyatomic molecules breaking into two heavy fragments. Dissociative photoionization (DPI) of the N2O linear molecule into the N2O+(C 2Σ+) ionic state, induced by linearly polarized synchrotron radiation (P), is chosen as an example. The ion–electron kinetic energy correlation enables the identification of all the DPI processes producing the NO+, N+, N2+, and O+ fragments. The IχA+(θe,φe) molecular frame photoelectron angular distributions (MFPADs), deduced from the spatial analysis of the (VNO+/N+,Ve,P) vector correlations, exhibit remarkable features. When the N2O molecule is aligned parallel to the polarization axis, a preferred electron emission from the N2O+ molecular ion in the direction perpendicular to the molecular axis, as well as a strong forward–backward asymmetry that favors electron emission along the molecular axis in the same direction as the N+ or N fragment, are demonstrated. The measured MFPADs are found in good agreement with the reported multichannel Schwinger configuration interaction calculations, when molecular rotation prior to dissociation is taken into account. This comparison provides an estimation of the lifetime of the N2O+(C 2Σ+) state prior to dissociation into the dominant channels [NO+(X 1Σ+)+N(2P)] and [N+(3P)+NO(X 2Π)], which is found to be about 2 ps.

Vector correlations in dissociative photoionization of O2 in the 20–28 eV range. II. Polar and azimuthal dependence of the molecular frame photoelectron angular distribution

A combined experimental and theoretical study of the polar and azimuthal dependence of the molecular frame photoelectron angular distributions (MFPADs) for inner-valence-shell photoionization of the O2 molecule into the O2+(B 2Σg−,3 2Πu,c 4Σu−) states is reported. The measured MFPADs, for each orientation of the molecular axis with respect to the linear polarization of the synchrotron radiation, are derived from the spatial analysis of the (VO+,Ve,P) vector correlation, where the nascent ion and electron velocity vectors VO+ and Ve are determined for each dissociative photoionization (DPI) event using imaging and time of flight resolved coincidence technique as described in the companion paper of this series [J. Chem. Phys. 114, 6605 (2001)]. Expressed in the general form of four FLN(θe) functions which contain all the dynamical information about the photoionization processes, they are compared with the MFPADs computed using the multichannel Schwinger configuration interaction method. A very satisfactory agreement is found. When the lifetime of the O2+ ionic states is a significant fraction of the rotational period, the rotational motion of the molecule is included in the quantal derivation of the MFPADs. Measured MFPADs are also reported for the additional DPI process identified in Paper I, and for DPI involving the excitation of the neutral (3 2Πu,4sσg) Rydberg state.

Ion–electron velocity vector correlations in dissociative photoionization of simple molecules using electrostatic lenses

A new development of electrostatic lenses for ion and/or electron trajectory focusing has been implemented in a double velocity spectrometer which combines time of flight resolved coincidence and imaging techniques using fast position sensitive detectors. Ions and electrons produced by photoionization are extracted from the interaction region by a unique uniform electrostatic field, while the electrostatic lenses create a nonuniform field outside the extraction region. The space focusing reducing the effect of the finite dimensions of the interaction region on one side, and the global bending of the ion and/or electron trajectories preserving the time of flight information on the other side, enable a significant improvement of the resolution of the three measured velocity components for each particle. Such a device is particularly well adapted for the study of vector correlations in dissociative photoionization of simple molecules in the vacuum ultraviolet photon energy range. The gain achieved in the energy resolution of the processes by ion–electron kinetic energy correlation, as well as in the polar and azimuthal angle resolution in the I(θe,φe) molecular frame photoelectron angular distributions, is illustrated on the example of dissociative photoionization of the NO molecule.

High‐voltage electron collection by a spherical satellite

The numerical solution to the cold electron flow equations is presented for the region surrounding an ionospheric satellite at high positive potential. The momentum, continuity, and Poisson equations are solved simultaneously for satellite potentials of 1000, 10,000, 30,000, and 100,000 kT (kT = 0.17 eV). The electron velocity vectors in the sheath region are presented. The electron current density to the satellite surface is also reported. Electrons impact the satellite surface with average velocity vectors having angles of incidence (relative to the surface normal) that increase from the satellite's magnetic pole to equator. A toroidal flow develops in the vicinity of the magnetic equator and expands away from the satellite surface as the surface potential is increased. The current density to the satellite surface increases with increasing satellite potential and decreases with increasing polar angle.

Generation of a given linear polarized radiation in a plane undulator

The distribution of the undulator magnetic field providing generation of monochromatic radiation with a relatively large angle between the electron velocity vector and the undulator axis is found. The possible trajectories of the particle motion are investigated.

Optical properties of bipolar flare kernels associated with asymmetric magnetic loops

Observations are presented for nine flares containing two principal patches of emission, or kernels, in which the kernel associated with weaker magnetic field has the greater Hα line width. The observations are interpreted in terms of an asymmetric bipolar magnetic loop from which high energy electrons precipitate predominantly at the loop footpoint of weaker field. Calculations are presented which indicate that, for an isotropic distribution of electron velocity vectors at their initial point of injection, the observations are consistent with a location for the injection in the upper part of the loop. The same type of model predicts the associated microwave burst to be stronger near the opposite (strong field) footpoint (Kundu and Vlahos, 1979).

Line Shapes and Intensities for Disk Sources Used in an Homogeneous Magnetic Field Beta-Ray Spectrometer with New and Conventional Slit Geometries

This paper is primarily concerned with the effect on the line profile shape and intensity of the angle φ, the angle made by the projection of the electron velocity vector on a plane perpendicular to the instrument axis at the source with the radius of the source point. Quantitative results are quoted for several geometries. The line profile, expected intensity, and optimum source size for a commonly used slit geometry utilizing an entrance slit for take-off angle selection is found to differ significantly from previously quoted results, the intensity for the same half-width for optimum source size being 46% of the earlier work. A new slit geometry consisting of an additional baffle near the source which restricts φ is discussed and is found to improve the expected intensity for the same line half-width by 24% for an optimized Hubert slit system which is already found in this paper to be 28% better than the best of previous slit geometries. Finally, a geometry which selects φ properly is shown to remove all dependence on source size from the resolution.

Die Laufzeit, Elektronenbahnen, Kathodenfeldstärke und Potential der Raumladungsdiode für jede Anfangsgeschwindigkeit, Anfangsrichtung und Strom

The basic equations of the space charge field yield for thex-component of the electron velocity-vector in a planar diode a non-linear differential equation of the third degree and third order. This differential equation and its solution can be used to calculate—without the integration of the Poisson equation—the transit times of electrons, the cathode field, the potential and the electron paths as a function of two reduced parameters alone for all values of the initial velocity and current under partial and complete space charge. The generality of the solution is discussed and other applications of the new method used are stated.