Transverse Electron Velocities Research Articles

Terahertz to near infrared radiation generation using two-colour counter and co-polarized laser pulses propagating in homogeneous plasma

This study deals with the generation of terahertz (THz) to near infrared (NIR) radiation fields using two-colour linearly polarized copropagating laser pulses having either counter or co-polarization state. The frequency difference between the two laser pulses is considered to be integral multiple of the plasma frequency. Perturbation technique and quasistatic approximation have been used to obtain radiation field equations. Analytical and two-dimensional particle in cell simulation studies of the proposed configuration show that the transverse and axial plasma electron velocities arising due to nonlinear coupling of the two pulses are responsible for generation of off-axis linearly polarized radiation fields which propagate through plasma into vacuum. The frequency of generated radiation is ∼40 THz (∼60 THz), when the frequency difference of the laser pulses is two (three) times the plasma frequency. Analytical results are validated using VSim particle in cell simulation code.

E and B modes of the CMB y-type distortions: polarised kinetic Sunyaev-Zeldovich effect from the reionisation and post-reionisation eras

We study the E and B mode polarisation of the cosmic microwave background (CMB) originating from the transverse peculiar velocity of free electrons, at second order in perturbation theory, during the reionisation and post-reionisation eras. Interestingly, the spectrum of this polarised kinetic Sunyaev-Zeldovich (SZ) effect can be decomposed into a blackbody part and a y-type distortion. The y-distortion part is distinguishable from the primary E and B modes and also the lensing B modes. Furthermore, it is also differentiable from the other y-type signals, such as the thermal SZ effect, which are unpolarised. We show that this signal is sensitive to the reionisation history, in particular to how fast reionisation happens. The E and B modes of y-type distortion provide a way to beat the cosmic variance of primary CMB anisotropies and are an independent probe of the cosmological parameters. The blackbody component of the pkSZ effect would be an important foreground for the primordial tensor modes for tensor to scalar ratio r ≲ 3 × 10-5.

Generation of terahertz radiation by short laser pulses propagating in obliquely magnetized plasma

This paper presents an analytical and simulation study of terahertz (THz) radiation generation using short, circularly polarized laser pulses propagating in plasma embedded in arbitrarily oriented magnetic field. Perturbation technique is used to obtain generated electric and magnetic wakefields within and behind the laser pulse. Coupling of components of the obliquely applied magnetic field with transverse and axial plasma electron velocities leads to the generation of linearly as well as elliptically polarized transverse electromagnetic radiation oscillating at THz frequency, under appropriate conditions. The amplitude of these fields and ellipticity of the elliptically polarized THz radiation can be varied with the help of the obliqueness of the external magnetic field. Analytical results are validated using VSim PIC simulation code.

Thermionic emission laws for general electron dispersion relations and band structure data

In this article, a thermionic electron emission theory for general electron dispersion relations E(k) is presented, relating electron energy E to wave-vector magnitude k = |k|. This theory does not require the construction of a model Hamiltonian for the electrode's materials, like Dirac or Weyl Hamiltonians. Instead, use is made of the material's band structure data, e.g., the parabolic E(k) approximation for the Richardson–Dushman equation and linear E(k), as used for graphene and 3D Dirac semimetals. This new theory confirms previous findings on parabolic E(k), e.g., that the emission current is independent of effective electron mass in the material as long as it is larger than real electron mass m0. For effective mass lower than m0, the emission is reduced and tends to zero for vanishing effective mass. For materials with negative electron affinity, additional terms arise in the emission current equation. It turns out that the linear E(k) dispersion, e.g., for Dirac semimetals, does not have the potential to surpass the Richardson emission in materials with the same work function. In addition, a more rigorous electron emission theory is established by utilizing real anisotropic band structure data En(k) for electrode materials. For collimated electron emission normal to the surface, the transverse electron velocities tend to zero, i.e., the transverse derivatives of En(k) have to be comparatively small. If stable electrode materials of this kind can be realized, a considerable increase of electron emission by a factor 100 or more can be achieved, compared to the Richardson–Dushman theory, especially for small lattice constants perpendicular to the emission direction.

Electron-optical system for a high-current Ka-band relativistic gyrotron

An electron-optical system for a high-current relativistic Ka-band gyrotron was developed and experimentally tested. The system consists of a coaxial magnetically insulated diode forming a rectilinear hollow beam and an additional short coil (kicker) pumping the transverse electron velocities. An electron beam with a particle energy of 500 keV, a current of 1.5–2 kA, and a pitch-ratio of up to 1 has been produced. The beam is intended for a gyrotron with the output power of 200 MW. The measured beam characteristics are in good agreement with the results of calculations. The influence of the beam and gyrotron cavity axis misalignment on gyrotron operation is analyzed using PIC simulations.

Gyrotron generation of broadband chaotic radiation under overlapping of high- and low-frequency resonances

Significant (up to 10%) broadening of the band of noise-like radiation in gyrotrons is possible due to specific tuning of gyrofrequency relative to the critical frequency of the working mode when the high- and low-frequency cyclotron resonances are substantially separated at the given translation and transverse velocities of electrons. The generation bands at the resonances are overlapped under operation above the threshold. The analysis with allowance for finiteness of the electron transit time in the interaction space and, hence, different slopes of the dispersion characteristics of electron beam and wave is critically important for correct investigation of the generation regimes in the framework of the average approach. The results are verified using direct 3D particle-in-cell simulation of the chaotic generation regimes of the gyrotron generation in the 8-mm-wavelength range.

Measurement of the drift velocity and transverse diffusion of electrons in liquid xenon with the EXO-200 detector

The EXO-200 Collaboration is searching for neutrinoless double beta decay using a liquid xenon (LXe) time projection chamber. This measurement relies on modeling the transport of charge deposits produced by interactions in the LXe to allow discrimination between signal and background events. Here we present measurements of the transverse diffusion constant and drift velocity of electrons at drift fields between 20~V/cm and 615~V/cm using EXO-200 data. At the operating field of 380~V/cm EXO-200 measures a drift velocity of 1.705$_{-0.010}^{+0.014}$~mm/$\mu$s and a transverse diffusion coefficient of 55$\pm$4~cm$^2$/s.

Numerical simulation of a triode source of intense radial converging electron beam

The results of numerical simulations of a triode source of an intense radial converging electron beam are presented. The role of the initial transverse velocity of electrons, defocusing effect of the controlling grid, the beam self-magnetic field, backscattering of electrons, and ion flow from the target is analyzed. It was found that the ion flow from the target essentially increases the value of the electron current. The influence of the beam self-magnetic field on electron trajectories leads to the fact that there is a critical value of the cathode-grid voltage dividing the mode of the source operation into stable and unstable. The influence of initial transverse electron energies on the beam focusing is essentially higher than the influence of the controlling grid. Backscattering of the beam electrons from the target surface increases the target ion current so that the source operation may become unstable and the distribution of the beam power density on the target becomes nonuniform with a maximum in the center. Electrons passing by the target drift along the source axis. This leads to diminishing the power density at the center of the target and to the exit of peripheral electrons from the source. Conditions for achieving required electron beam parameters (the electron kinetic energy—120 keV, the beam energy density on the target ∼40 J/cm2 on a maximum possible length of the target surface) were determined.

Beyond the ponderomotive limit: Direct laser acceleration of relativistic electrons in sub-critical plasmas

We examine a regime in which a linearly polarized laser pulse with relativistic intensity irradiates a sub-critical plasma for much longer than the characteristic electron response time. A steady-state channel is formed in the plasma in this case with quasi-static transverse and longitudinal electric fields. These relatively weak fields significantly alter the electron dynamics. The longitudinal electric field reduces the longitudinal dephasing between the electron and the wave, leading to an enhancement of the electron energy gain from the pulse. The energy gain in this regime is ultimately limited by the superluminosity of the wave fronts induced by the plasma in the channel. The transverse electric field alters the oscillations of the transverse electron velocity, allowing it to remain anti-parallel to laser electric field and leading to a significant energy gain. The energy enhancement is accompanied by the development of significant oscillations perpendicular to the plane of the driven motion, making trajectories of energetic electrons three-dimensional. Proper electron injection into the laser beam can further boost the electron energy gain.

Dynamics of transverse electron velocities in the process of generation in multiwave Cherenkov devices

The dynamics of transverse velocities of electrons of a relativistic beam in a multiwave Cherenkov generator are studied in a computational experiment. It is demonstrated that the average transverse velocity of particles is increased considerably when the output radiation power is raised.

Analytical model of an isolated single-atom electron source.

An analytical model of a single-atom electron source is presented, where electrons are created by near-threshold photoionization of an isolated atom. The model considers the classical dynamics of the electron just after the photon absorption, i.e. its motion in the potential of a singly charged ion and a uniform electric field used for acceleration. From closed expressions for the asymptotic transverse electron velocities and trajectories, the effective source temperature and the virtual source size can be calculated. The influence of the acceleration field strength and the ionization laser energy on these properties has been studied. With this model, a single-atom electron source with the optimum electron beam properties can be designed. Furthermore, we show that the model is also applicable to ionization of rubidium atoms, and thus also describes the ultracold electron source, which is based on photoionization of laser-cooled alkali atoms.

Electron beam in the presence of a periodic magnetic field with allowance for the thermal velocities of electrons

Equations are derived to study the effect of the initial transverse thermal velocities of electrons on the configuration of an intense electron beam in an electron-optical system with a significant divergence for the case of the beam focusing by a periodic magnetic field. It is demonstrated that the minimization of the effect of thermal velocities of electrons in the electron-optical system with the given level of the periodic focusing field and the cathode radius and temperature and the limiting compression of the beam in the presence of such a field is reached with the shaping systems in which an optimal magnetic flux passes through the cathode and the flux depends on the parameters of the thermal beam and the focusing field.

Optimization of the Cavity Length of the Gyrotrons Operated at the Second Gyrofrequency Harmonic with One-stage Recovery of the Residual Energy of an Electron Beam

We find an optimal cavity length for gyrotrons operated at the second gyrofrequency harmonic with energy recovery for a 20% spread of transverse electron velocities, which is typical of such devices. It is shown that the efficiency-optimal length of the gyrotron cavity increases if the scheme of residual-energy recovery is used.

Spectrum of velocities and dynamics of electron beams in divergent magnetic fields

The dynamics of an electron beam in divergent magnetic fields has been studied. The changes in the longitudinal and transverse electron velocities in the beam and the effect of the magnetic field parameters on the dispersion of longitudinal electron velocities have been analyzed. A possibility of high-efficiency conversion modes in divergent magnetic fields has been established by methods of numerical simulation.

Measurements of the transverse electron velocities in high-current microsecond relativistic electron beams in a strong magnetic field

An analyzer is created for time-resolved measurements of the electron pitch-angles in high-current microsecond relativistic electron beams in a strong magnetic field. The electron pitch-angles in a 500-keV relativistic electron beam with a current density of ∼1 kA/cm2 and a 1-µs flat-top current profile are measured. The diode proposed previously by the authors allows one to produce a high-current electron beam in which pitchangles vary only slightly with time and over the beam cross section.

Harnessing of the Axial Kinetic Electron Energy of a Large-Orbit Gyrotron by an Assistant Azimuthal Background Magnetic Field

A new method of providing a background magnetic field was proposed for a large-orbit gyrotron in a coaxial waveguide for an improvement in the device performance with respect to the gain and efficiency. The method, which consists in providing an assistant azimuthal magnetic field, over and above the conventional DC axial background field, was studied, using a kinetic theory. The method was compared with an earlier method of providing a DC radial background electrical field. The adjustment of the background fields and that of the DC kinetic energy distribution between the axial and transverse electron velocities of the beam provided a simultaneous increase in the gain and efficiency of the device. This may be attributed to the axial beam kinetic energy being harnessed by the method.

Small-angle approximation in the description of radiative collective effects within an ultrarelativistic electron bunch.

The problem of the evaluation of radiative collective effects accompanying accelerated motion of a short ultrarelativistic electron bunch in vacuum is considered within the framework of the small-angle approximation; second order expansion in the transverse velocity of electrons is performed in order to obtain an analytical expression for energy spread within the bunch. Comparison with earlier results by other authors shows good agreement.

Hall effects on the Walén relation in rotational discontinuities and Alfvén waves

For Alfvénic fluctuations in magnetohydrodynamics (MHD) the perturbed transverse velocity Vt and magnetic field Bt can be related by the Walén relation, Vt = ±Bt/(μ0ρ)1/2 ≡;±VAt, where ρ is the plasma density, VAt is the transverse Alfvén velocity, and the plus (minus) sign is for antiparallel (parallel) propagation. However, observations of Vt and Bt for Alfvén waves and rotational discontinuities in the solar wind and at the magnetopause showed an obvious deviation from the relation. In this paper, modifications of the Walén relation for linear and nonlinear Alfvén waves and rotational discontinuities (RDs) are examined in the Hall‐MHD formulation. Let Vit (≈ Vt) be the transverse ion velocity and Vet be the transverse electron velocity. It is found that Vit = ±Bt(z)/(μ0ρ1)1/2 = ±(ρ(z)/ρ1)1/2 VAt(z) and Vet = ±(ρ1/μ0)1/2Bt(z)/ρ(z) = ±(ρ1/ρ(z))1/2 VAt(z)for RDs in Hall‐MHD, where ρ1 is the upstream plasma density. The ion and electron Walén ratios are defined as Ai = Vit/VAt and Ae = Vet/VAt, respectively. It is found in Hall‐MHD that , AiAe = 1 and Ai < 1 (Ai > 1) for Alfvén waves and RDs with right‐hand (left‐hand) polarization. The Hall dispersive effect may modify the ion Walén ratio by ΔAi≈±0.14 for the magnetopause RDs and by ΔAi≈±0.07 for the interplanetary RDs.

Analysis of a large-orbit gyrotron in a coaxial waveguide under assistant background fields

The dispersion relation of a large-orbit gyrotron in a coaxial waveguide excited in the transverse-electric mode was developed starting from the beam-present wave equation. The relativistic Vlasov's equation was solved under tenuous beam approximations for the perturbed electron distribution function, hence the required current density to be used in the wave equation was found. The analysis was generalized, with respect to background fields, by considering a dc radial electric field and a dc azimuthal magnetic field, over and above conventional dc axial magnetic field. The dispersion relation was solved for the complex frequency for a given propagation constant and the imaginary part interpreted for the growth rate as well as the saturated efficiency of the device. Similarly, for a given frequency the dispersion relation was solved for the complex propagation constant and the imaginary part interpreted for the gain of the device, if configured as an amplifier. Two peaks were obtained in the gain-frequency response corresponding to two points of intersection between the beam-mode dispersion line and the waveguide-mode dispersion curve. The improvement in the growth rate, gain and saturated efficiency was predicted by the application of the additional background fields. A redistribution of beam kinetic energy between the axial and transverse electron velocities led to a remarkable enhanced saturated efficiency at the second peak. A detailed study of the variation of device performance with respect to the gain and saturated efficiency was presented, for a wide range of the dc background field and electron kinetic energy distribution parameters.

Some additional observations of the vortex instability in electron beams

A number of observations have been made of the electron vortices that form in high-density sheet beams traveling along magnetic field lines. The observations were done in sealed off high vacuum tubes. The tubes were equipped with pinhole cameras that permitted measurement of the current densities and the transverse velocities of the electrons in various parts of the beam. The vortex centers were, single sign of charge, plasmas and with increasing current in the beam, the charge density in the center increased until the Brillouin value was reached. Beyond this, the beam discontinuously went through a sequence of shapes, generally with fewer but larger vortices. The pinhole camera was used to measure the transverse velocities of electrons in various parts of the vortex and a surprising broad distribution was found in the center of the vortex of the high current forms.