Divergence angle consideration in energy spread measurement for high-quality relativistic electron beam in laser wakefield acceleration

The thorough exploration of the transverse quality represented by divergence angle has been lacking yet in the energy spread measurement of the relativistic electron beam for laser wakefield acceleration(LWFA). In this work, we fill this gap by numerical simulations based on the experimental data, which indicate that in a C-shape magnet, magnetic field possesses the beam focusing effect, considering that the divergence angle will result in an increase in the full width at half maxima(FWHM) of the electron density distribution in a uniformly isotropic manner, while the length-to-width ratio decreases. This indicates that the energy spread obtained from the electron deflection distance is smaller than the actual value, regardless of the divergence angle. A promising and efficient way to accurately correct the value is presented by considering the divergence angle(for instance, for an electron beam with a length-to-width ratio of 1.12, the energy spread correct from 1.2% to 1.5%), providing a reference for developing the high-quality electron beam source.

Local wavelength evolution and Landau damping of electrostatic plasma wave driven by an ultra-relativistic electron beam in dense inhomogeneous plasma

Evolution of an electrostatic plasma wave driven by a low-density ultra-relativistic electron beam in dense inhomogeneous plasma is considered. In particular, the wavelength variation as observed at fixed locations in the plasma is analyzed in terms of the wave characteristics. It is shown that for a negative density gradient, the observed local wavelength decreases monotonically with time, but for a positive density gradient, it first increases and then decreases with time, accompanied by reversal of the wave phase. However, in both cases the local wavelength eventually decreases with time since Landau damping becomes significant as the wavelength becomes of the order of the plasma Debye length. Results from particle-in-cell simulations agree well with theoretical analyses of the wavelength variation.

The influence of magnetic field on the beam quality of relativistic electron beam long-range propagation in near-Earth environment

In recent years,it has been proposed to use satellite-mounted radio-frequency(RF)accelerators to produce high-current relativistic electron beams to complete debris removal tasks.However,when simulating the long-range propagation(km-range)process of the electron beam,it is difficult to directly use the particle-in-cell method to simultaneously consider the space charge effect of beam and the influence of the geomagnetic field.Owing to these limitations,in this paper,we proposed a simplified method.The ps-range electronic micropulses emitted by the RF accelerator were transmitted and fused to form a ns-range electron beam;then,combined with the improved moving window technology,the model was constructed to simulate the long-range propagation process of the relativistic electron beam in near-Earth environment.Finally,by setting the direction of movement of the beam to be parallel,perpendicular and at an inclination of 3°to the magnetic field,we analyzed and compared the effects of the applied magnetic fields in different directions on the quality of the beam during long-range propagation.The simulation results showed that the parallel state of the beam motion and magnetic fields should be achieved as much as possible to ensure the feasibility of the space debris removal.

Characterization of relativistic electrons generated by a cone guiding laser pulse

We demonstrated the interaction of a gold cone target with a femto second（fs） laser pulse above the relativistic intensity of 1.37×10 18 μm 2 W/cm 2.Relativistic electrons with energy above 2 MeV were observed.A 25%-40% increase of the electron temperature is achieved compared to the case when a plane gold target is used.The electron temperature increase results from the guiding of the laser beam at the tip and the intense quasistatic magnetic field in the cone geometry.The behavior of the relativistic electrons is verified in our 2D-PIC simulations.

Axial effect analysis of relativistic electron beam propagation in vacuum

In geostationary orbits and other quasi-vacuum environments,relativistic electron beams are affected by the initial emittance and space charge effects during the propagation process,resulting in beam quality degradation.Furthermore,axial energy distribution change in the beam and the axial transient electromagnetic effect caused by current changes in the head and tail regions of the beam also cause the beam to expand and affect its quality.In this study,the particle-in-cell method was used to construct a long-range propagation model of a relativistic electron beam in a vacuum environment.By calculating and simulating the axial energy distribution of the beam and the changes in the transient electromagnetic field,the axial effect during the propagation process was analyzed,and the parameter change law of the effective propagation of the beam was explored.This provided a theoretical reference for a more accurate assessment of the beam quality during propagation.

Large-scale episodic enhancements of relativistic electron intensities in Jupiter's radiation belt

Previous studies indicate that,in the Jovian magnetosphere,the long-term trend of the radial profile of relativistic electron intensities is primarily shaped by slow radial diffusion.However,measurements by the Galileo spacecraft reveal the existence of transient increases in MeV electron intensities well above the ambient distribution.It is unclear how common such transient enhancements are,and to which dynamic processes in Jupiter's magnetosphere their occurrence is linked.We investigate the radial distributions of >11 MeV and >1 MeV electron intensities from 9R_(J) to 40R_(J)(R_(J)=71492km denotes the Jovian radius),measured by the Galileo spacecraft from 1996 to 2002.We find transient enhancements of MeV electrons during seven Galileo crossings,mostly occurring around~20R_(J).An apparent dawn-dusk asymmetry of their occurrence is resolved,with a majority of events discovered at dawn.This dawn-dusk asymmetry,as well as the average recurrence time scale of a few days,implies a potential relationship between the MeV electron transients and the storm-like dynamics in the middle and outer magnetosphere detected using a variety of Galileo,Juno and remote sensing aurora observations.We suggest that the observations of some of these transients in the inner magnetosphere may result from a synergy between the convective transport by a large-scale dawn-dusk electric field and the sources provided by injections in the middle magnetosphere.

Wave growth rate in a cylindrical metal waveguide with ion-channel guiding of a relativistic electron beam

This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam-wave interaction, it solves relativistic Lorentz equation and Maxwell＇s equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.

Attosecond x-Ray Pulse Generation by Linear Thomson Scattering of Intense Laser Beam with Relativistic Electron

Abstract Linear Thomson scattering of a short pulse laser by relativistic electron has been investigated using computer simulations. It is shown that scattering of an intense laser pulse of -33 fs full width at half maximum, with an electron of γ0 = 10 initial energy, generates an ultrashort, pulsed radiation of 76 attoseconds with a photon wavelength of 2.5 nm in the backward direction. The scattered radiation generated by a highly relativistic electron has superior quality in terms of its pulse width and angular distribution in comparison to the one generated by lower relativistic energy electron.

Modulational Instability of Ion—Acoustic Waves in a Warm Plasma with a Relativistic Electron Beam

The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting of warm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schr?dinger equation including one additional term that comes from the effect of relativistic electron beam is derived. It is found that the inclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could not admit any stationary soliton waves.

Multi-layer structure formation of relativistic electron beams in plasmas

A two-dimensional electromagnetic particle-in-cell simulation model is proposed to study the density evolution and collective stopping of electron beams in background plasmas.We show here the formation of the multi-layer structure of the relativistic electron beam in the plasma due to the different betatron frequency from the beam front to the beam tail.Meanwhile,the nonuniformity of the longitudinal wakefield is the essential reason for the multi-layer structure formation in beam phase space.The influences of beam parameters(beam radius and transverse density profile)on the formation of the multi-layer structure and collective stopping in background plasmas are also considered.

Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

It is known that ion-focused regime(IFR)can effectively suppress expansion of a relativistic electron beam(REB).Using the particle-in-cell Monte Carlo collision(PIC-MCC)method,we numerically investigate the propagation of an REB in neutral gas.The results demonstrate that the beam body is charge neutralization and a stable IFR can be established.As a result,the beam transverse dimensions and longitudinal velocities keep close to the initial parameters.We also calculate the charge and current neutralization factors of the REB.Combined with envelope equations,we obtain the variations of beam envelopes,which agree well with the PIC simulations.However,both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range propagation.It is proved that decreasing the initial pulse length of the REB can avoid the influence of electron avalanche.Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses.Further,a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.

Electromagnetic field of a relativistic electron vortex beam

Electron vortex beams(EVBs)have potential applications in nanoscale magnetic probes of condensed matter and nanoparticle manipulation as well as radiation physics.Recently,a relativistic electron vortex beam(REVB)has been proposed[Phys.Rev.Lett.107174802(2011)].Compared with EVBs,except for orbital angular momentum,an REVB has intrinsic relativistic effect,i.e.,spin angular momentum and spin-orbit coupling.We study the electromagnetic field of an REVB analytically.We show that the electromagnetic field can be separated into two parts,one is only related to orbital quantum number,and the other is related to spin-orbit coupling effect.Exploiting this separation property,the difference between the electromagnetic fields of the REVB in spin-up and spin-down states can be used as a demonstration of the relativistic quantum effect.The linear momentum and angular momentum of the generated electromagnetic field have been further studied and it is shown that the linear momentum is weakly dependent on the spin state;while the angular momentum is evidently dependent on the spin state and linearly increases with the topological charge of electron vortex beam.The electromagnetic and mechanical properties of the REVB could be useful for studying the interaction between REVBs and materials.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave（SCW）, with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam（REB） parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Transport of Relativistic Electrons Scattered by the Coulomb Force and a Thermionic Energy Converter with a Built-in Discharge Tube

A transport equation of momentum for relativistic electrons scattered isotropically was previously reported. Here, a momentum-transport equation for relativistic electrons “scattered anisotropically” by the Coulomb force is inquired into. An ideal plasma consisting of electrons and deuterons is treated again. Also, to raise a generation-ability of a thermionic energy converter, a means of introducing external electric and magnetic fields within “a converter in which an emitter plate and a collector plate face simply each other” is proposed.

Characterization of relativistic electrons generated by a cone guiding laser pulse

We demonstrated the interaction of a gold cone target with a femto second(fs) laser pulse above the relativistic intensity of 1.37×10 18 μm 2 W/cm 2.Relativistic electrons with energy above 2 MeV were observed.A 25%-40% increase of the electron temperature is achieved compared to the case when a plane gold target is used.The electron temperature increase results from the guiding of the laser beam at the tip and the intense quasistatic magnetic field in the cone geometry.The behavior of the relativistic electrons is verified in our 2D-PIC simulations.

Butterfly distribution of Earth＇s radiation belt relativistic electrons induced by dayside chorus

Previous theoretical studies have shown that dayside chorus can produce butterfly distribution of energetic electrons in the Earth＇s radiation belts by preferentially accelerating medium pitch angle electrons, but this requires the further confirmation from high- resolution satellite observation. Here, we report correlated Van Allen Probes data on wave and particle during the 1 I-13 April, 2014 geomagnetic storm. We find that a butterfly pitch angle distribution of relativistic electrons is formed around the location L = 4.52, corresponding to the presence of enhanced dayside chorus. Using a Gaussian distribution fit to the observed chorus spectra, we calculate the bounce-averaged diffusion rates and solve two-dimensional Fokker-Planck equation. Numerical results demonstrate that acceleration by dayside chorus can yield the electron flux evolution both in the energy and butterfly pitch angle distribution comparable to the observation, providing a further evidence for the formation of butterfly distribution of relativistic electrons driven by very low frequency （VLF） plasma waves.

Transport of ultraintense laser-driven relativistic electrons in dielectric targets

Ultraintense laser-driven relativistic electrons provide a way of heating matter to high energy density states related to many applications. However, the transport of relativistic electrons in solid targets has not been understood well yet,especially in dielectric targets. We present the first detailed two-dimensional particle-in-cell simulations of relativistic electron transport in a silicon target by including the field ionization and collisional ionization processes. An ionization wave is found propagating in the insulator, with a velocity dependent on laser intensity and slower than the relativistic electron velocity. Widely spread electric fields in front of the sheath fields are observed due to the collective effect of free electrons and ions. The electric fields are much weaker than the threshold electric field of field ionization. Two-stream instability behind the ionization front arises for the cases with laser intensity greater than 5 × 1019W/cm^2 that produce high relativistic electron current densities.

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

Relativistic and distorted wave effects on Xe 4d electron momentum distributions

The relativistic and distorted wave effects are investigated for the electron momentum distributions of Xe 4d electrons.The theoretical results show good agreements with the experimental data measured previously with electron momentum spectroscopy. The distorted wave effect and the relativistic effect are found to play important roles in the low and high momentum regions, respectively.

Simulation of Secondary Electron and Backscattered Electron Emission in A6 Relativistic Magnetron Driven by Different Cathode

Prticle-in-cell（PIC） simulations demonstrated that,when the relativistic magnetron with diffraction output（MDO） is applied with a 410 kV voltage pulse,or when the relativistic magnetron with radial output is applied with a 350 kV voltage pulse,electrons emitted from the cathode with high energy will strike the anode block wall.The emitted secondary electrons and backscattered electrons affect the interaction between electrons and RF fields induced by the operating modes,which decreases the output power in the radial output relativistic magnetron by about 15%（10%for the axial output relativistic magnetron）,decreases the anode current by about 5%（5%for the axial output relativistic magnetron）,and leads to a decrease of electronic efficiency by 8%（6%for the axial output relativistic magnetron）.The peak value of the current formed by secondary and backscattered current equals nearly half of the amplitude of the anode current,which may help the growth of parasitic modes when the applied magnetic field is near the critical magnetic field separating neighboring modes.Thus,mode competition becomes more serious.