Cold Relativistic Electron Beam Research Articles

Slipping instability of an inhomogeneous relativistic electron beam

The charged particle beams, such as electrons, ions, and plasma compression flow, have received considerable attention due to their applications in science and technology; therefore, studying the stability of these beams is of particular importance. Here, we examine theoretically the stability properties of a cold relativistic electron beam with a transverse velocity shear and non-uniform density profile. We consider a plane-parallel beam propagating along an external magnetic field and evaluate its macroscopic equilibrium state. We derive the dispersion relation of the slipping instability based on the linear electrodynamics of an inhomogeneous plasma and kinetic theory. In this model, the oscillation spectrum and the growth rate are derived by using the eikonal equation and the quasi-classical quantization rule. A linear velocity shear and a non-linear density gradient are assumed. Furthermore, we analyze numerically the dispersion relation of the slipping instability. The impacts of the inhomogeneity parameter and the relativistic factor on the properties of the slipping instability are discussed.

Nonlinear ion acoustic wave structure in electron–ion plasma in presence of fully relativistic electron beam

Analytical description of large amplitude nonlinear ion acoustic (IA) waves in the presence of a cold relativistic electron beam is presented. The pseudopotential method is adopted to observe the effects of various parameters like beam density, ion temperature, etc. on the IA wave structures. Furthermore, the maximum amplitude of the IA wave is estimated, and its variation with fully relativistic electron beam parameters is investigated. The maximum allowed amplitude of the wave is found to decrease with the increase in the electron beam density as well as in the ion temperature. The Mach number has the effect to increase the maximum amplitude of the electric field.

Nonlinear characteristics of relativistic Pierce diodes in stationary state

Time independent states are explored theoretically for generalized Pierce diode (non-neutral plasma diode with ionic background), which is driven by a cold relativistic electron beam. The region between the electrodes is assumed to be filled uniformly with static ions. Injected beam is monochromatic, i.e., all the electrons are emitted with the same kinetic energy (relativistic). Relativistic effects are explored both for collisionless and collisional systems. The formulation of the model is based on the fluid-Maxwell's equations and it is solved by two methods: in the absence of any dissipative source, Eulerian description is employed, whereas to incorporate the effects of collisional drag Lagrangian formulation is found to be useful. The steady-state solutions are visualized through the “Bursian” and “Non-Bursian” branches in a parametric plane. It is observed that the magnitude of the maximum current density of a Pierce diode increases with the relativistic factor of the injected beam. Other factors like the density of background ions and particle collision also have significant influence on the space-charge-limited flow and other steady state properties. Obtained results are relevant to comprehend the working mechanism of many diode-based instruments such as thermionic energy converters, microwave emitter, Q-machines, etc.

A study on the steady-state solutions of a relativistic Bursian diode in the presence of a transverse magnetic field

A comprehensive study on the steady states of a planar vacuum diode driven by a cold relativistic electron beam in the presence of an external transverse magnetic field is presented. The regimes, where no electrons are turned around by the external magnetic field and where they are reflected back to the emitter by the magnetic field, are both considered in a generalized way. The problem is solved by two methods: with the Euler and the Lagrange formulation. Taking non-relativistic limit, the solutions are compared with the similar ones which were obtained for the Bursian diode with a non-relativistic electron beam in previous work [Pramanik et al., Phys. Plasmas 22, 112108 (2015)]. It is shown that, at a moderate value of the relativistic factor of the injected beam, the region of the ambiguous solutions located to the right of the SCL bifurcation point (space charge limit) in the non-relativistic regime disappears. In addition, the dependencies of the characteristic bifurcation points and the transmitted current on the Larmor frequency as well as on the relativistic factor are explored.

Kinetic description of a free electron laser with an electromagnetic-wave wiggler and ion-channel guiding by using the Einstein coefficient technique

A theoretical study of electron trajectories and gain in a free electron laser (FEL) with an electromagnetic-wave wiggler and ion-channel guiding is presented based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.

Gamma-ray free-electron lasers: Quantum fluid model

A quantum fluid model is used to describe the interaction of a nondegenerate cold relativistic electron beam with an intense optical wiggler taking into account the beam space-charge potential and photon recoil effect. A nonlinear set of coupled equations is obtained and solved numerically. The numerical results indicate that intense γ-ray free-electron laser emission, with intensities approaching the Schwinger limit, can be driven by the strong nonlinear space-charge wave, for feasible values of the electron beam parameters. However, the achievement of this regime of extreme intensities depends rather critically on the choice of the detuning and of the signal initial phase at the entrance of the interaction region.

Kinetic description of a wiggler-pumped ion-channel free-electron laser by applying the Einstein coefficient technique

AbstractA kinetic theory is used to investigate the theory of a free-electron laser with a helical wiggler and an ion channel based on the Einstein coefficient method. The laser gain in the low-gain regime is obtained for the case of a cold tenuous relativistic electron beam, where the beam plasma frequency is much less than the radiation frequency, propagating in this configuration. The resulting gain equation is analyzed numerically over a wide range of system parameters.

Cherenkov free electron laser in an asymmetric dielectric liner waveguide

The small signal gain of a Cherenkov free electron laser is derived. The device consists of two different dielectric liner parallel plate waveguides driven by a cold relativistic electron beam. The results are compared with a standard Cherenkov free electron laser in a symmetric liner waveguide. It is observed that the asymmetric liner CFEL results agree well with the symmetric liner CFEL near the beam threshold but differ substantially at points far away from the beam threshold voltage.

Relativistic Bursian diode equilibria

A comprehensive study of steady-states of a planar vacuum diode driven by a cold relativistic electron beam is presented. The emitter electric field as a characteristic function for their existence is evaluated in dependence of the diode length, the applied potential V, and the relativistic beam factor at injection γ0. It is used to classify the different branches of possible solutions, which encompass electron flows that are (i) transmitted through the diode completely, (ii) partially reflected from a virtual cathode (VC) either within the diode region or at the collector side, and (iii) reflected totally. As a byproduct, the V and γ0 dependences of both bifurcation points of the minimum potential and of the transmitted current are obtained and the ultrarelativistic limit, γ0⪢1, is performed. In this highly relativistic regime, the density of electrons appears to be constant across the diode region except for a small area around the VC.

WEIBEL, TWO-STREAM, FILAMENTATION, OBLIQUE, BELL, BUNEMAN...WHICH ONE GROWS FASTER?

Many competing linear instabilities are likely to occur in astrophysical settings, and it is important to assess which one grows faster for a given situation. An analytical model including the main beam plasma instabilities is developed. The full 3D dielectric tensor is thus explained for a cold relativistic electron beam passing through a cold plasma, accounting for a guiding magnetic field, a return electronic current and moving protons. Considering any orientations of the wave vector allows to retrieve the most unstable mode for any parameters set. An unified description of the Filamentation (Weibel), Two-Stream, Buneman, Bell instabilities (and more) is thus provided, allowing for the exact determination of their hierarchy in terms of the system parameters. For relevance to both real situations and PIC simulations, the electron-to-proton mass ratio is treated as a parameter, and numerical calculations are conducted with two different values, namely 1/1836 and 1/100. In the system parameters phase space, the shape of the domains governed by each kind of instability is far from being trivial. For low density beams, the ultra-magnetized regime tends to be governed by either the Two-Stream or the Buneman instabilities. For beam densities equalling the plasma one, up to four kinds of modes are likely to play a role, depending of the beam Lorentz factor. In some regions of the system parameters phase space, the dominant mode may vary with the electron-to-proton mass ratio. Application is made to Solar Flares, Intergalactic Streams and Relativistic shocks physics.

Beam-plasma dielectric tensor with Mathematica

We present a Mathematica notebook allowing for the symbolic calculation of the 3 × 3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summary Title of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère–Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the dimensionless variables. Restrictions on the complexity of the problem: Temperature effects are limited to small, i.e. non-relativistic, temperatures. The kinetic counterpart of the present Mathematica will usually not compute the required integrals. Typical running time: About 1 minute on a Intel Centrino 1.5 GHz Laptop with 512 MB of RAM. Unusual features of the program: None.

Linear theory of plasma C-caronerenkov masers.

A different theoretical model of \ifmmode \check{C}\else \v{C}\fi{}erenkov instability in the linear amplification regime of plasma \ifmmode \check{C}\else \v{C}\fi{}erenkov masers is developed. The model assumes a cold relativistic annular electron beam propagating through a column of cold dense plasma, the two bodies being immersed in an infinite magnetic guiding field inside a perfect cylindrical waveguide. In order to simplify the calculations, a radial rectangular distribution of plasma and beam density is assumed and only azimuthal symmetric modes are under investigation. The model's difference consists of taking into account the whole plasma and beam electromagnetic structures in the interpretation of the \ifmmode \check{C}\else \v{C}\fi{}erenkov instability. This model leads to alternative results such as the possibility of emission at several frequencies. In addition, the electric field is calculated taking into account its radial phase dependence, so that a map of the field in the interaction region can be presented. \textcopyright{} 1996 The American Physical Society.

Analysis of free-electron lasing stimulated by a counterpropagating plasma wave

A relativistic fluid theory is constructed to analyze the inverse Compton scattering of an unmagnetized counterpropagating plasma wave by a cold relativistic electron beam. A Langmuir wave and electromagnetic plasma wave wigglers are considered, and the properties of the two types of wigglers are comparatively discussed. The growth rates are comparable to those of the ac free-electron laser and the free-electron lasers with magnetostatic wigglers in the Raman regime.

Development and quality measurements of cold relativistic electron beam for low-γ free-electron lasers

A relativistic electron beam source with low temperature (cold) using a field emission cathode and uniform electrostatic acceleration has been developed for use in low-γ free-electron lasers. An energy of 0.51 MeV and a current of 60 A (200 A/cm2) were obtained. The energy spread and the angular velocity spread were measured to be ΔE/E=0.14% and β⊥/β∥ =4×10−2, respectively.

The microwave generation mechanism of arelativistic electron beam propagating through the dielectric-loaded cylindrical waveguide

The general dispersion relation is derived for the fundamental transverse magnetic modes driven by a cold relativistic electron beam in a dielectric-loaded cylindrical waveguide using the fluid Maxwell equations. It is then reduced to the algebraic equation for the space charge and cyclotron modes using a tenuous beam approximation. Solutions of the resulting equation are obtained by varying several parameters, such as the external magnetic field the dielectric constant and the thickness of the dielectric material. It is shown that the growth rate of the slow cyclotron instability is greatly increased for the region of B/sub o/<or approximately=1000 G to the extent that it becomes comparable to the growth rate of a slow space-charge instability. In this region the magnetic-field effect on the slow space-charge mode is shown to increase the growth rate by up to 10%. In the limit of the critical external magnetic field defined as the field below which no beam equilibrium exists, it is found that two slow modes of cyclotron and space-charge modes become degenerate with a finite value of growth rate.<<ETX>>

Measurement of the Energy Spread of the Cold Relativistic Electron Beam Using Thomson Backscattering of a High Power CO2 Laser

The energy spread of the cold relativistic electron beam was measured by the Thomson backscattering of a high power CO2 laser. The energy spread was about 1.2% of the total energy. The wavelength and the power of the scattered light were in good agreement with the theoretically calculated values.

Development of cold electron beam sources for a Raman type free electron laser

Two types of very cold relativistic electron beam sources for Raman FEL experiments have been developed. Using one of them as an electron beam source for a Raman type FEL, intense electromagnetic radiation pulses of about 100 kW were obtained in the millimeter wavelength region with an energy conversion efficiency of about 2%.

Stimulated Raman scattering from a relativistic electron beam

A plane transverse electromagnetic wave propagating antiparallel to a cold relativistic electron beam extending over all space is backscattered from a negative energy space-charge wave into a frequency up-converted plane transverse electromagnetic wave. Parametric and nonlinear three-wave interactions are analytically examined in a systematic manner taking account of all the nonlinearities. With the inclusion of appropriate phenomenological collision terms, and frequency and wave-number mismatches, the amplitude threshold, the growth rate, and the saturation values are determined. A heuristic estimation reveals wave amplification to be limited by the beam velocity. An expression for maximum amplification is obtained. Representative numerical results are presented to display the characteristics of the nonlinear three-wave interaction.

The Cerenkov Maser at Millimeter Wavelengths

The dispersion relation for the transverse magnetic modes (TMon,) of a partially filled, dielectric-lined, cylindrical waveguide driven by a cold relativistic electron beam is derived. The effect of a gap between the electron beam and the dielectric liner is included. The dispersion relation is then used to calculate the growth rate for the Cerenkov instability in the collective tenuous beam limit. Expressions are developed for the minimum current necessary for oscillation threshold and for the power output of the Cerenkov maser in the collective regime.

Electron beam dynamics in combined guide and pump magnetic fields for free electron laser applications

The propagation of a cold relativistic electron beam in a free electron laser with an axial guide magnetic field is considered. The possibility of several steady-state helical trajectories for the electrons is shown, and the stability against perturbations and accessibility of such steady states is considered. Necessary and sufficient conditions for the stability are derived and indicate the importance of the transition region at the entrance of the laser. Possible modes of operation of the laser in different steady-state regimes are suggested and illustrated by numerical examples.