Hollow Relativistic Electron Beam Research Articles

Magnetron Amplifier-Type Helix Loaded Waveguide Analysis Based on Dispersion Relation

The theory of tenuous hollow relativistic electron beam in the magnetron-type helix loaded waveguide was presented in the presence of sheath and axial magnetic field. The dispersion relation was obtained with the aid of the proper boundary conditions. The effects of electron beam, helix, and vane parameters on the gain and Doppler-shifted frequency were investigated numerically. The numerical results show that the presence of the vane considerably increases the gain. It has been shown that the maximum values of the gain occur at lower harmonics and the maximum values of the Doppler-shifted frequency occur at higher harmonics. The results show that the gain of the system increases when the helix move away from the vane.

Melting effects of high-current relativistic electron beam on aluminum alloy 1933

Melting effects of the irradiation by the intense microsecond relativistic hollow electron beam on the wrought aluminum alloy 1933 were studied. The fracture mechanisms for both irradiated and non-irradiated samples and changes in their structure and chemical composition were investigated. The thermal model describing the beam-metal interaction was developed based on the hyperbolic relaxation heat transfer equation, the weakly coupled theory of thermoelasticity, and the Stefan problem. The finite difference method was used to perform calculations according to this model. The areas of modified and non-irradiated material were determined both experimentally and numerically; the quenched, heat-affected and shockwave-affected zones were localized.

Theory of Magnetron Amplifier in a Helix-Loaded Waveguide With the Inner Dielectric Material

The theory of the propagation of the magnetized hollow relativistic electron beam with a dielectric rod at its axis through the sheath helix that inserted into the magnetron-type conductor is presented. The dispersion relation is obtained with the aid of the proper boundary conditions. The effects of an electron beam, inner dielectric, helix, and magnetron-type conductor parameters on the growth rate are studied numerically. The numerical results show that the presence of the cavity considerably increases the growth rate. In the fast wave mode, we have the maximum value of the growth rate when the dielectric rod and the electron beam are close to each other. The maximum growth rates for the fast and slow wave modes occur to the special value of the helix radius. The results show that the growth rate increases with the decreasing of the axial momentum spread. Comparison of the two modes shows that the growth rate of the slow wave mode is higher than that of the fast wave mode, but the bandwidth of the fast wave mode is wider than that of the slow wave mode.

Controlling hollow relativistic electron beam orbits with an inductive current divider

A passive method for controlling the trajectory of an intense, hollow electron beam is proposed using a vacuum structure that inductively splits the beam's return current. A central post carries a portion of the return current (I1), while the outer conductor carries the remainder (I2). An envelope equation appropriate for a hollow electron beam is derived and applied to the current divider. The force on the beam trajectory is shown to be proportional to (I2-I1), while the average force on the envelope (the beam width) is proportional to the beam current Ib = (I2 + I1). The values of I1 and I2 depend on the inductances in the return-current path geometries. Proper choice of the return-current geometries determines these inductances and offers control over the beam trajectory. Solutions using realistic beam parameters show that, for appropriate choices of the return-current-path geometry, the inductive current divider can produce a beam that is both pinched and straightened so that it approaches a target at near-normal incidence with a beam diameter that is on the order of a few mm.

The use of a high-current electron beam in plasma relativistic microwave oscillators

Relativistic microwave electronics faces the problem of using high currents of relativistic electron beams; i.e., it is possible to use beams the current of which is lower than that of actually existing high-current accelerators. We show the possibility of increasing the power of radiation generated in a plasma relativistic microwave oscillator (PRMO) due to an increase in the absolute value of current. For the beam currents close to the value of limiting vacuum current, the efficiency of microwave generation decreases; therefore, we study PRMO schemes with a high value of limiting vacuum current, i.e., schemes with a small gap between a hollow relativistic electron beam and the waveguide wall. The results of the experiment and numerical simulation are discussed.

Electromagnetic Wave Propagation in an Annular Electron Beam With Ion Channel Guiding

The dispersion characteristics of electrostatic and electromagnetic modes of an electron tube, with ion channel guiding, in a cylindrical waveguide are presented. The analysis takes into account a relativistic hollow electron beam guided by an ion channel. Dispersion relations are derived and solved numerically to study the waveguide, betatron, and space charge modes. The effect of the annular electron beam thickness on frequencies of the electrostatic and electromagnetic waves is investigated. This paper reveals the strong dependence of the electromagnetic and electrostatic waves' frequencies on the electron beam thickness. The results of this paper are compared with previous works where an electron tube is guided with an axial magnetic field.

Limit currents of a relativistic electron beam in a drift chamber with a coaxial cross section

Formulas for the limit vacuum and Pears currents of a thin hollow relativistic electron beam propagating in a cylindrical drift chamber of the coaxial cross section are derived.

同轴波导环形相对论电子束空间极限电流

同轴波导环形相对论电子束空间极限电流

The self-consistent theory of the electron distribution and electro-magnetic field of a relativistic hollow electron beam in ion-channel

The effect of space-charge and relativistic self magnetic-field on the self-consistent equilibrium of the system with a relativistic hollow electron beam and ion-channel is studied. The distribution function and the relationship between location and energy of electron beam are derived by use of kinetic theory. The self-consistent field in ion-channel has also been established. It is clearly shown that the self-consistent equilibrium of the system exists. The relation of location of beam and radius of ion-channel was presented using numerical calculation. The distribution of electro-magnetic field in ion-channel is also given. The theory which is used in apparatus design is afforded by the research.

Diagnostics of a hollow relativistic electron beam from the transfer function of a converting target

Methods for measuring angular, geometrical, and energy characteristics of a hollow relativistic electron beam using the transfer function of a converting target are developed. A relationship between the anisotropy parameters of bremsstrahlung behind the target, angular characteristics of electrons, and geometrical parameters of the electron beam in the target plane is established. The energy balance equation that describes the interaction between the electron beam and converting target is studied. The transfer function of the target and its behavior versus electron energy are found. The time and integral characteristics of the electron beam are examined.

Nonlinear characteristics of a cylindrical Cherenkov laser at millimeter wavelengths

Nonlinear characteristics of a cylindrical Cherenkov laser, which is composed of a dielectric-loaded coaxial waveguide and a hollow relativistic electron beam, are investigated with the use of particle simulation. The results obtained in this paper are compared with those for parallel plate and rectangular models. Numerical results show that, in the cylindrical Cherenkov laser, the electromagnetic (EM) wave grows exponentially in the longitudinal direction and reaches saturation, as is the case with the parallel plate and rectangular models. However, the efficiency of energy transfer from the electron beam to the EM wave in the cylindrical model is not in good agreement with that for the parallel plate model, especially for the case of a small radius of the inner conductor. Thus, we propose a modified parallel plate model whose growth characteristics are the same as those for the cylindrical model. With the use of the corresponding modified parallel plate model, one can calculate growth characteristics for the cylindrical model at a particular frequency more easily.

A theory of two-stream instability in two hollow relativistic electron beams

Stability properties of two-stream instability of two hollow electron beams are investigated. The equilibrium configuration consists of two intense relativistic hollow electron beams propagating through a grounded conducting cylinder. Analysis of the longitudinal two-stream instability is carried out within the framework of the linearized Vlasov–Maxwell equations for the equilibrium distribution function, in which beam electrons have a Lorentzian distribution in the axial momentum. Dispersion relation of the longitudinal two-stream instability is derived. Stability criteria from this dispersion relation indicate that the normalized velocity difference Δβ between the beams should be within a certain range of value to be unstable. Growth rate of the instability is a substantial fraction of the real frequency, thereby indicating that the longitudinal two-stream instability is an effective means of beam current modulation. Transverse instability of hollow electron beams is also investigated. Dispersion relation of the coupled transverse oscillation of the beams is derived and numerical investigation of this dispersion relation is carried out. Growth rate of the kink instability is a substantial fraction of the diocotron frequency, which may pose a serious threat to the two-stream klystron.

Contribution to the theory of thin hollow relativistic electron beams

Contribution to the theory of thin hollow relativistic electron beams

Contribution to the linear theory of the channeling of radiation by thin electron beams in free-electron lasers

The dispersion relations describing the intensification and channeling of electromagnetic waves by thin -ribbon and hollow relativistic electron beams are derived for free-electron lasers, based on stimulated undulator radiation. Systems with flat magnetic and electric undulators as well as with axisymmetric magnetic undulator are examined. The Compton and Raman interaction regimes are investigated. It is shown that the channeling process accompanying the emission of H-polarized waves is different from the channeling process in the case of E-polarized waves, because the ratio of the components of the waves that transfer eiectromagnetic energy and are responsible forthe coupling with the electron beam is different.

Influence of the return current effects on the diocotron instability of a relativistic hollow electron beam

Influence of the return current effects on the diocotron instability of a relativistic hollow electron beam propagating through a background plasma is investigated within the framework of a cold fluid model. The return current density induced in the background plasma is taken to be steadily proportional to the axial electron beam current density. By making use of the linearized fluid-Maxwell equations, a dispersion relation for the eigenfrequencies of the system is derived and used to examine instabilities. It is found that as the fraction of current neutralization increases, lower mode instabilities become dominant while higher mode perturbations are stabilized except in the case of very thin beams. It is also observed that for all values of the fraction of current neutralization, increasing the plasma density gradient or decreasing the beam thickness causes a destabilizing influence.

Optimization of the beam configuration in the Raman-type free-electron laser

A theoretical discussion is given for the two-dimensional Raman-type free-electron laser composed of a hollow relativistic electron beam of arbitrary thickness contained in a parallel plate waveguide and an array of permanent magnets for the pumping source. Under the influence of the magnetostatic field pump, the coupling between the scattered wave of the even TE mode (positive-energy wave) and the electron plasma wave of the odd TM mode (negative-energy wave) is investigated in detail. With the aid of numerical illustrations, the electron plasma wave with odd symmetry is found to be split into two modes: one mode is dominant for a thick beam and the other mode dominant for a thin beam. For the case where the scattered wave interacts with the electron plasma wave of the latter mode, an optimum beam thickness is obtained for which the growth rate becomes maximum. The optimum beam thickness is found to be comparable with the wavelength of the scattered wave and yet considerably greater than the reactive skin depth of the electron beam. In addition, the efficiency for energy conversion is found to be greatly improved by utilizing a hollow beam instead of a solid beam.

Extraction and propagation of an intense, rotating electron beam

A hollow relativistic electron beam produced in a strong axial magnetic field has been extracted into a neutral gas cell where the field is zero. In the field-free region, equilibrium is dictated by a balance between the vz×Bθ radial pinch force and the centrifugal outward force. Extraction and propagation of these beams has been studied experimentally with a variety of diagnostics. A strong, low-frequency filamentation instability is observed after extraction. In general, 80% of the beam energy has been extracted and propagated 75 cm. Beam equilibrium properties are in good agreement with simple theory with the exception of the azimuthal plasma current.

Optimum beam thickness for the Raman-type free-electron laser using a two-dimensional hollow beam

The effect of an arbitrary beam thickness is investigated for a two-dimensional Raman-type free-electron laser composed of a hollow relativistic electron beam and a parallel plate waveguide containing it. On the basis of the fluid theory for electron beams, analytical expressions are given for the dispersion relation and the spatial growth rate of a scattered wave (even TE mode) and an electron plasma wave (even TM mode) coupled under the influence of a pump wave (even TE mode). Then, from the numerical analysis for an important case where both the pump and scattered waves are the lowest-order even TE mode, the following interesting results are obtained. First, the hollow beam can propagate two distinct modes of the electron plasma wave with even symmetry characterized by different field distributions. One mode (mode 1) corresponds to the normal mode of the solid beam while the other mode is inherent to the hollow beam. In addition, the growth rate for the mode 1 is considerably larger than that for the mode 2. In particular, the optimum beam thickness is found for which the growth rate for the mode 1 becomes maximum and yet that for the mode 2 is sufficiently small.

Stability of charged beam propagation through a relativistic hollow electron beam

Stability properties of a charged beam propagation through a relativistic hollow electron beam are investigated, in connection with present experimental applications in the collective particle accelerator. The stability analysis is carried out for long axial wavelength and low-frequency perturbations. A closed algebraic dispersion relation for coupled transverse oscillations is obtained for the solid and hollow beams with sharp-boundary density profiles. One of the most important features in the analysis is that the typical growth rate of the transverse oscillation is of the order of the hollow beam diocotron frequency ωD, thereby severely limiting the solid beam propagation through a relativistic hollow electron beam. Particularly, for a solid beam with a small radius, the fundamental mode perturbation (i.e., the dipole oscillation) is the most unstable mode.

Filamentation instability of a relativistic hollow electron beam

The filamentation instability properties of a relativistic hollow electron beam confined in axial flow by a uniform magnetic field, in the absence of background plasma, in a pipe are investigated via the Vlasov–Maxwell equations. The instability is found to be have two sidebands, one with a spectrum of positive wavenumbers k and the other with a spectrum of negative wavenumbers. The spectral point k = 0, associated with the diokotron instability, is excluded from the two unstable sidebands of the filamentation instability. Only in the limit of zero axial beam flow (γ→1), does the diokotron instability become asymptotically part of the filamentation instability spectrum. In this limit, the two sidebands of the filamentation instability merge asymptotically and symmetrically toward the diokotron instability spectral point, k = 0, in agreement with the basic driving physical mechanisms and geometry configurations for these two distinct and different instabilities.