Excitation of Electromagnetic Modes in a Dielectric-Loaded Waveguide via Cyclotron Resonance Interaction

An analytical treatment of the excitation of electromagnetic modes by an axial electron beam in a cylindrical waveguide partially loaded with a dielectric is presented. Equations describing the mode structure of the waves are obtained in cylindrical geometry. Using apropriate boundary conditions a dispersion relation is derived in the weak-beam approximation (?b >> ?). In addition to the conventional Cerenkov interaction, the slow-cyclotron resonance interaction (? ? ?V0 - ?c), which involves the coupling of the TM mode of the waveguide with the slow cyclotron beam mode, is also seen to be important. The growth rate of the instability scales as n01/2 (where n0 is the beam density), decreases with an increase in V0, and is rather insensitive to the variation in the magnetic field.     

The microwave generation mechanism of arelativistic electron beampropagating 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_o≲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     

Linear theory of plasma filled backward wave oscillator

An analytical and numerical study of backward wave oscillator (BWO) in linear regime is presented to get an insight into the excitation of electromagnetic waves as a result of the interaction of the relativistic electron beam with a slow wave structure. The effect of background plasma on the BWO instability is also presented.     

The dispersion relation of the charge and current compensated relativistic electron beam-plasma system

Analysing the general dispersion relation numerically, the unstable regions of the relativistic electron-beam plasma system were determined. The external parameters were varied to ensure more effective instability excitations. The full charge and current compensation presumptions lead to new synchronism predictions. The return current's slow space charge wave and return current's slow cyclotron wave are synchronous with the plasma ion wave.     

On the instability of electrostatic waves in a nonuniform electron–positron magnetoplasma

The dispersion properties of three-dimensional electrostatic waves in a nonuniform electron–positron (EP) magnetoplasma are analyzed. A new dispersion relation is derived by use of the electron and positron density responses arising from the electron and positron continuity and Poisson equations. In the local approximation, the dispersion relation admits two wave modes with different velocities. The growth rates of various modes are illustrated both analytically and numerically. Considering the temperature gradients produces a linearly stable transverse mode. The growth rate of the slow mode instability due to the density inhomogeneity only is the highest one, though it appears at higher thermal energy. The angle of the wave propagation affects drastically on the instability features in each case. The applications of the present analysis are briefly discussed.     

W波段带状注矩形单栅返波振荡器模拟研究

提出并研究了一种带状电子注矩形单栅返波振荡器。首先研究了矩形单栅慢波结构的色散特性和耦合阻抗特性,然后粒子模拟并优化设计了带状注矩形单栅高频结构,预群聚腔及输出一体化结构。研究结果表明:利用电压200kV、电压2kA、截面为24mm×0.5mm的带状电子注,驱动该矩形单栅返波振荡器,能够产生42 MW的输出功率,工作频率86GHz,效率为10.5%。     

Stability of second harmonic minority heating in magnetic mirror systems

A dispersion relation has been derived to study the stability of ion cyclotron (IC) propagation at the second harmonic of the minority component deuterium in a mirror confined plasma that has hydrogen as the majority species. We have worked in the frame of the majority ions; our dispersion relation can thus be used to study IC propagation in a single ion plasma also. Analysis of the dispersion relation yields two modes — one below and the other above the ion gyro-frequency Θ_H of hydrogen. The expression for the growth rate is used to explicitly show that an instability can arise in the plasma when the loss-cone indexj⩾3; this instability being a result of the coalescing of the two modes supported by the plasma. Unfortunately, the minority component deuterium does not decrease this instability and thus the proposed scheme of IC heating at the second harmonic of the minority component seems unsuited to mirror devices.     

Excitation of Convective Cells by Nonlinear Interaction of Interchange Mode

Convective Cell formation due to nonlinear interaction of interchange mode is studied using multiple time and space scales. Basic interchange mode equation is modified to obtain nonlinear localized structure with modulational perturbation in the drift direction and periodic boundary condition for the perturbation in the direction of the density gradient. To study modulational instability we have deduced nonlinear evolution equation for the first order perturbation from third order secularity elimination condition. Modulational instability, which is responsible for localized structure, is studied in two limits of the dispersion relation.     

Effect of longitudinal space-charge waves of a helical relativisticelectron beam on the cyclotron maser instability

The influence of the longitudinal space-charge waves of a coherently gyrophased helical relativistic electron beam on the cyclotron maser instability is investigated in a cylindrical waveguide configuration using a three-dimensional kinetic theory. A dispersion relation that includes waveguide effects is derived. The stability properties of the cyclotron maser interaction are examined in detail. It is shown that, in general, the effects of space-charge waves on a coherently gyrophased beam are suppressed in a waveguide geometry, in comparison with an ideal one-dimensional cyclotron maser with similar beam parameters     

Dynamics of the Magnetospheric Cyclotron ELF/VLF Maser in the Backward-Wave-Oscillator Regime. I. Basic Equations and Results in the Case of a Uniform Magnetic Field

We consider the nonlinear dynamics of absolute instability of whistler-mode waves in the Earth's magnetosphere in the presence of a step-like deformation in the distribution function of energetic electrons. Development of this instability, implying the transition of the magnetospheric cyclotron maser to the regime of a backward-wave oscillator (BWO), was proposed earlier as a generation mechanism of magnetospheric chorus emissions. We derive simplified nonlinear equations describing the dynamics of the magnetospheric BWO in the case of low efficiency of wave-particle interactions. Numerical simulations of these equations confirm qualitative similarity of the laboratory and magnetospheric BWOs and justify quantitative estimates of parameters of chorus emissions. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 9, pp. 719–729, September 2005.     

Efficiency enhancement of high power vacuum BWO's using nonuniformslow wave structures

The Sinus-6, a high-power relativistic repetitively-pulsed electron beam accelerator, is used to drive various slow wave structures in a BWO configuration in vacuum. Peak output power of about 550 MW at 9.45 GHz was radiated in an 8-ns pulse. We describe experiments which study the relative efficiencies of microwave generation from a two-stage nonuniform amplitude slow wave structure and its variations without an initial stage. Experimental results are compared with 2.5 D particle-in-cell computer simulations. Our results suggest that prebunching the electron beam in the initial section of the nonuniform BWO results in increased microwave generation efficiency, Furthermore, simulations reveal that, in addition to the backward propagating surface harmonic of the TM₀₁ mode, backward and forward propagating volume harmonics with phase velocity twice that of the surface harmonic play an important role in high-power microwave generation and radiation     

Dynamics of the magnetospheric cyclotron ELF/VLF maser in the backward-wave-oscillator regime. II. The influence of the magnetic-field inhomogeneity

We study the influence of the magnetic-field inhomogeneity on the nonlinear dynamics of the absolute instability of whistler-mode waves in the Earth’s magnetosphere in the presence of a step-like deformation in the distribution function of energetic electrons. Development of this instability, implying the transition of the magnetospheric cyclotron maser to the regime of a backward-wave oscillator (BWO), was proposed earlier as a generation mechanism of magnetospheric chorus emissions. We analyze the results of numerical simulations of the simplified nonlinear equations describing the magnetospheric-BWO dynamics in the case of low efficiency of wave-particle interactions. We found that the case of an inhomogeneous magnetic field where the system length is much greater than the length characterizing the linear stage of the BWO regime has important specific features compared with the case of a homogeneous medium. The main feature of the nonlinear wave dynamics in the magnetospheric BWO in an inhomogeneous magnetic field consists in the fact that for a sufficiently large excess over the generation threshold, a sequence of separate wave packets, i.e., discrete elements, is formed. The frequency within each packet varies in time, and these discrete elements are close in their properties to the chorus elements observed in the magnetosphere. The results of calculations confirm the quantitative estimates of parameters of chorus emissions, which were performed earlier on the basis of the BWO model. ^†Deceased Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 11, pp. 977–987, November 2008.     

Effect of relativistic elliptical beam modulation on excitation of surface plasma waves in a magnetized dusty plasma column with elliptical cross section

Abstract

The excitation of surface plasma waves due to the interaction of an elliptical relativistic density modulated electron beam with the magnetized dusty plasma column with elliptical cross-section has been studied. The dispersion relation of surface plasma waves has been retrieved from the derived dispersion relation by considering that the beam is absent and there is no dust in the plasma elliptical cylinder. It is shown that the Cherenkov and fast cyclotron interactions appear between the beam and eigen-modes of plasma column. The growth rate of the instability increases with the beam density and modulation index as one-third power of the beam density in Cherenkov interaction and is proportional to the square root of beam density in fast cyclotron interaction. The numerical results and graphs are presented, too.     

Studies of relativistic backward-wave oscillator operation in thecross-excitation regime

We first reported the operation of a relativistic backward-wave oscillator (BWO) in the so-called cross-excitation regime in 1998. This instability, whose general properties were predicted earlier through numerical studies, resulted from the use of a particularly shallow rippled-wall waveguide [slow wave structure (SWS)] that was installed in an experiment to diagnose pulse shortening in a long-pulse electron beam-driven high-power microwave (HPM) source. This SWS was necessary to accommodate laser interferometry measurements along the SWS during the course of microwave generation. Since those early experiments, we have studied this regime in greater detail using two different SWS lengths. We have invoked time-frequency analysis, the smoothed-pseudo Wigner-Ville distribution in particular, to interpret the heterodyned signals of the radiated power measurements. These recent results are consistent with earlier theoretical predictions for the onset and voltage scaling for this instability. This paper presents data for a relativistic BWO operating in the single-frequency regime for two axial modes, operating in the cross-excitation regime, and discusses the interpretation of the data, as well as the methodology used for its analysis. Although operation in the cross-excitation regime is typically avoided due to its poorer efficiency, it may prove useful for future HPM effects studies     

Theoretical models for designing a 220-GHz folded waveguide backward wave oscillator

In this paper,the basic equations of beam-wave interaction for designing the 220 GHz folded waveguide(FW)backward wave oscillator(BWO) are described.On the whole,these equations are mainly classified into small signal model(SSM),large signal model(LSM),and simplified small signal model(SSSM).Using these linear and nonlinear one-dimensional(1D) models,the oscillation characteristics of the FW BWO of a given configuration of slow wave structure(SWS) can be calculated by numerical iteration algorithm,which is more time efficient than three-dimensional(3D)particle-in-cell(PIC) simulation.The SSSM expressed by analytical formulas is innovatively derived for determining the initial values of the FW SWS conveniently.The dispersion characteristics of the FW are obtained by equivalent circuit analysis.The space charge effect,the end reflection effect,the lossy wall effect,and the relativistic effect are all considered in our models to offer more accurate results.The design process of the FW BWO tube with output power of watt scale in a frequency range between 215 GHz and 225 GHz based on these 1D models is demonstrated.The 3D PIC method is adopted to verify the theoretical design results,which shows that they are in good agreement with each other.     

Composite right/left-handed circular meta-waveguide

A new realization of a cylindrical meta-waveguide is proposed. The guide is a metallic cylinder loaded azimuthally with conducting rods short circuited to the outer cylinder. It can be simplified to a planar periodically cascaded coupled lines. However, the actual circuit is described in cylindrical coordinates as screw or helically periodic structure. The dispersion relation was obtained from the circuit model and from the actual structure using EM simulation, with a good agreement between both. An 8-cell structure was simulated to show the overall guide transmission characteristic. The major advantage of this new guide is that it does not contain any dielectrics, which makes it favorable in applications involving electron beams such as Backward Wave Oscillator BWO, Gyrotron BWO, and Cherenkov backward wave detector.     

Dispersion relation for the lowest mode of the ion-acoustic instability in a high-current ion laser

The lowest frequency mode of the ion-acoustic instability in a high-current low-pressure wall-confined discharge, which serves as an active medium of cw ion gas lasers, is studied experimentally. The dispersion relation for this mode is obtained using the spectral correlation analysis of spontaneous plasma emission. The dependences obtained are compared with the available theoretical models of ion-acoustic instability in low-pressure discharges.     

Stability of Waves in Relativistic Plasma

The dispersion relation of electromagnetic waves propagating perpendicular to an applied uniform magnetic field B₀ in relativistic plasma is derived. Waves propagating perpendicular to the uniform applied magnetic field can be separated into two modes - one is the linearly polarized transverse wave and the other is a hybrid mode. In the present analysis, dispersion relation of the first mode i. e., for a pure transverse wave is analysed under the assumption that the wavelength is much longer than the cyclotron radii of the electrons. A stability criterion which limits the thermal energy of the electrons along B₀ is obtained.     

Relativistic backward wave oscillator using a selective mode converter

A new version of the relativistic backward wave oscillator (BWO) is proposed and investigated experimentally, where the cutoff (for the working mode mode) taper at the cathode end is replaced by a selective Bragg-type mode converter. In the experimental BWO model, which operates in the three-centimeter range and is equipped with a mode converter based on a slightly corrugated waveguide, a radiated power of 700 MW in pulses of duration up to 100 ns with an output spatial structure similar to a Gaussian wave beam is obtained at an accelerating potential of 0.8 MV and a focusing magnetic field of 7 kOe. Zh. Tekh. Fiz. 69, 102–105 (November 1999)     

Coaxial configuration of the dielectric Cherenkov maser

The linearized Lorentz force, continuity equation, and Maxwell's equations are used to calculate the system dispersion relation for a coaxial configuration of the dielectric Cherenkov maser. The system consists of two coaxial conductors lined with dielectric and an annular relativistic electron beam, which propagates between the two liners. The dispersion relation for the beam and dielectric-lined coaxial waveguide structure and the no-beam system that describes the dependence of the generated frequency on the coaxial waveguide parameters are presented. Using the linearized dispersion relation, the growth rate for the beam-TM_0n waveguide mode instability is calculated in the strong-coupling tenuous beam limit