Interaction of surface electromagnetic waves with an electron beam moving along the interface between metamaterials

Excitation of surface polaritons by an infinitely narrow electron beam propagating in the vacuum gap between a metal-like medium and an artificial dielectric with a negative permeability is studied theoretically. A dispersion relation is derived for the waves excited by the beam for an arbitrary thickness of the gap. The possibility of the emergence of absolute instability is demonstrated for an infinitely narrow vacuum gap, and the corresponding increments are calculated with allowance for small dissipative losses.     

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.     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

On the quantum theory of beam instability in plasma

The quantum theory of induced Cherenkov radiation by an electron beam of longitudinal waves in isotropic plasma is presented. Nonrelativistic quantum nonlinear equations of Cherenkov beam-plasma instability are obtained. A quantum dispersion relation is derived in the linear approximation and instability development increments are determined.     

Upconversion of whistler waves by gyrating ion beams in a plasma

A gyrating ion beam, with a ring-shaped distribution in velocity, supports negative energy beam modes near the harmonics of beam gyro-frequency. An investigation of the non-linear interaction of high-frequency whistler waves with the negative energy beam cyclotron mode is made. A non-linear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion-beam frequency upconverts the whistler waves separated by harmonics of beam gyro-frequency. The expression for the growth rate of whistler mode waves has been derived. In Case 1, a high-amplitude whistler wave decays into two lower frequency waves, called a low-frequency mode and a side band of frequency lower than that of pump wave. In Case 2 a high-amplitude whistler wave decays into two lower frequency daughter waves, called the low-frequency mode and whistler waves. Generation mechanism of these waves has application in space and laboratory plasmas.     

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     

Excitation of excitons in semi-infinite solids with a nonrelativistic electron beam

The instability of an infinite thin electron beam propagating in vacuum over the surface of an isotropic nongyrotropic crystal is investigated. The possibilities of exciting additional longitudinal waves and polarization waves are analyzed. The dispersion laws of exciton-beam coupled waves are obtained. It is demonstrated that the interaction of the beam with the additional bulk longitudinal wave and the surface polarization wave leads to the appearance of the absolute instability.     

Linear analysis of cyclotron-cherenkov and cherenkov instabilities in dielectric-loaded coaxial waveguides

We present, based on the cold fluid theory, linear analysis of the Cherenkov and cyclotron-Cherenkov instabilities which are driven when a linear electron beam is injected into a dielectric-loaded waveguide immersed in an axial magnetic field. In the analysis we consider azimuthally symmetric TM_0n modes. We derive dispersion relations for three types of waveguide, and compare computationally obtained linear growth rates of both instabilities. For the type A, which consists of a metallic cylinder with dielectric liner on its inner surface, the growth rate of the Cherenkov instability is larger than that of the cyclotron-Cherenkov instability. For the type B, which consists of a dielectric core and an outer metallic cylinder, both growth rates are comparable. And for the type C, which consists of a metallic core with dielectric liner on its surface and an outer metallic cylinder, the growth rate of the latter instability is higher than that of the former instability. Finally, for the type C, obtained are dependences of the oscillation frequency and the growth rates of both instabilities on the following parameters: the beam energy, the beam current, the axial magnetic field, the dielectric constant, and the thickness of the dielectric.     

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.     

Electrostatic stability of the liquid layer surface on a hard wettable cylindrical substrate

The wave motion in a cylindrical layer of an ideal conducting liquid on a hard rod kept at a constant electrical potential is calculated accurate to the first order of smallness in dimensional perturbation of the free surface. The instability of the free surface is also considered. A dispersion relation is derived. It is shown that the range of instability waves depends on only the electric field strength near the free surface and the instability increments of capillary waves decrease as the layer gets thinner. The influence of the hard rod becomes tangible only when its radius becomes comparable to the thickness of the liquid layer.     

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.     

On the stability of a cylindrical jet moving in a material medium along an external electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a jet of an ideal incompressible dielectric liquid moving in an ideal incompressible dielectric medium along an external uniform electrostatic field. A tangential discontinuity in the velocity field on the jet surface is shown to cause Kelvin-Helmholtz periodical instability at the interface and destabilize axisymmetric, flexural, and flexural-deformational waves. Both the flexural and flexural-deformational instabilities have a threshold and are observed not at an arbitrarily small velocity of the jet but starting from a certain finite value. It is shown that the instability of waves generated by the tangential discontinuity of the velocity field is periodic only formally (from the pure mathematical point of view). Actually, the jet disintegrates within the time of instability development, which is shorter than the half-cycle of the wave.     

On the Stability of the Surface of a Short Charged Jet Moving with Respect to an External Material Medium

The problem of the stability of capillary waves on the surface of a charged jet of an ideal incompressible electroconducting liquid, which moves with respect to a material dielectric medium, is considered. There is a tangential discontinuity of the velocity field on the interface between the media. Solutions to the problem in two idealized models have been compared, i.e., when the jet has a finite and infinite length. It has been shown that the instability increments and the wave numbers of the most unstable waves, computed in both models, are linearly related, and velocity of motion of the jet acts as a coefficient of proportionality.     

On the capillary stability of a cylindrical dielectric liquid jet in a longitudinal electrostatic field

A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a cylindrical jet of an ideal incompressible dielectric liquid subjected to an electrostatic field aligned with the symmetry axis of the jet. It is shown that only long axisymmetric waves can experience capillary instability in such a system. The wavenumber range into which unstable waves fall begins with a zero value, and its width depends on the permittivities of the liquid and ambient and on the electrostatic field strength squared. As the field strength grows, the wavenumber range for unstable waves rapidly narrows and the capillary instability growth rate, as well as the wavenumber of the wave with the greatest growth rate, decreases.     

Hose instability of a beam of charged particles penetrating a plasma

Employing the phenomenological approach, the dispersion relation for the “hose” instability of a beam of charged particles passing through a plasma has been presented. Energy transfer from the beam is considered. Also, the behavior of the hose instability amplitude under various plasma conditions is discussed in detail.     

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     

On the stability of capillary waves on the surface of a charged jet moving relative to the environment

A dispersion relation is derived for capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface of a charged cylindrical jet of an ideal incompressible conducting liquid moving relative to an ideal incompressible dielectric medium. It is shown that a tangential discontinuity in the velocity field on the surface of the jet leads to periodic instability of waves (similar to the Kelvin-Helmholtz instability) at the interface and destabilizes both axisymmetric and flexural waves. The wavenumber range for unstable waves and the instability growth rate increase with the field strength and relative speed of motion, varying as the square of these parameters. In the case of the neutral jet, the flexural instability is of the threshold character and sets in starting from a certain finite value of the speed rather than at an arbitrary small speed.     

离子束-等离子体系统中的参量不稳定性

本文研究了外pump电场E_0在离子束-等离子体系统中所激发的静电低频参量不稳定性。导出了这种低频波的一般色散关系,并用数值方法分析了一维质子束-等离子体系统的参量不稳定性的激发过程。结果表明:离子束对等离子体中参量不稳定性的激发有极重要的影响。当没有离子束时,只能激发一种模式的波;一旦将离子束引入等离子体中,就可以在系统中激发两个波长较长的低频波。     

受激拉曼散射对非线性介质波导的时空不稳定性影响

基于非线性包络方程我们研究了平面非线性介质波导中的时空不稳定性,得到了有拉曼散射效应情形下不稳定性调制的增益谱的表达式.结果表明在正常和反常两种群速度色散情形下,拉曼散射效应都会导致出现新的不稳定性区域,并且使原有的每一个谱分量的增益上升从而使谱的范围扩大.并通过分析反常色散情况下四种不同函数分布的非线性色散介质系数对不稳定性增益谱的影响,得到呈双曲函数分布的非线性色散介质最为理想.     

Collective and single-particle Cherenkov effects in a spatially bounded system near the nontransparency band

Using the linear approximation, we consider beam instabilities like a collective and a singleparticle stimulated Cherenkov effect developing in a longitudinally bounded electrodynamic system near its nontransparency band, i.e., when the electromagnetic wave excited by the beam has a zero group velocity. A dispersion equation is obtained which determines instability development increments with allowance for the exit of the radiation from the electrodynamic system. Solutions to the dispersion equation for various parameters of the electron beam and the electrodynamic system are investigated.