Transverse oscillations of a long-pulse electron beam on alaser-formed channel

An intense relativistic electron beam may be transported in low-pressure gas using an ion channel which focuses and guides the beam. The beam can be unstable to the growth of transverse oscillations caused by the electric force between the beam and channel-the ion hose instability. Beam propagation on channels created by photoionization of gas with an excimer laser is discussed. Ion hose oscillations have been recorded which have a betatron wavelength of approximately 1.5 m. The growth rate of the ion hose instability in the linear regime was measured as 1.67±0.45. At this level of growth, the amplitude of beam oscillations equals the channel radius after a period of one-third of an ion oscillation time     

Relativistic warm plasma waveguide under the effects of plasma electrons and HF electrical field on Buneman instability

The stabilization effect of a strong HF (pump) electrical field and plasma electrons on a two-stream (Buneman) instability in a plane relativistic warm plasma waveguide is investigated; using the separation method to solve the two-fluid plasma model we separate the problem into two parts. The “temporal” (dynamical) part enables us to determine the frequencies and growth rates of unstable waves; this part within the redefinition of natural frequencies coincides with the system describing HF suppression of Buneman instability in uniform unbounded plasma. Natural frequencies of oscillations and spatial distribution of the amplitude of the self-consistent electrical field are determined from the solution of a boundary-value problem (“space part”) taking into account specific spatial distribution of plasma density. Plasma electrons are considered to have a relativistic thermal velocity. It is shown that the growth rate of instability in relativistic warm plasma is reduced compared to non-relativistic (cold or warm) plasma and relativistic cold plasma. In addition, it is found that the plasma electrons have no effect on the solution of the space part of the problem.     

线偏振激光在磁化等离子体中的调制不稳定性

 采用洛伦兹变换推导了线性偏振激光在磁化等离子体中的非线性色散关系,根据Karpman方法推导出横波的非线性控制方程,利用线性偏振激光在磁化等离子体中的非线性色散关系和非线性控制性方程,分析了在磁化等离子体中有限振幅的扰动引起的调制不稳定性,得到了线性偏振激光的调制不稳定的时间增长率与扰动波数之间的函数关系。分析结果表明：激光等离子体的临界面附近的磁调制不稳定性的时间增长率显著增大。     

Electron spin resonance and antiferromagnetic resonance of single crystals of yttrium doped with gadolinium

The nonlinear interaction of oscillation modes is investigated on the basis of Lagrangian formalism. Equations describing the changes of the bound mode amplitudes versus time, are obtained. It is shown that the energy transformation between different modes is of a periodic nature: if in the initial moment of time an appreciable part of the energy is contained, for example, in them-th mode, then after a period of timeTt (called a time of nonlinear interaction) the energy will be transformed to then-th mode. Expressions forT _t for cases with the interaction of two and three modes are obtained. As a particular case the process of nonlinear interaction of the electron “transverse” and “longitudinal” oscillations in the highfrequency hybrid resonance region of a “weakly” inhomogeneous plasma was investigated.     

弹性微管内气泡的非线性受迫振动

将弹性管壁视为膜弹性结构, 探索在外部声场作用下弹性微管内液柱-气泡-管壁构成耦合振动系统的非线性特征. 利用逐级近似法对系统非线性共振频率、基频和三倍频振动幅值响应、 分频激励共振机理等进行了理论分析. 基频和三倍频振动的幅-频响应数值结果表明: 气泡的轴向共振和管壁共振不能同时出现; 两垂直方向的振动均表现出幅值响应多值性, 进而可能引起系统的不稳定声响应; 三倍频振动在低频区的声响应强于高频区. 关键词： 弹性微管 受迫振动 非线性振动 气泡声响应     

Low-frequency current oscillations in a linear hot-cathode discharge

Low-frequency (ω ⪡ ω_pi) plasma oscillations in the transition regime between the high and the low current mode of a thermionic hot-cathode discharge are investigated experimentally. This type of current oscillation often shows chaotic dynamics. The current oscillations are related to nonlinear short wavelength potential structures which are identified as ion bunches formed by a fluctuating ionization front. These ion bunches are separated by ion holes and move at ion thermal speed rather than ion acoustic speed. By entering the negative space charge region of the cathode sheath, the ion bunches trigger electron current fluctuations that provide the required feedback mechanism for the observed wave train formation.     

Doppler-shifted cyclotron resonance in tungsten plates with atomic pure surface

The surface resistance of thin monocrystalline W plates as a function of the constant magnetic field H directed along the normal to the sample surface is studied in the r.f. spectrum region. The sample surface was cleaned in high vaccum (10^-11 torr) or coated with the monomolecular impurity film. The oscillating with the magnetic field part R_osc due to the Doppler-shifted cyclotron resonance is studied. The doppleron oscillation amplitude is found to depend on the surface state and increases with the crystal cleaning. The observed changes are caused by the increase of the specular reflection coefficient for resonance electrons. With the deviation of the magnetic field from the normal to the plate surface, the doppleron wave undergoes a collisionless magnetic Landau damping and the signal amplitude decreases down to values comparable with that of Gantmakher-Kaner oscillations. Cleaning of the surface (and related increase of specularity) gives rise to a further decrease of the doppleron amplitude and appearance of additional interference maxima induced by the Gantmakher-Kaner effect.     

光受激发射的稳定性

本文推导出描述三能级Laser工作过程的准经典方程组,并分析了输出振动的稳定性。在阈值以上,当T₁?T₂,q^-1时,只在1/(qT₂)>1时,输出振幅是稳定的(其中T₁,T₂,q^-1分别是分子纵向、横向及谐振腔的弛豫时间)。在稳定区域,趋向平衡的时间与T₁成正比。当分子线宽小于谐振腔宽度时,输出是不稳定的,而在1/(qT₂)减小时,平衡点由稳定变到不稳定时产生一个稳定的极限环,即输出振幅逐渐开始振动。关于稳定性的结论在气体Laser中是可以检验的。本文指出,在红宝石Laser中看到的输出不稳定,可能就是谐振腔的q很大的结果。     

Review of relaxation oscillations in plasma processing discharges

Relaxation oscillations due to plasma instabilities at frequencies ranging from a few Hz to tens of kHz have been observed in various types of plasma processing discharges. Relaxation oscillations have been observed in electropositive capacitive discharges between a powered anode and a metallic chamber whose periphery is grounded through a slot with dielectric spacers. The oscillations of time-varying optical emission from the main discharge chamber show, for example, a high-frequency (\sim 40~kHz) relaxation oscillation at 13.33Pa, with an absorbed power being nearly the peripheral breakdown power, and a low-frequency ( \sim 3 Hz) oscillation, with an even higher absorbed power. The high-frequency oscillation is found to ignite plasma in the slot, but usually not in the peripheral chamber. The kilohertz oscillations are modelled using an electromagnetic model of the slot impedance, coupled to a circuit analysis of the system including the matching network. The model results are in general agreement with the experimental observations, and indicate a variety of behaviours dependent on the matching conditions. In low-pressure inductive discharges, oscillations appear in the transition between low-density capacitively driven and high-density inductively driven discharges when attaching gases such as SF₆ and Ar/SF₆ mixtures are used. Oscillations of charged particles, plasma potential, and light, at frequencies ranging from a few Hz to tens of kHz, are seen for gas pressures between 0.133 Pa and 13.33 Pa and discharge powers in a range of 75--1200 W. The region of instability increases as the plasma becomes more electronegative, and the frequency of plasma oscillation increases as the power, pressure, and gas flow rate increase. A volume-averaged (global) model of the kilohertz instability has been developed; the results obtained from the model agree well with the experimental observations.     

Electromagnetically Induced Transparency of Two Intense Circularly-Polarized Lasers in Cold Plasma: Beat-Wave Second Harmonic Effect

In the present paper the problem of nonlinear interaction of two mildly-relativistic circularly polarized lasers in a cold plasma is studied in order to investigate electromagneticaily induced transparency （EIT）. Based on a relativistic kinetic model, by expansion of relativistic Lorentz factor in terms of lasers amplitude, we obtain the coupled nonlinear dispersion relations. It is observed that due to resonance in the second harmonic of plasma beat-wave, the new EIT pass-band is created in the high intensities of lasers. The effect of amplitude and frequency variation on the dispersion is numerically investigated.     

Numerical simulations of pulsating detonations: II. Piston initiated detonations

Extremely long time, high-resolution one-dimensional numerical simulations are performed in order to investigate the evolution of pulsating detonations initiated and driven by a constant velocity piston, or equivalently by shock reflection from a stationary wall. The results are compared and contrasted to previous simulations where the calculations are initiated by placing a steady detonation on the numerical grid. The motion of the piston eventually produces a highly overdriven detonation propagating into the quiescent fuel. The detonation subsequently decays in a quasi-steady manner towards the steady state corresponding to the given piston speed. For cases where the steady state is one-dimensionally unstable, the shock pressure begins to oscillate with a growing amplitude once the detonation speed drops below a stability boundary. However, the overdrive is still being degraded by a rarefaction which overtakes the front, but on a time-scale which is very long compared with both the reaction time and the period of oscillation. As the overdrive decreases, the detonation becomes more unstable as it propagates and the nature (e.g. period and amplitude) of the oscillations change with time. If the steady detonation is very unstable then the oscillations evolve in time from limit cycle to period doubled oscillations and finally to irregular oscillations. The ultimate nature of the oscillations asymptotically approaches that of the saturated nonlinear behaviour as found from calculations initiated by the steady state. However, the nonlinear stability of the steady detonation investigated in previous calculations represents only the very late time (O(10⁵) characteristic reaction times) behaviour of the piston problem.     

Collisionless self-consistent trapping of electrons into a nonstationary potential well: Dynamics of trapped electrons

The subject of investigation is the early stage of self-consistent trapping of electrons into a potential well that forms during the development of aperiodic Pierce instability. An analytical estimate for threshold gap δ_th = d _th/λ_D (λ_D is the Debye beam length) above which the trapping begins is derived. The nonlinear dynamics and distribution function of trapped electrons are studied in detail using a numerical method ((E, K) code). It is found that the trapped particles produce a localized steep-edge bunch, which “dangles” around between the electrodes, causing potential oscillations. Trapped electrons render the well shallower. Some of the particles in the bunch are shown to periodically escape to the electrodes. As a result, the potential oscillation amplitude fades away and the mean depth of the well increases.     

Modulational instability of relativistic ion-acoustic waves in aplasma with trapped electrons

The association between the modified Korteweg-de Vries solitary wave and the modulationally unstable envelope solitary wave in a weakly relativistic unmagnetized plasma with trapped electrons is discussed. The effect of trapped electrons modifies the nonlinearity of the nonlinear Schrodinger equation and gives rise to the propagation of the modulationally unstable ion-acoustic solitary wave. The amplitude of the envelope solitary wave increases while the number of trapped electrons decreases. The velocity of the solitary wave decreases with increasing ionic temperature and increasing particle velocities. The ion oscillation mode, which satisfies the nonlinear dispersion relation, is also derived. The theory is applied to explain space observations of the solar energetic flows in interplanetary space and of the energetic particle events in the Earth's magnetosphere     

An equation of oscillations for the arrangement of attracting solids on the equilibrium line of a balance with account for nonlinearity of up to the seventh power

The accuracy of calculating the gravitational constant, G, using a method based on the numerical integration of an equation of oscillations and a method based on the nonlinear oscillation theory is analyzed. Taking account of a higher (the seventh) power at an amplitude of 80 mrad reduces the error of calculating the moment of attraction forces by 47 times. This reduces the error of calculating G from 15 to 0.3 ppm.     

Self-sustained oscillations of turbulent pipe flow terminated by an axisymmetric cavity

Turbulent flow through a long pipe terminated by an axisymmetric cavity can give rise to self-sustained oscillations exhibiting a very strong coherence, as evidenced by the narrow-band character of corresponding amplitude spectra. These oscillations, associated with the turbulent axisymmetric jet passing through the cavity, are strongly influenced by the acoustic modes of the pipe. The frequencies of oscillation lie within or near the range of most “unstable” frequencies of the turbulent jet previously predicted by using concepts of inviscid hydrodynamic stability theory; consequently, these experiments show truly self-excited and strongly coherent “instability” of a fully turbulent, low Mach number (～10^?2), axisymmetric flow undergoing separation, corroborating previous experiments involving the external forcing of free turbulent jets. As flow velocity or cavity length is varied, both upward and downward jumps in oscillation frequency are observed; the sign (up or down) of these jumps tends to systematically alternate with increase of velocity or length. The role of these frequency jumps is, in effect, to allow the oscillation of the flow to remain “locked-on” to a pipe mode over a wide range of impingement length or flow velocity. Moreover, these jumps exhibit two types of behavior: for the first kind, the predominant frequency makes a relatively continuous transition between stages and the frequency of the neighboring stage appears as a secondary component; for the second kind, there is a dead zone (where no oscillation occurs) between stages. The consequence of externally exciting the system is strongly dependent on whether the self-sustaining oscillation is relatively near, or well away from, a frequency jump. During excitation, the amplitudes of pressure fluctuations in the cavity substantially exceed the corresponding no-flow values only in regions away from the frequency jumps; at locations of jumps, there can be significant attenuation of the no-flow excitation amplitude. For the type of frequency jump involving a “dead zone”, enhancement of a given mode of oscillation can be achieved by externally exciting not only the given mode, but also neighboring modes. For the other type of jump, involving a relatively continuous transition from one stage to the next, the predominant mode of oscillation following the jump is that mode giving maximum amplitude response to excitation before the jump.     

Experimental Evidence of Parametric Instabilities in an Unmagnetized Plasma Subjected to a Strong H.F. Electric Field

Experimental evidence of parametric excitation, by an intense external H.F. field, of an electron surface mode and an ion wave is presented. The pumping electromagnetic energy density is equal to or slightly larger than the thermal energy density of the electrons. The value of f_pc/f₀ (electron plasma frequency/external field frequency) is that for an electron surface wave. Depending on the pressure and field intensity, this decay instability can lead to three types of low frequency oscillations, with frequencies close to the ion plasma frequency. Two of these are described by Aliev and Silin's intense field theory: one is the volume ion plasma oscillation and the other a surface ion plasma oscillation. The third corresponds to no known ion eigenmode. Several other features of the theory by Aliev and co-workers are also confirmed experimentally, such as the harmonic excitation of the instability (nf₀ ≈ f_pe/√2, where n is an integer), the instability amplitude as a function of f_pe/f₀ (above threshold conditions), the value of the mismatch parameter as a function of field strength and ion mass, and the existence of a fine structure corresponding to the symmetric and antisymmetric electron surface oscillations. Even at high pump field strengths, the decay products are nearly monochromatic i.e. the plasma does not become turbulent.     

On stochastic stabilization of the Kelvin-Helmholtz instability by three-wave resonant interaction

An analytical investigation of the effect of three-wave resonant interactions with the linearly unstable wave is proposed. We consider the waves in the Kelvin-Helmholtz model, consisting of two fluid layers with different densities and velocities. We suppose that the velocity shear is weakly supercritical, the instability is of the algebraic type, i.e., the amplitude of the unstable wave grows linearly, and the instability occurs within the framework of a single mode. The amplitudes of two other waves taking part in the nonlinear interaction are assumed to be stable. The initial amplitudes of these waves are supposed to be small in comparison with the initial amplitude of the unstable wave. We present an analysis of the system of amplitude equations derived for this case using JWKB-method. As a result, we obtain equations that couple solutions pre- and post-passing the singular point, i.e., the point where the amplitude of the unstable wave has a local minimum. These equations give us the transformation rule of a parameter that characterizes the phase shift between fast and slow waves and defines the behavior of the system. This parameter is constant between two singular points and varies by chance at a singular point. As long as it stays positive, the amplitude of the wave remains limited and performs stochastic oscillations. If this parameter passes over zero, then we leave the region of stabilization and turn out in the region, where the amplitude grows infinitely. Accordingly, the transition to the region of instability happens stochastically. However, if the time interval, when the amplitude remains bounded, is large enough, the proposed scenario can be treated as a partial stabilization of instability.     

Nonstationary self-effect of wave fields in beat accelerators

The nonstationary self-effect of wave fields in the excitation of plasma oscillations is studied analytically and numerically. It is assumed that the self-effect is determined by the dependence of the relativistic electron mass on oscillation amplitude in the plasma wave excited at the beat frequency. The dynamics of the wave field self-effect are analyzed for a medium with the corresponding type of nonlinear response relaxation. It is shown that there are exact self-similar solutions of nonstationary equations in the form of compressible filaments (homogeneous wave ducts). The maximum amplitudes of electromagnetic and plasma waves are estimated on the basis of those solutions. Qualitative relationships and conclusions have been confirmed numerically. The cascade processes, by which the electromagnetic wave is scattered by plasma oscillations, are also taken into account. It is shown that cascading does not affect the estimate for the maximum amplitude of the plasma wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 671–690, June, 1996.The authors express their gratitude to E. I. Rakova for help in the preparation of this paper.For numerical calculations we used the working station granted by the Commission of the European Communities-DG III/ESPRIT-Project ACTCS 9282.This work was supported in part by the Russian Foundation for Fundamental Research (Project Code 96-02-19482) and the International Science Foundation (Project Code R8K300).     

Neutrino beam plasma instability

We derive relativistic fluid set of equations for neutrinos and electrons from relativistic Vlasov equations with Fermi weak interaction force. Using these fluid equations, we obtain a dispersion relation describing neutrino beam plasma instability, which is little different from normal dispersion relation of streaming instability. It contains new, nonelectromagnetic, neutrino-plasma (or electroweak) stable and unstable modes also. The growth of the instability is weak for the highly relativistic neutrino flux, but becomes stronger for weakly relativistic neutrino flux in the case of parameters appropriate to the early universe and supernova explosions. However, this mode is dominant only for the beam velocity greater than 0.25c and in the other limit electroweak unstable mode takes over.     

Relativisitic longitudinal non-Abelian oscillations in quark-antiquark plasma

We study the relativistic version of the non-Abelian, longitudinal wave in quark-antiquark plasma reported earlier by Bhat et al [Phys. Rev. D39, 649 (1989)]. We have also relaxed various approximations they made in their analysis. Both the quark and antiquark dynamics are taken in our analysis. The non-linearity arising from non-Abelian field as well as from plasma are included. Hence it is an exact longitudinal mode in relativistic quark-antiquark plasma, relevant to the study of quark gluon plasma. We find that earlier results are reproduced for non-relativistic and low amplitude oscillations, but are modified for relativistic or large amplitude waves. Further more, the above results are based on just four first-order equations for gauge invariant quantities derived from gauge covariant twelve first-order equations.