Nonlinear resonance of plasma waves in the thermal irregularities of ionospheric plasma

We study the effect of striction plasma density disturbances on the generation intensity of longitudional cold and plasma oscillations due to polarization of the magnetic field-aligned ionospheric plasma irregularities with δN_o<0 by a powerful radio wave. It is assumed that the plasma density level inside the irregularity intersects the upper-hybrid resonance level, in the vicinity of which the cold oscillations excited directly by a powerful radio wave are transformed to shorter-wave plasma oscillations. We consider the short plasma wave limit to reduce the problem to a system of two coupled equations for the cold wave induction and plasma wave electric field. The first equation is supplemented by a local source equal to the integral of the plasma wave electric field in the resonance region. The second equation involves the cold wave induction at the resonance point and describes the electric field of interacting waves in the resonance vicinity. We use simplifications connected with the small absorption of plasma waves propagating inside the irregularity and weak radiation of these waves outside the irregularity. These conditions correspond to the generation of eigenmodes of plasma oscillations trapped in the irregularity. We have obtained a resonance-type nonlinear equation for the electric field intensity (or energy flux) of eigenmode plasma waves with allowance for striction disturbances of the plasma density profile in the resonance region. It is shown that the striction expulsion of plasma is responsible for the occurrence of coefficients describing the change in the intensity of excitation and radiation of plasma waves at the irregularity boundary. Such an expulsion leads to variations of the efficient generation band of plasma eigenmodes with the total phase increment of the wave in the irregularity. It also leads to a change in the phase shift of the plasma wave reflected from the resonance. These coefficients and the nonlinear phase shift are expressed in terms of real wave functions of the nonlinear Airy equation which describes the electric field of the excited waves in the resonance vicinity when the dissipation is absent. Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 3, pp. 270–297, March, 1998.     

Dispersion properties and field structures of eigenmodes of nonuniform plasma waveguides in a longitudinal magnetic field

We study the field structure and dispersion properties of a hybrid eigenmode guided by a nonuniform magnetized plasma waveguide. It is shown that the rotational and quasi-potential waves contribute to the formation of such a mode in the whistler frequency range. Depending on the plasma density, the rotational component of the hybrid mode is determined by either waves with complex transverse wave numbers or whistler waves, or by true surface waves. In the presence of an axial nonuniformity of the plasma in a channel, the transverse field structure of the propagating mode changes, which is stipulated by changes in both the values of transverse wave numbers and their dependence on the radial coordinate. It is found that the spectrum of axial wave numbers of eigenmodes of a plasma waveguide undergoes a pronounced condensation when smoothing the waveguide walls. The damping of the hybrid mode of a nonuniform waveguide due to electron collisions is found and it is shown that collisional losses determine the damping of waves trapped in the waveguide in the experiments on ionization self-channeling of whistler waves. We have found the effect of “displacing” the strong field from the inner core to the background outer region of the waveguide with increasing plasma density on its axis and broadening background region. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 7, pp. 607–617, July 2006.     

Determination of the Phase Shift of a Plasma Wave Reflected from the Edge of a Small-Scale Irregularity

In our papers [1,2], a nonlinear theory has been developed for excitation of plasma-wave eigenmodes inside field-aligned small-radius inhomogeneities in experiments on ionospheric heating by powerful radio waves. This theory takes into account the striction effects of plasma expulsion near the plasma resonance level where a trapped wave is reflected from the edge of the irregularity. The results of this theory depend strongly on the phase of the linear (i.e., weak-field) reflection coefficient. In this paper, we calculate this parameter for irregularities of different shapes.     

Radial magnetosonic eigenmodes in a toroidal plasma with an ion-ion hybrid layer

The conditions for excitation of a standing magnetosonic wave structure in the region between the ion-ion hybrid cut-off layer and an antenna situated near the wall on the outside of a toroidal plasma have been derived. It is shown that low-order radial eigenmodes may be excited under usual conditions, but the order of the mode increases as the plasma density and its size increase. Such radial eigenmodes are shown to be more easily tracked than the usual magnetosonic toroidal eigenmodes.     

Penetration of an ordinary wave into a weakly inhomogeneous magnetoplasma at oblique incidence

A theory is given describing the propagation of high-frequency electromagnetic waves in a plane-stratified weakly inhomogeneous plasma. The density gradient is supposed to be perpendicular to the external magnetic field and the wave vector is expected not to be generally parallel to the plane given by both the preceding vectors. The analysis points out that the ordinary wave can penetrate through the plasma resonance region if the direction of vacuum wave vector is chosen appropriately. Analytical expressions for the reflecion and transmission coefficients are obtained and their dependence on the direction cosines of the wave vector of the incident is studied. The paper further shows in outline that, after transmission through the plasma resonance, the ordinary wave is transformed into an extraordinary wave and the latter is reflected back to the region of the hybrid resonance. In this region the extraordinary wave is fully transformed into the Bernstein modes.     

Resonance Y-type soliton solutions and some new types of hybrid solutions in the(2+1)-dimensional Sawada–Kotera equation

In this paper, based on N-soliton solutions, we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in (2+1)-dimensional integrable systems. Then, we take the (2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint. Next, by the long wave limit method, velocity resonance and module resonance, we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves, breather waves, high-order lump waves respectively. Finally, we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic.     

Doppler-shifted cyclotron absorption of electron Bernstein waves via N( parallel)-upshift in a Tokamak plasma

Extraordinary (X) waves are perpendicularly injected for electron Bernstein (B) wave heating into an Ohmically heated plasma from the inboard side in the WT-3 tokamak. Measurements show that absorption does not take place at the electron cyclotron resonance layer nor the upper hybrid resonance layer, but does happen midway between them. This is consistent with the ray tracing prediction, i.e., the poloidal field and poloidal inhomogeneity of toroidal field lead the B waves to have a large parallel refractive index N( parallel) (>1), and the B waves are damped away via the Doppler-shifted cyclotron resonance.     

Effects of Spatial Variation of Thermal Electrons on Whistler-Mode Waves in Magnetosphere

A ray-tracing method is developed to evaluate the wave growth/damping and specifically propagation trajectories of the magnetospherically reflected Whistler-mode waves. The methodology is valid for weak wave growth/damping when plasma is comprised of a cold electron population and a hot electron population, together with background neutralizing ions, e.g. protons. The effect of anisotropic thermal electrons on the propagation of Whistler-mode waves is studied in detail. Numerical results are obtained for a realistic spatial variation model of plasma population, including the cold electron density distribution, and the thermal electron density and temperature distribution. It is found that, analogous to the case of the typical cold plasma approximation, the overall ray path of Whistler-mode waves is insensitive to the thermal electron density and temperature anisotropy, and the ray path reflects where wave frequency is below or comparable to the local lower hybrid resonance frequency flhr. However, the wave growth is expected to be influenced by the thermal electron population. The results present a first detailed verification for the validity of the typical cold plasma approximation for the propagation of Whistler-mode waves and may account for the observation that the Whistler-mode waves tend to propagate on a particular magnetic shell L where the wave frequency is comparable to fthe.     

Analysis of long wavelength electromagnetic scattering by a magnetized cold plasma prolate spheroid

Abstract

Using dielectric permittivity tensor of the magnetized prolate plasma, the scattering of long wavelength electromagnetic waves from the mentioned object is studied. The resonance frequency and differential scattering cross section for the backward scattered waves are presented. Consistency between the resonance frequency in this configuration and results obtained for spherical plasma are investigated. Finally, the effective factors on obtained results such as incident wave polarization, the frequency of the incident wave, the plasma frequency and the cyclotron frequency are analyzed.     

电磁波在大面积等离子体片中传播特性的分析

脉冲磁约束线形空心阴极放电形成的大面积等离子体片可应用于等离子体天线、隐身及模拟超音速飞行器表面的等离子体鞘套. 本文首次利用实测等离子体片电子密度时空分布和横向场传播矩阵法, 研究了电磁波在等离子体片中反射率、透射率、吸收率随频率及脉冲放电时间的变化特征. 结果表明: 极化方向平行磁场的电磁波, 在小于截止频率的低频带内具有较高的反射率和吸收率, 增大电流, 反射率增加, 吸收率下降, 在大于截止频率的高频带内反射率和吸收率较低, 增大电流, 透射率下降, 吸收率升高; 极化方向垂直磁场的电磁波在高混杂谐振频率附近存在吸收率明显增强的吸收带, 谐振吸收峰值与放电电流无关; 脉冲放电期间, 电磁波的反射率、透射率与吸收率由不稳定过渡到稳定的时间约为100 μs, 过渡时间随着放电电流的增加而增大, 极化方向垂直磁场、小于截止频率的电磁波在稳定放电阶段谐振吸收较强. 本文的研究成果对利用等离子体片实现对电磁波的稳定高反射作用具有重要意义.     

Soliton Molecules,Asymmetric Solitons and Hybrid Solutions for(2+1)-Dimensional Fifth-Order Kd V Equation

Soliton molecules were first discovered in optical systems and are currently a hot topic of research. We obtain soliton molecules of the(2+1)-dimensional fifth-order Kd V system under a new resonance condition called velocity resonance in theory. On the basis of soliton molecules, asymmetric solitons can be obtained by selecting appropriate parameters. Based on the N-soliton solution, we obtain hybrid solutions consisting of soliton molecules,lump waves and breather waves by partial velocity resonance and partial long wave limits. Soliton molecules,and some types of special soliton resonance solutions, are stable under the meaning that the interactions among soliton molecules are elastic. Both soliton molecules and asymmetric solitons obtained may be observed in fluid systems because the fifth-order Kd V equation describes the ion-acoustic waves in plasmas, shallow water waves in channels and oceans.     

Lower hybrid resonance at low collision frequencies

For low collision frequencies the power transfer to a plasma in the domain of the lower hybrid resonance is measured under linear conditions. Geometrical resonances due to radial eigenmodes are observed to be strongly suppressed as compared to theoretical expectations.     

The influence of striction density perturbations on the excitation of plasma oscillations inside thermal inhomogeneities of plasma

In this paper, we continue our studies begun in [Izv. Vyssh. Uchebn. Zaved., Radiofiz.,41, No. 3, 270 (1998)].Calculating the coefficients and nonlinear phase shift in the equation for plasma-wave intensity introduced in the eralier paper, we have solved the problem of the influence of striction perturbations of the plasma density on the excitation of shortwave plasma oscillations by an electromagnetic wave; the above oscillations are captured in a volume of inhomogeneities, which are extended along the magnetic field and have reduced electron density that crosses the level of the upper-hybrid resonance. The dissipative processes of absorption and emission of plasma waves beyond the inhomogeneity are assumed to be weak. The variation of excitation and reflection of plasma waves from the resonance level due to deformation of the plasma- density profile is described. The band of effective generation of eigenmodes of captured oscillations as a function of the total wave-phase increment in an inhomogeneity is determined. The effect of penetration of the field of a high-power plasma wave into the non-transmittance region as a result of the striction expulsion of plasma is calculated. With allowance for the nonlinear phenomena in question, we estimated the heating of artificial inhomogeneities of thermal origin as a result of collisional absorption of the plasma oscillations excited in a volume of inhomogeneities under the action of a high-power radio wave. The materials of this paper were reported at the IIIrd International School on Space Plasma Physics. Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow Region, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 10, pp. 1226–1247, October 1998.     

低频Alfvén波多波相干加热粒子模拟

采用粒子模拟方法,考察多支沿背景磁场方向传播的低频Alfvén波对磁化等离子体的加热过程,研究不同频率的多支低频Alfvén波相干加热.结果表明可以通过调整波的频率比实现对非共振加热过程和随机加热过程这两个阶段的强化.符合相干共振条件的多波加热会强化低频Alfvén波对粒子拾取,进而强化非共振加热,明显提高加热效率.在多波加热的过程中,如果多支波之间的频率差足够小,则多波在调制过程中会形成波包.波包的出现标志着粒子各向异性的强化,从而提升随机加热效率.     

Peculiarities of electron-beam interaction with waves in partially plasma-filled corrugated waveguide

It is shown when the cross-section of a waveguide is partially filled by magnetized plasma, slow and fast E-waves can exist simultaneously at the same frequency, which is lower than the plasma frequency. In the case of spatially periodic corrugation of the waveguide wall, the waves can be coupled, forming new waves with hybrid properties in a certain frequency range. The interaction of an electron beam with the hybrid waves differs from the interaction with a slow plasma wave in a waveguide with smooth walls or with the wave in an evacuated corrugated waveguide. For example, when two waves traveling in the same direction are coupled, the increments of the hybrid waves have values on the order of but somewhat smaller than those of the increment of a slow plasma wave in a smooth waveguide.Moscow Radio-Engineering Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 34, No. 7, pp. 825–836, July, 1991.     

Generation of electromagnetic waves by a rotating plasma

Generation of electromagnetic waves by an annular shell of plasma rotating in crossed radial electrostatic and axial magnetic fields in a cylindrical resonator is investigated theoretically. Dispersion relations are obtained describing the interaction of the waves with the plasma. It is shown that generation of waves by a narrow plasma shell is possible due to a cyclotron resonance, Čerenkov resonance, or plasma resonance. Here we consider a Čerenkov resonance, where the velocities of the plasma components and the phase velocities of the waves are perpendicular to the constant magnetic field. The frequencies and growth rates of the waves are found under conditions of the above-mentioned resonances in a uniform and in a nonuniform plasma shell. Advantages and disadvantages of wave generation under various conditions are noted. Zh. Tekh. Fiz. 69, 16–21 (February 1999)     

Modulation instability of lower hybrid waves leading to cusp solitons in electron–positron(hole)–ion Thomas Fermi plasma

Following the idea of three‐wave resonant interactions of lower hybrid waves, it is shown that quantum‐modified lower hybrid (QLH) wave in electron–positron–ion plasma with spatial dispersion can decay into another QLH wave (where electron and positrons are activated, whereas ions remain in the background) and another ultra‐low frequency quantum‐modified ultra‐low frequency Lower Hybrid (QULH) (where ions are mobile). Quantum effects like Bohm potential and Fermi pressure on the lower hybrid wave significantly reshaped the dispersion properties of these waves. Later, a set of non‐linear Zakharov equations were derived to consider the formation of QLH wave solitons, with the non‐linear contribution from the QLH waves. Furthermore, modulational instability of the lower hybrid wave solitons is investigated, and consequently, its growth rates are examined for different limiting cases. As the growth rate associated with the three‐wave resonant interaction is generally smaller than the growth associated with the modulational instability, only the latter have been investigated. Soliton solutions from the set of coupled Zakharov and NLS equations in the quasi‐stationary regime have been studied. Ordinary solitons are an attribute of non‐linearity, whereas a cusp soliton solution featured by nonlocal nonlinearity has also been studied. Such an approach to lower hybrid waves and cusp solitons study in Fermi gas comprising electron positron and ions is new and important. The general results obtained in this quantum plasma theory will have widespread applicability, particularly for processes in high‐energy plasma–laser interactions set for laboratory astrophysics and solid‐state plasmas.     

Adaptive finite elements method for the solution of the Maxwell equations in inhomogeneous magnetized plasma

The wave propagation in magnetized cold plasma inhomogeneous in one direction (the slab plasma model) involves solution of the set of the second order ODE’s. Several problems have to be treated in the numerical solution. An initial value approach cannot be used for the boundary problem where exponentially growing solution exists. The equations are stiff (the O and X modes have different wavelengths) and there is also, in the cold plasma model, a singularity of the solution in the upper hybrid resonance. For the boundary problem of this type, the finite elements method fits well. To remove the singularity at UHR, we introduce small ad hoc collisions. In warm plasma, the O and X waves are converted in the UHR region to the electron Bernstein waves. It is well known that the power of the O and X waves absorbed in UHR region in a weakly collisional cold plasma represents the power converted to EBW. To minimize the computational requirements of the algorithm, an adaptive mesh, based on the local error estimation, is constructed. The code is used to analyze electron cyclotron emission (ECE) from the spherical tokamak MAST.     

Radiated Electromagnetic Waves in an Inhomogeneous Magnetoplasma near the Upper Hybrid Frequency

Properties of several plasma waves in a wavenumber space are investigated in a hot magnetized plasma. The properties are applied to investigate ray trajectories of radiated electromagnetic waves to an inhomogeneous plasma and mode conversion of the extraordinary mode into electrostatic cyclotron harmonic waves at the upper hybrid frequency layer. The wave fronts of the mode-converted cyclotron harmonie wave from the extraordinary wave are made clear. Furthermore, ray trajectories of radiated cyclotron harmonic waves and the mode-converted extraordinary mode are obtained.     

Experimental observations of mode-converted ion cyclotron waves in a tokamak plasma by phase contrast imaging

The process of mode conversion, whereby an externally launched electromagnetic wave converts into a shorter wavelength mode(s) in a thermal plasma near a resonance in the index of refraction, is particularly important in a multi-ion species plasma near the ion cyclotron frequency. Using phase contrast imaging techniques (PCI), mode-converted electromagnetic ion cyclotron waves have been detected for the first time in the Alcator C-Mod tokamak near the H-3He ion-ion hybrid resonance region during high power rf heating experiments. The results agree with theoretical predictions.