Anfachung und Dämpfung von Ionisationswellen in MHD-Kanälen und ihr Einfluß auf die effektive elektrische Leitfähigkeit,den effektiven Hall-Parameter und die mittlere Elektronentemperatur

The phase velocity, the amplification rate and the critical Hall parameter are theoretically determined for ionization waves in a weakly ionized plasma streaming across a strong external magnetic field and bearing a current flowing perpendicular to both the magnetic field and the stream velocity. The investigations hold for seeded rare gases at any degree of seed ionization. The critical Hall parameter β_c depends on the degree of ionization, the ionization energy and the temperatures of electron gas T₀ and neutral gas T_g · β_c is always greater than one, if 0 < T₀ — T_g ? T₀ holds. The three-dimensional treatment indicates the existence of waves with a nonvanishing wave vector component in the direction of the magnetic field. The influence of ionization waves on mean current density, mean Hall field intensity and mean electron temperature is determined up to second order terms in the relative fluctuations of the electron temperature. The amplification of ionization waves reduces the effective electric conductivity, the effective Hall parameter and the mean electron temperature compared to the undisturbed state. Similar results are also obtained for steady state homogeneous isotropic turbulence and a special case of axially symmetric turbulence. Furthermore, a component of the electric field in direction or in opposite direction to the magnetic field vector may be generated by non isotropic and non homogeneous turbulence.     

Längsfeldstärke,Elektronentemperatur, mittlere Neutralgasdichte,Ionenstromdichte auf die Wand und mittlere Entladungsstromdichte in der Freifallsäule bei hohem Ionisationsgrad

On the basis of a foregoing paper new theoretical results for the positive column at low pressure and strong ionization, especially for discharges in noble gas ion lasers, are given. The mean velocity v_n0 of the neutral atoms reemitted from the wall is taken into account. The electric conductivity is calculated for an argon plasma. The formulas connecting the electron temperature, the mean neutral gas density, and the electric field strength are derived. The electron temperature, the axial electric field intensity, the degree of ionization, the axial electron drift velocity, the ion flux to the wall, and the force density causing the main part of gas pumping along the column are calculated as functions of the product of the mean current density and the tube radius, and of v_n0 for argon. The axial drift velocity of the electrons is still smaller than the mean thermal electron velocity for high discharge currents, except at very low gas pressures. In general, the ion flux to the wall is not directly proportional to the discharge current. The factor for the determination of the charged particle density by means of probe measurements at the wall is discussed. The self-magnetic field affects the discharge only at high electron temperature, high degree of ionization, and relatively large tube radius, i.e. at high current density and low gas pressure in not too narrow discharge channels.     

非线性不可压缩霍尔磁流体方程组的精确解

得到了不可压缩理想霍尔磁流体方程组的平面波精确解,这些平面波是斜传播的左旋圆极化波或右旋圆极化波,并且涨落速度和涨落磁场通过波数联系起来。讨论了这些平面波解的叠加性质。当波的传播方向平行时,任意两支圆极化平面波都可以叠加;而当波的传播方向不平行时,只有极化方向相同,波数相同,且各自的旋度与自身都是同方向(或都是反方向)的两支圆极化平面波才可以叠加。     

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得到了不可压缩理想霍尔磁流体方程组的平面波精确解,这些平面波是斜传播的左旋圆极化波或右旋圆极化波,并且涨落速度和涨落磁场通过波数联系起来。讨论了这些平面波解的叠加性质。当波的传播方向平行时,任意两支圆极化平面波都可以叠加;而当波的传播方向不平行时,只有极化方向相同,波数相同,且各自的旋度与自身都是同方向(或都是反方向)的两支圆极化平面波才可以叠加。     

Surface gravity waves in deep fluid at vertical shear flows

Special features of surface gravity waves in a deep fluid flow with a constant vertical shear of velocity is studied. It is found that the mean flow velocity shear leads to a nontrivial modification of the dispersive characteristics of surface gravity wave modes. Moreover, the shear induces generation of surface gravity waves by internal vortex mode perturbations. The performed analytical and numerical study show that surface gravity waves are effectively generated by the internal perturbations at high shear rates. The generation is different for the waves propagating in the different directions. The generation of surface gravity waves propagating along the main flow considerably exceeds the generation of surface gravity waves in the opposite direction for relatively small shear rates, whereas the latter wave is generated more effectively for high shear rates. From the mathematical standpoint, the wave generation is caused by non-self-adjointness of the linear operators that describe the shear flow.     

Three-dimensional structures of MHD flow in a disk generator

Three-dimensional nonuniform plasmas and boundary layers have been studied numerically under an MHD interaction. The nonuniform plasma of “streamer” owing to weak ionization of seed material has a spiral structure in the r-&thetas; plane, and the plasma becomes almost uniform between the walls in the r-z plane. This structure is almost the same as that in our previous paper (1997), where the gas (heavy particle) properties are assumed to be invariant and steady. In addition to the streamer, the nonuniform plasma of “domain” owing to weak ionization of noble gas is revealed. The domain has the structure perpendicular to the streamer. In a strong MHD interaction case, the static pressure considerably increases in the upstream region of a generation channel, and the pseudo-shock waves appear in the generator, but the plasma is almost uniform along the &thetas; direction. The boundary layer in the strong MHD interaction is considerably thick, and in the broad region near the wall the Hall current flows reversely. In the weak MHD interaction case, the plasma forms a nonuniform structure along the &thetas; direction, and the Hall current does not always flow in the opposite direction even on the insulator wall since the azimuthal electric field is not zero     

Mutual rectification of alternating currents in graphene in the field of two electromagnetic waves

For graphene placed in a dc magnetic field and exposed to two electromagnetic waves of the same polarization but different frequencies, an expression for the direct current density in a direction perpendicular to the polarization plane of the waves is derived. The direct current component is nonzero for the wave frequency ratio equal to two; it is proportional to the magnetic field strength, the electric field strength of the higher-frequency wave, and the squared electric field strength of the lower-frequency wave. The physical mechanism of the current generation is similar to the Hall effect.     

Excitation of an elastic half-space by a buried line source of conical waves

A formal solution is obtained to the problem of a buried line source of conical waves propagating at a constant phase velocity c in an isotropic elastic half space. By applying the boundary conditions at the free surface, it is determined that the reflected field, in addition to the incident field, requires addition of a scalar potential and two components of the vector potential. The latter is in contrast to the case of cylindrical waves where only one component of the vector potential is needed. The formal solution for the conical wave source goes over to that for the two dimensional cylindrical wave case in the limit of infinite phase velocity c.     

无旋性前进重力波传递在均匀流中的Lagrangen解析解与试验验证Ⅱ.试验验证

针对文献[1]中的无旋性自由表面周期性规则前进重力波传递在均匀流中,本文以与前进波波向同向与反向的均匀流两种特例情况,进行试验测量,所得的波形曲线、流速分布、流体质点的运动轨迹与运动周期及其质量传输速率与Lagrange平均高程等特性,均与文献[1]中全以Lagrange方式所得的三阶解结果符合得很好.这证实本研究取定的标注流体质点的参数,正好为其在原静止水中的位置坐标值.同时亦证实波流场中由流体质点所构成的波形曲线,其波长皆同于(纯)前进波,而其传播速度为(纯)前进波波速与均匀流流速之和是具Doppler效应的;而流体质点的运动周期与其运动周期平均高程、及其质量传输速率扣掉均匀流流速等,都与(纯)前进波的相符.另外,亦揭示出流体质点的运动轨迹,在前进波波向与均匀流同向中,当流体质点在波谷断面处时沿前进波波向的流速分量为反向、零与正向时,则其形状分别为朝波向前进的扁长辐状余摆线、在波谷断面处成尖点朝下的滚轮状线与短辐形余摆线;而在前进波波向与均匀流反向中,当流体质点的质量传输速率为沿前进波波向为正向与零时,则其形状分别为朝波向前进的缩短的扁长辐形余摆线与长轴在前进波波向上椭圆形封闭曲线;而当流体质点的质量传输速率为反前进波波向,但质点在波峰断面处时沿前进波波向的流速分量分别为正向、零与反向时,则其形状分别为反波向前进的倒扁长辐形余摆线、在波峰断面处成尖点朝上的倒滚轮状线与倒短辐形余摆线.     

Magnetoacoustic waves in magnetizable liquids

Within the framework of the Neuringer-Rosenzweig equations, the solutions describing transverse linearly polarized and longitudinal plane-polarized magnetoacoustic waves are obtained for magnetizable liquids with an arbitrary orientation of the wavevector and the magnetization vector. In the general case, the group velocity vector of magnetoacoustic waves has a component orthogonal to the wavevector. For the solutions obtained here, the velocity of sound decreases from the maximal value for a wave propagating along the magnetization vector to the minimal value corresponding to a wave propagating at right angles to the magnetization vector. Exact solutions of the equations for magnetizable liquids are obtained in the form of the Riemann waves which are transformed into the magnetoacoustic waves under investigation for small perturbations of the parameters of the liquid and magnetic field.     

Streuung elektromagnetischer Oberflächen- und Volumenwellen an rauhen Oberflächen. Teil I. Allgemeine Grundlagen

Scattering of Electromagnetic Surface and Bulk Waves from Rough Surfaces. Part I. General Theory A classical theory of scattering of electromagnetic surface and bulk waves on rough surfaces (dielectrics or conductors) is given. The primary wave creates a surface polarization on the rough boundary presenting the source for the radiation of scattering. These roughness-caused polarization must be considered in the wave equations and in the boundary conditions of the fields, too. General expressions for the spectral power density of surface and bulk scattering waves will be given. The excitation of surface polarization can result from primary waves homogenously or inhomogenously.     

无旋性前进重力波传递在均匀流中的Lagrange解析解与试验验证Ⅰ.理论解析解

对于三维空间等深水中,无旋性自由表面周期性规则前进重力波传递在均匀流中的波流场,依质量守恒取一波长的流体质点的运动位移的波长平均高程,所得其标注参数恰为其在原静止水中的位置下,完全以Lagrange方式的参数控制式,解出此波流场至第三阶的全Lagrange形式解且得到检核验证;其中波流交互作用效应存在于Lagrange流速势中,使得波流场中的压力不受均匀流的影响.而Euler形式解所无法描述的流场特性,包括大于前进波周期的流体质点的运动周期,与其受前进波引起的质量传输速度、它们间的关系、及流体质点对其运动周期平均的高程与成因等,都说明是随流体质点所在的高程向下做指数函数样递减;而流体质点的三维空间螺旋曲线式的运动轨迹与烟线,其随均匀流的流向流速而变化的情况,例如其在均匀流于前进波波向有同向的流速分量时,是受流体质点恰在波谷断面处时的流速大小而变的形式,与其在均匀流于前进波波向有反向的流速分量时,则受流体质点恰在波峰断面处时的流速大小而变的形式,有很大不同的倒反形式甚至以封闭曲线形式呈现.最后,说明波流场变成稳定性运动流场时的特性,并证实其在无流时退化成纯前进波的情况.     

Analogien zwischen außerordentlichen und ordentlichen Wellen nach nichtorthogonaler Koordinatentransformation und die parabolischen Näherungsgleichungen

Within the limits of Linear Optics we treat analogies between ordinary and extraordinary waves in uniaxial media which become conspicuous through a nonorthogonal transformation of coordinates. To any ordinary wave solution in unbounded uniaxial media we can construct a corresponding extraordinary wave solution by interchanging electrical and magnetical field components. Boundary conditions for instance for ideal conducting plane surfaces approximately preserve their original form, if the optical axis or the middle wave vector are normal to the surface. The parabolic approximative equations for slowly varying amplitudes are derived, the polarisation of these waves being considered as a slowly varying quantity. Further these approximative equations are expanded to include frequency dispersion. Through the specified transformation we can simplify problems with extraordinary waves.     

Collective modes and the periodicity of quantum Hall stripes

We investigate the quantum Hall stripe phase at filling factor 9/2 at the microscopic level by probing the dispersion of its collective modes with the help of surface acoustic waves with wavelengths down to 60 nm. The dispersion is strongly anisotropic. It is highly dispersive and exhibits a roton minimum for wave vectors aligned along the easy transport direction. In the perpendicular direction, however, the dispersion is featureless, although not flat as predicted by theory. Oscillatory behavior in the absorption intensity of the collective mode with a wave vector perpendicular to the stripes is attributed to a commensurability effect. It allows us to extract the periodicity of the quantum Hall stripes.     

Traveling Wave Solutions of the Incompressible Ideal Hall Magnetohydrodynamics

The solutions of incompressible ideal Hall magnetohydrodynamics are obtained by using the traveling wave method.It is shown that the velocity and magnetic field parallel to the wave vector can be arbitrary constants.The velocity and magnetic field perpendicular to the wave vector are both helical waves.Moreover,the amplitude of the velocity perpendicular to the wave vector is related to the wave number and the circular frequency.In addition,further studies indicate that,no matter whether the uniform ambient magnetic field exists or not,the forms of the travelling wave solutions do not change.     

Zur Reflexion und Transmission elektromagnetischer Wellen bei senkrechtem Einfall auf ebene Grenzflächen zwischen unterschiedlich absorbierenden Medien

On Reflection and Transmission of Electromagnetic Waves Propagating Perpendicular to Plane Surfaces between Different Absorbing Media Born and Ladenburg already in 1911 pointed out that to describe reflection and transmission of electromagnetic waves through a plane surface between two different absorbing media in addition to the usual Poynting vectors of the running waves the so called “mixed” Poynting vector is necessary to maintain the balance of energy on the boundary plane. The flow of energy connected with this vector always points toward the region of maximal wastage of this energy and is closely related to the spatial modulation of the energy consumption within the partially standing interference pattern between the incoming and the reflected wave. In almost all substances the energy absorption is caused by the electric field whereas practically a direct contribution from the magnetic field can be neglected. But taking account of these magnetic effects we may get a better understanding of the mixed Poynting vector. To that end we add to the second of the Maxwell equations a quantity analogous to the electric current term in the first Maxwell equation. The amplitude of the “mixed” Poynting vector then turns out to depend essentially on the ratio of the energy absorption by the electric and the magnetic field. To confirm this fact we consider a medium, which shows in addition to the usual electric losses also magnetic ones of comparable magnitudes. In such materials the resultant energy consumption is distributed more similar to the spatial distribution of the fieldenergy. As a result the amplitude of the mixed Poynting vector disappears if the percentage of energy absorption by the electric and the magnetic field and their energy densities themselves are made equal to each other.     

Modulation of discharge parameters caused by acoustic wave

The propagation of acoustic waves in a partially ionized plasma in an external electric field is studied theoretically. It is assumed that an acoustic wave propagating through ionized gas causes only perturbations in ion gas. The problem is studied in the hydrodynamic approach and the basic equation is solved by means of Laplace transformation. It was found that waves can propagate in plasma also at other frequencies and wave numbers except the wave with the frequency and wave number of the neutral sound wave. Relations are derived for the density of the perturbation current and the intensity of modulated light irradiated from the plasma and the possible mechanism of the interaction of an acoustic wave with a discharge is taken into account. The necessity of further theoretical and experimental investigation is shown in conclusion.The author is much indebted to Prof. J. Kracík, Dr. Sc., for his valuable remarks and stimulating discussions.     

Dynamics of Spiral Waves Induced by Periodic Mechanical Deformation with Phase Difference

The dynamics of spiral waves under the influences of periodic mechanical deformation are studied. Here, the mechanical deformation propagating along the medium with phase differences are considered. It is found that weak mechanical deformation may lead to resonant drift of spiral waves. The drift direction and velocity can be changed by the wave length of the deformation. Strong mechanical deformation may result in breakup of spiral waves. The characteristics of breakup are discussed. The critical amplitudes are determined by two factors, i.e. the wave length and frequency of the periodic mechanical deformation. When the wave length of mechanical deformation is comparable to the spiral wave, simulation shows that the critical amplitude is substantially increased. As the frequency of the mechanical deformation is around 1.5 times of the spiral wave, the critical amplitudes are minimal.     

Quasilinear model of deformation of a stratified three-dimensionally inhomogeneous flow above a randomly inhomogeneous surface

We study the deformation of the wind velocity profile due to resonant interactions with waves radiated by the flow over a statistically homogeneous topography. The wind whose velocity vector changes its direction within a layer of finite thickness is considered. Quasilinear equations for the velocity components of the mean flow are derived under large Richardson, numbers and small Froude numbers. It is shown that the modulus of the wind velocity is constant in time and its direction angle satisfies the Riemann equation for simple waves. The flow deformation is determined by the average wave resistance force per unit square. The deformation of the wind velocity profile takes place within the layer between the Earth’s surface and the level where the wind change its direction to the opposite one. At large time scales, the wind velocity vector in this layer approaches the direction opposite to the near-surface one. Institute of Applied Physics, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 255–265, March 1999.