Screening of low-frequency electric fields by a set of screens: A thin unclosed ellipsoidal sheath plus a thin-walled penetrable cylinder

The problem of penetration of a low-frequency electric field into a thin-walled infinitely long conducting cylinder with an ideally thin unclosed ellipsoidal perfectly conducting sheath on its axis is solved by the method of paired equations, which is combined with addition theorems and relevant averaged boundary conditions. The effect of the vertex angle of the unclosed ellipsoidal sheath on the coefficient of field attenuation inside the sheath is numerically evaluated for different screen geometries.     

Shielding of low-frequency electric fields by a set of shields consisting of a thin unclosed spherical sheath and thin-walled pervious spherical shell

The penetration of low-frequency electric fields through a thin-walled spherical conducting shell in the presence of a thin unclosed spherical perfectly conducting sheath is considered. The problem is solved by the method of pair summational equations with averaged boundary conditions. The effect of the central angle of the unclosed spherical sheath and field source position on the field attenuation inside the closed thin-walled shell is studied numerically for different shell thicknesses and materials.     

基于行波管螺旋导电面模型的空间电荷场研究

通过分析行波管螺旋导电面模型中的电磁场，给出了色散和耦合阻抗计算公式，并深入研究了非线性理论中的空间电荷降低因子.结果表明，螺旋导电面模型相对理想导电圆筒中的空间电荷降低因子在较高频段变化不大.空间电荷降低因子的变化反映了螺旋线外电磁场对电子注的作用，同样的慢波结构，较高频率的电磁场应有较大的影响.因此，使用螺旋导电面模型在较高频段计算空间电荷降低因子是不合适的. 关键词： 行波管 非线性 螺旋导电面 空间电荷降低因子 色散 耦合阻抗     

The sheath criterion for a collisional plasma sheath at the presence of external magnetic field

The Bohm sheath criterion is modified for collisional plasma containing Boltzmann electrons and cold fluid ions at the presence of external magnetic field. Based on fluid model, the effects of the strength and the orientation of an external magnetic field on the upper and lower limits of Bohm sheath criterion have been studied by considering the collision frequency between ions and neutrals. The results show that the sheath criterion depends on the orientation and magnitude of magnetic field and the ion flow velocity at the sheath boundary.     

Field of an electric dipole surrounded by a nonuniform cylindrical plasma sheath

We analyze and solve the problem of the field of a dipole surrounded by a cylindrical plasma sheath with a piecewise-linear profile of dielectric permittivity ε including the point at which ε = 0. The predominant influence of the region in which ε = 0 on the formation of the dipole field is shown. The resonant properties of the solution in the case of a small cross-sectional size of the cylindrical sheath are studied. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 5, pp. 396–405, May 2007.     

磁场中等离子体鞘层的结构

采用流体力学理论，研究了斜磁场作用下的等离子体鞘层结构.在不同大小及方向的磁场作用下，对鞘层的离子，电子密度分布，离子流速度分布，电势分布和Bohm判据进行了讨 论.结果显示磁场对鞘层的结构有明显的影响.在静电力和洛仑兹力的作用下，离子流作螺旋进动，离子密度分布产生振荡. 关键词： 磁鞘 等离子体 磁场     

Self-consistent nonlinear resonance and hysteresis of a charged microparticle in a RF sheath

A self-consistent model is proposed to study nonlinear phenomena, such as secondary resonance and hysteresis in the vertical oscillations of a charged microparticle in a radio-frequency sheath. The motion of a single microparticle in the sheath is simulated by solving Newton's equation in which various forces acting on the particle are taken into account. The particle charging and the sheath electric field are described by a self-consistent model of the collisional radio-frequency sheath dynamics. It is found that the nonlinearity is related to the particle's charge, the sheath electric field, and the external excitation force, as well as the ion drag force and neutral-gas friction on the particle.     

Distribution characteristic of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction

It is of great importance for engineering applications to obtain the expression of scattering field for an ellipsoidal target irradiated by an electromagnetic wave from an arbitrary direction. Literature relevant to this problem is seldom found. In this paper, the scattering field for an ellipsoidal target is presented by utilizing the scale transformation of electromagnetic field and the rotation of coordinate system, with an electromagnetic wave projecting on the target from an arbitrary direction. The obtained result is in good agreement with the solution available from the literature if we consider the scale factors to be unity. Taking a conducting ellipsoidal target for sample, we perform the partial simulations of the ellipsoidal model and a plant leaf model by choosing different scale factors. The obtained results show that the distribution characteristic of scattering field is sensitively affected by the polarization of the incident wave and varies not much with the incident wave angle but changes with the observation point. At some points the scattering energy arrives at its maximum.     

Author's reply to "Good news: you can patch active plasma and collisionless sheath"

Godyak and Sternberg (2003) reassert their contention that one can obtain a satisfactory physical solution to the active plasma-collisionless sheath by patching together plasma and sheath. They choose to do it at an arbitrary point where the sheath electric field is kT/sub e/ /e/spl lambda//sub D/. If one tacks their sheath solution to the full plasma solution, then the field is infinity on the plasma side and finite on the sheath side. Alternatively, if one terminates the plasma solution where the plasma field is kT/sub e//e/spl lambda//sub D/, then one has continuity of electric field, but not of its gradient, since on the sheath side it is zero and on the plasma side of order L//spl lambda//sub D/, where L is the size of the plasma. Furthermore, in achieving continuity of the field, one has introduced discontinuities in the ion speed and in the particle densities. Thus, in no sense is a joining which denies the existence of a transition layer, smooth. J. Ockendon and H. Ockendon, my colleagues in the production of our paper describing the transition layer (Franklin et al., 1970), privately expressed disappointment in not finding a proof of the existence and uniqueness of our solution. Such a formal mathematical proof has been given recently by Slemrod (2002). Smooth joining of active plasma and collisionless sheath within the context of a fluid model or free fall model of the ion motion, does require a transition layer and of length scale intermediate between L and /spl lambda//sub D/.     

On the magnetization of a thin-walled cylindrical sheath with a magnetic field from the Rayleigh range inside

In terms of the general theory of magnetization of thin-walled sheaths, magnetization of a thin-walled indefinitely long circular cylindrical sheath that is placed in an external magnetic field and experiences the action of an internal magnetic field from the Rayleigh range is considered. It is shown that the solution of the problem can be reduced to solving infinite sets of nonlinear equations in the coefficients of Fourier series representing the components of the magnetization and internal magnetic field strength that are averaged over the thickness of the sheath and tangent to its surface. Approximate solutions to these sets of equations are obtained, and expressions for the coefficients multiplying the first terms of the series are given.     

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利用发射探针诊断了处于扩散等离子体流场中平板两侧的鞘层电势分布并给出鞘层厚度及边界电场。结合Child-Langmuir(CL)定律并利用一维流体模型,分析对比了鞘厚及边界电场。结果显示,上下游的鞘层呈现不对称结构,下游比上游厚,边界电场下游比上游弱,并且下游的预鞘还呈现类似虚阳极的结构。上下游CL鞘的厚度满足线性比例关系,比例系数约为1.2,且实验值与理论值非常接近。上下游CL鞘的边界电场与模型Te/(eλD)比较接近,上游Bohm鞘边界电场的实验结果与过渡区模型 较符合,但下游Bohm鞘的边界电场与现有模型有较大差异。     

Electrostatic problem for a thin, unclosed ellipsoidal shell and disk

The axisymmetric electrostatic problem of a thin, unclosed ellipsoidal shell and disk is solved. The capacitance coefficients are calculated for a representative set of values of the geometrical parameters of the conductors. Zh. Tekh. Fiz. 69, 1–5 (February 1999)     

Analytical solution for capacitive RF sheath

A self-consistent solution for the dynamics of a high voltage, capacitive radio frequency (RF) sheath driven by a sinusoidal current source is obtained under the assumptions of time-independent, collisionless ion motion and inertialess electrons. Expressions are obtained for the time-average ion and electron densities, electric field and potential within the sheath. The nonlinear oscillation motion of the electron sheath boundary and the nonlinear oscillating sheath voltage are also obtained. The effective sheath capacitance and conductance are also determined. It was found that: (1) the ion-sheath thickness S _m is √50/27 larger than a Child's law sheath for the DC voltage and ion current density; (2) the sheath capacitance per unit area for the fundamental voltage harmonic is 2.452 ϵ₀ /S_m, where ϵ₀ is the free space permittivity; (3) the ratio of the DC to peak value of the oscillating voltage is 54/125; (4) the second and third voltage harmonics are, respectively, 12.3 and 4.2% of the fundamental; and (5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 (λ_D/S_m)^2/3 (e ²n₀/mu_e), where n ₀ is the ion density, λ_D is the Debye length at the plasma-sheath edge, and u_e is the mean electron speed     

The effects of ion-neutral collision frequency on the plasma sheath dynamics for oblique entrance of ions into the sheath

Recently it has been shown that the magnetic field has significant effects on the characteristics of ions which enter the collisionless plasma sheath with an oblique incidence angle. Here, we have investigated these effects in collisional plasma sheath. Considering the ion-neutral collision, the basic equations of fluid model in a plasma sheath have been numerically solved in the presence of an external magnetic field where the ion collision frequency has a power law dependency to the ion flow velocity. The results show that the effects of magnetic field on the plasma sheath dynamics strongly depend on the ion-neutral collision frequency and its dependency to ion flow velocity.     

斜磁场中碰撞等离子体鞘层的玻姆判据

采用双流体模型研究了斜磁场作用下的碰撞等离子体鞘层的玻姆判据,讨论了磁场对鞘层玻姆判据的影响.结果表明:玻姆判据存在上限和下限,磁场强度、角度以及离子进入鞘层的状态都对离子马赫数的取值范围有影响.     

Levitation and dynamics of a collection of dust particles in afully ionized plasma sheath

Examines the dynamics of a collection of charged dust particles in the plasma sheath above a large body in a fully ionized space plasma when the radius of the large body is much larger than the sheath thickness. The dust particles are charged by the plasma, and the forces on the dust particles are assumed to be from the electric field in the sheath and from gravitation only. These forces will often act in opposite directions and may balance, making dust suspension and collection possible. The dust particles are supplied by injection or by electrostatic levitation. The ability of the sheath to collect dust particles, will be optimal for a certain combination of gravitation and plasma and dust particle parameters. In a dense dust sheath, the charges on the dust particles contribute significantly to the total space charge, and collective effects become important. These effects will reduce the magnitude of the sheath electric field strength and the charge on the dust particles. As dust particles are collected, the dust sheath is stretched and the largest dust particles may drop out, because the sheath is no longer able to suspend them. In a tenuous dust sheath, the inner layer, from the surface and about one Debye length thick, will be unstable for dust particle motion, and dust will not collect there. In a dense dust sheath, collective effects will decrease the thickness of this inner dust-free layer, making dust collection closer to the surface possible. By linearization of the force and current equations, the necessary and sufficient conditions for a stable dust sheath are found. The authors consider conditions which resemble those of planetary system bodies, but the results may also be of relevance to some laboratory plasmas     

Electron states and light absorption in a thin ellipsoidal quantum lens in the presence of a strong magnetic field

Within the framework of adiabatic approximation the energy levels and direct interband light absorption in a thin ellipsoidal quantum lens in the presence of a magnetic field are studied. Analytical expressions for the particle energy spectrum and for the absorption threshold frequencies in the regime of strong size quantization for the cases of ellipsoidal and spherical cross-section segments are obtained. Selection rules for quantum transitions are revealed.     

Model of plasma sheath region using variable particle weights

The interaction of low temperature plasma with a probe is studied in this contribution. We would like to describe the transport of charged particles through the sheath region. A model of this sheath region is created. In the model we describe ions and electrons by molecular dynamics, with Monte Carlo method for collisions. This model is one dimensional in space and two dimensional in the velocity space and was modified for planar, spherical and cylindrical geometry. To reduce the number of particles, we introduced variable weights of particles. This approach enables to speed up the algorithm and to correctly compute the values of the electric current.     

Behaviour of a dust cloud in the plasma sheath adjacent to a conducting wall

The location of a dust cloud under the combined influence of the sheath electric and gravity forces is studied. It is found that a charged dust cloud, which is located at a distance of several electron Debye radius from the wall, greatly affects the potential profile of the sheath electric field and of the potential well. The present theoretical results are in good agreement with experimental observations.