Scattered electromagnetic and plasma waves of a conducting cylinder coated with a compressible plasma

Summary When an electromagnetic wave is incident upon an interface between a free space and a compressible plasma, both an electromagnetic wave and a plasma wave are excited. This paper solves the scattering problem of an infinitely long conducting cylinder which is coated with a layer of compressible plasma. The source is assumed to be a magnetic line current which gives rise to an incident magnetic field with only an axial component. Complete expressions for both the scattered electric and magnetic fields and the guided pressure field are obtained. Scattering by a compressible plasma column and that by a conducting cylinder coated with an incompressible plasma layer are special cases of the present problem.     

Self-similar solution to the problem of the expansion of a cylindrical column of conducting gas in a longitudinal magnetic field

The nonstationary radial motion of a long cylindrical column of conducting gas in a time-varying longitudinal magnetic field is considered. Exact solutions are found by the method of separating the variables for the system of equations of magnetohydrodynamics on the assumption that the statistical pressure of the plasma at the boundary of the column is proportional to the external magnetic pressure. Some numerical computations are performed and the energetic characteristics of the interaction process are calculated. The ratio of the useful work done by the gas over an infinite time interval to the initial energy of the column is given as a function of the magnetic Reynolds number. We note that a similar method was applied in [1], where not only was the average temperature taken over the cross section, but the inertia of the medium was also neglected. When the inertia is taken into account, we have the additional requirement that the statistical pressure be proportional to the magnetic pressure at the boundary of the column.A physically similar model may be interpreted, for example, as the expansion of a compressible conducting gas column in a nonconducting incompressible fluid situated in a permeable cylinder of some radius R infinite along the axis of symmetry. The requirement that the statistical pressure be proportional to the magnetic pressure reduces to the condition that the external pressure on the boundary of the permeable cylinder of radius R should vary according to a specific law, which may easily be determined.     

Magnetic Field Effects on Axis-Switching and Instabilities in Rectangular Plasma Jets

The effect of an external magnetic field on the evolution of rectangular plasma jets is examined. Specifically investigated is the influence of a primarily axial magnetic field on the uniquely characteristic axis-switching phenomenon of rectangular jets and flow instabilities. The results indicate that the magnetic field decelerates the jet (more rapid spreading), prevents axis-switching and inhibits instabilities. The key physical mechanisms underlying the changes are (1) the ability of the magnetic field to reverse the direction of vorticity and (2) transfer of energy from kinetic to magnetic forms. This study has important implications for magneto-hydro-dynamic flow control and propulsion applications.     

A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

A self similar method is used to analyze numerically the one-dimensional, unsteady flow of a strong cylindrical shock wave driven by a piston moving with time according to an exponential law in a plasma of constant density. The plasma is assumed to be a non-ideal gas with infinite electrical conductivity permeated by an axial magnetic field. Numerical solutions in the region between the shock and the piston are presented for the cases of adiabatic and isothermal flow. The general behaviour of density, velocity, and pressure profiles remains unaffected due to presence of magnetic field in non-ideal gas. However, there is a decrease in values of density, velocity and pressure in case of magnetogasdynamics as compared to non-magnetic case. It may be noted that the effect of magnetic field on the flow pattern is more significant in case of isothermal flow as compared to adiabatic flow. The effect of non-idealness, specific heat exponent and magnetic field strength on the variation of shock strength across the shock front is also investigated.     

电感式磨粒监测传感器的磁场均匀性研究

在介绍电感式磨粒监测传感器结构原理的基础上 ,提出可采用检测线圈内部磁场均匀性的方法来弥补颗粒运动轨迹和流型变化带来的检测误差 ,以提高检测灵敏度 .通过分析不同几何尺寸的线圈中轴线上磁场的变化情况 ,并借助直螺线管的径向和轴向公式 ,对轴外磁场均匀性进行了探讨 .数学模型和优化结果表明 :在检测传感器线圈中部范围内为非匀强磁场 ,且呈非线性变化 ,细长管磁场相对均匀 ;当选取 R/ L <0 .2 ,磁场在线圈轴向长度范围内 ,径向在90 %范围内可近似看作均匀磁场 .所得结果可以确定传感器检测区域的磁场均匀性范围 ,为设计电感式磨粒监测传感器提供依据 .     

Electromagnetic disturbance created by an expanding conducting cylinder in a magnetic field

We examine the electromagnetic disturbance created by a linearly expanding, ideally conducting cylinder in an external uniform magnetic field with account for effects of order v/c (v is the boundary velocity).The problem of uniform magnetic field compression in a contracting cylindrical cavity with ideally conducting walls with radius decreasing linearly with time was solved in [1]. As far as we know the corresponding external problem has not been investigated.     

Radiation from a ring source around a compressible plasma column

The electromagnetic waves and plasma oscillations excited by a magnetic current ring source around an infinitely long compressible plasma column are studied. The governing partial differential equations for the electromagnetic and plasma modes are first formulated. They are then converted to ordinary differential equations by means of the Fourier transformation. The fields outside the plasma column are composed of a surface wave part contributed by the poles on the path of integration and a radiated part arising from branch points. The far zone radiation field is evaluated by the method of steepest descent through a saddle point. The presence of the plasma column modifies the radiated electromagnetic field of the ring source, and the radiation pattern depends on the plasma parameters in a complicated way. This work was supported by the U.S. Army Research Office - Durham (N.C.) and by the National Science Foundation.     

Influence of hall currents on the acceleration of a conducting gas in its own magnetic field

In [1] the author gave a solution of the problem of how the Hall currents influence the flow pattern of a conducting gas which is accelerated in a channel to high velocities in external electric and magnetic fields. The present article considers the influence of Hall currents on the acceleration of a plasma in its own magnetic field, i.e., the magnetic field induced by the currents flowing in the plasma.     

Three-dimensional rotational MHD flows in bounded volumes

Three-dimensional laminar flows of a viscous conducting gas in the neighborhood of a rotating disk are considered. The simultaneous impact of an external magnetic field, suction from the disk surface, and the axial temperature gradient as well as the action of the external axial magnetic field on three-dimensional flows in the neighborhood of rigid permeable surfaces are first studied. An exact analytic solution of the system of the boundary layer equations is obtained. It is found that the direction of the radial flow initiated in the boundary layer can be varied by changing the temperature ratio in the external flow and on the disk for various Prandtl numbers Pr. An approximate solution of the problem of flow in the rotating cylinder in the presence of a retarding cover is constructed on the basis of the approach developed for extended disks.     

Numerical simulation of plasma motion in a magnetic field. Two-dimensional case

A model of dynamics and heating of a plasma cloud in a magnetic field is considered in a two-temperature approximation. Based on a predictor-corrector-type implicit difference scheme, spreading of a plasma cloud in an external magnetic field is numerically simulated, and the influence of this field on spread dynamics is evaluated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 121–132, May–June, 2007.     

Temperature distribution for MHD flow between coaxial cylinders with discontinuity in wall temperatures

The temperature distribution in the MHD axial flow between two coaxial infinite cylinders under a transverse radial magnetic field has been found out when there is a discontinuity in the wall temperatures at a section of the channel. The numerical values of temperature distribution at large distances from the section have been worked out first for various Hartman numbers. To this is superimposed the perturbation introduced due to discontinuity. Near the region of discontinuity the approximate matching is done by using the finite difference method. Tables and graphs are given to depict the behaviour with various Hartman numbers. A relief of the temperature distribution is also given. It is found that the temperature shows a decreasing tendency with increasing Hartman number, a well-known characteristic of such type of problems.     

Simulation of the motion and heating of an irregular plasma

A physicomathematical model for plasma heating and confinement is formulated on the basis of some assumptions on the behavior of a dense plasma cloud in a magnetic field. The model allows for the ionization and heating of the plasma cloud by the surrounding deuterium plasma due to heat conduction and heating by a superthermal electron current. The expansion of a plasma cloud in an external magnetic field is studied using some simplifications in a magnetohydrodynamic approximation. Plasma heating is modeled by an external source. The basic equations include continuity, motion, energy, and magneticfield equations. For numerical solution of the problem, we developed a finitedifference scheme of the type of a universal algorithm with splitting into physical processes and spatial directions, which allowed us to obtain separate solutions of the equations of magnetic induction and gas dynamics. Calculations of the propagation of a plasma cloud heated by a source in an external magnetic field were performed. The mechanism of the effect of the magnetic field and heat source on plasma cloud expansion is determined. The results agree qualitatively with experimental data.     

Hydromagnetic capillary instability of a liquid jet with an axial flow

The hydromagnetic capillary instability of a jet of inviscid, impressible fluid of infinite electrical conductivity and subjected to a uniform axial magnetic field is studied, taking into account an axial flow in the jet. The results show that while the axial flow promotes instability due to capillary effects and the axial-flow effects can be completely suppressed by a magnetic field of sufficient strength.     

Equilibrium and stability of a z pinch in a multipole magnetic field

In the theoretical investigation of the dynamic stabilization of a current-carrying plasma filament by a high-frequency multipole magnetic field it is usually assumed that the cross section of the filament has a circular form in equilibrium [1, 2]. This considerably simplifies the calculations but it does not correspond to reality, since the surface of the plasma must be fluted in the multipole field. An attempt to estimate the influence of the deformation of the filament cross section on its stability against bending in the special case of quadrupole field was made in [3], in which the parameters were determined of the elliptical cross section corresponding to a plasma filament with current in a quadrupole field and an expression was found for the electrodynamic force acting on the filament in the case of long-wavelength kink perturbations. However, this force was calculated incorrectly in [3]. In the present paper a study is made of the equilibrium and stability of a current-carrying plasma filament against kink perturbations in the general case of a multipole stabilizing field. Under the assumption that the flute depth is small, the equilibrium form of the cross section of the current-carrying plasma filament in the multipole magnetic field is found and the components of the force exerted by the field on the perturbed filament are calculated. It is shown that the external field interacts with the current in the perturbed filament only in the case of a quadrupole field. The results are discussed in connection with the problem of multipole dynamical stabilization of a z pinch against kink perturbations.     

Resonance behaviour of viscoelastic fluid in Poiseuille flow in the presence of a transversal magnetic field

The oscillatory flow of a viscoelastic fluid in a circular pipe under the influence of a transversal magnetic field is studied. Exact solutions for the axial velocity and flow rate are presented. The velocity enhancement and the resonance behaviour are analysed both numerically and asymptotically in the case of small pipe radii. Approximations for the resonance frequencies and the achievable velocity enhancements are derived. Copyright © 2005 John Wiley & Sons, Ltd.     

Deformation of a long,current-carrying elastic cylinder of square cross-section: numerical solution by boundary integrals

The static, plane uncoupled problem of thermo-magnetoelasticity for a long elastic cylinder of square cross-section carrying a steady, axial electric current is investigated numerically by a boundary integral method. The lateral surface of the cylinder may be subjected, additionally, to an external distribution of pressures. The deformation is induced by the combined action of Joule heat, the magnetic forces due to the current and the external pressure. Following a smoothing process of the boundary, the applied numerical method yields the values of all quantities of practical interest at the boundary. The corresponding values in the bulk and the magnetic field in the space surrounding the conductor may be easily determined by quadrature. The results are represented graphically and discussed.     

Magnetic nanoparticles and concentrated magnetic nanofluids： Synthesis, properties and some applications

This paper reviews some recent results concerning chemical synthesis of magnetic nanoparticles and preparation of various types of magnetic nanofluids. Structural properties and behaviour in external magnetic field of magnetic nanofluids will be emphasized with relation to their use in leakage-free rotating seals and in biomedical applications.     

Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field

Experimental investigation is conducted to get insight into convective heat transfer features of the aqueous magnetic fluid flow over a fine wire under the influence of an external magnetic field. The convective heat transfer coefficient of the aqueous magnetic fluid flow around the heated wire is measured in both the uniform magnetic field and the magnetic field gradient. The effects of the external magnetic field strength and its orientation on the thermal behaviors of the magnetic fluids are analyzed. The experimental results show that the external magnetic field is a vital factor that affects the convective heat transfer performances of the magnetic fluids and the control of heat transfer processes of a magnetic fluid flow can be possible by applying an external magnetic field.     

横向磁场中轴向运动铁磁梁的磁弹性主共振

研究在外激励力与磁场作用下轴向运动铁磁梁的磁弹性非线性主共振问题．基于弹性理论和电磁理论,给出梁的动能和弹性势能表达式,根据哈密顿原理,推导出磁场中轴向运动铁磁梁的磁弹性双向耦合非线性振动方程．通过伽辽金积分法进行离散,得出两端简支边界条件下铁磁梁磁弹性非线性强迫振动方程．应用多尺度法对方程进行求解,得出幅频响应方程．最后通过算例,给出铁磁梁的幅频特性曲线、振幅-磁感应强度和振幅-外激励力曲线并进行分析．结果显示,在幅频响应曲线中铁磁梁的轴向运动速度、外激励力、轴向拉力越大,共振振幅越大;而磁感应强度越大,振幅越小．     

Spontaneous rotation in the exact solution of magnetohydrodynamic equations for flow between two stationary impermeable disks

Magnetohydrodynamic (MHD) flow of a viscous electrically conducting incompressible fluid between two stationary impermeable disks is considered. A homogeneous electric current density vector normal to the surface is specified on the upper disk, and the lower disk is nonconducting. The exact von Karman solution of the complete system of MHD equations is studied in which the axial velocity and the magnetic field depend only on the axial coordinate. The problem contains two dimensionless parameters: the electric current density on the upper plate Y and the Batchelor number (magnetic Prandtl number). It is assumed that there is no external source that produces an axial magnetic field. The problem is solved for a Batchelor number of 0–2. Fluid flow is caused by the electric current. It is shown that for small values of Y, the fluid velocity vector has only axial and radial components. The velocity of motion increases with increasing Y, and at a critical value of Y, there is a bifurcation of the new steady flow regime with fluid rotation, while the flow without rotation becomes unstable. A feature of the obtained new exact solution is the absence of an axial magnetic field necessary for the occurrence of an azimuthal component of the ponderomotive force, as is the case in the MHD dynamo. A new mechanism for the bifurcation of rotation in MHD flow is found.