Enhanced Current Penetration in Plasmas Due to Anomalous Viscosity

An investigation is made of the anomalous current penetration in a plasma in the presence of turbulence-induced viscosity. Exact similarity solutions are found for the characteristic nonlinear diffusion equation determining the, current penetration and approximate solutions are presented, which describe the evolution of smooth initial current profiles. Comparisons with previous numerical results show good agreement. The results indicate that the anomalous viscosity should be very efficient in smoothing out sharp current gradients, but should not be important on length scales comparable to the minor radii of modern tokamaks.     

Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.     

有流存在时三层流体界面波的二阶Stokes波解

以小振幅波理论为基础，利用摄动方法研究了有背景流场存在时密度三层成层状态下的界面内波，得到了各层流体速度势的二阶渐近解及界面内波波面位移的二阶Stokes波解，并讨论了界面波的Kelvin-Helmholtz不稳定性.结果表明：有流存在的情况下三层密度成层流体界面内波的一阶渐近解(线性波解)、频散关系及二阶渐近解不仅依赖于各层流体的厚度和密度，也依赖于各层流体的背景流场；界面内波波面位移的二阶Stokes波解不仅描述了界面波之间的二阶非线性相互作用，也描述了背景流与界面波之间的二阶非线性相互作用；当每层流 关键词： 界面波 均匀流 二阶Stokes波解 Kelvin-Helmholtz不稳定性     

Pipe Shape Solution of Faddeev Model

Utilizing the results that the Faddeev model is equivalent to the mesonic sector of the SU（2） Skyrme model, where the baryon number current vanishes everywhere, some exact solutions including the vortex solutions of the Faddeev model axe discussed. The solutions are classified by the 2, the new multisoliton solutions are obtained and the pipe shape found. first Chern number. When the Chern number equals distribution of the energy density of the solutions are     

Model of a wedge-electrode corona discharge under saturation: Exact solutions

Analytical solutions for the distributions of the electric field potential and electric charge density are derived for the outer region of a steady-state unipolar corona discharge from an ideal wedge-shaped electrode under the conditions of space-charge-limited current. Two situations are considered: a corona is initiated only from the edge of the wedge and from the entire surface of the electrode. In the former case, general solutions are obtained by sewing together exact cylindrically symmetric solutions in the drift space and plane symmetric solutions in space-charge-free regions. In the latter case, the field distribution near the edge turns out to be self-similar, i.e., invariant under extensions in the cross-sectional plane of the wedge, with the center at the top of the wedge. For both models, the dependences of the saturation current per edge’s unit length on the apex angle and applied potential difference are obtained.     

Current transport along grain boundaries in d-wave superconductors

The use of a classic phase retrieval algorithm has been previously used to determine the local critical current J_c(x) along the length of grain boundary Josephson junctions that can be characterized using a standard s-wave model. The phase retrieval approach has been modified for use with d-wave dominated superconductors to allow for negative local currents along the boundary. In general solutions to the 1-D phase problem are not unique, however in the present work special constraints are employed experimentally to ensure uniqueness. The various current distribution solutions and their possible uniqueness are explored. The solutions are consistent with most existing d-wave Josephson junction boundary models and can be used to understand the basic current distribution along 45° YaBa₂Cu₃O_7−x grain boundary junctions as well as providing a means for mapping the location of self-generated flux cores.     

Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained.     

Analytical model of a corona discharge from a conical electrode under saturation

Exact partial solutions are found for the electric field distribution in the outer region of a stationary unipolar corona discharge from an ideal conical needle in the space-charge-limited current mode with allowance for the electric field dependence of the ion mobility. It is assumed that only the very tip of the cone is responsible for the discharge, i.e., that the ionization zone is a point. The solutions are obtained by joining the spherically symmetric potential distribution in the drift space and the self-similar potential distribution in the space-charge-free region. Such solutions are outside the framework of the conventional Deutsch approximation, according to which the space charge insignificantly influences the shape of equipotential surfaces and electric lines of force. The dependence is derived of the corona discharge saturation current on the apex angle of the conical electrode and applied potential difference. A simple analytical model is suggested that describes drift in the point-plane electrode geometry under saturation as a superposition of two exact solutions for the field potential. In terms of this model, the angular distribution of the current density over the massive plane electrode is derived, which agrees well with Warburg??s empirical law.     

Simple but Reliable Solutions for Spiral MRI Gradient Design

The efficiency of gradient design in MRI is limited by the simple fact that the gradient coil current and slew rate cannot exceed hardware threshold values. In spiral MRI, which requires gradients to be very rapidly switched between positive and negative values, minimization of the acquisition time is achieved by maintaining the current and slew rate as high as possible during the entire measurement. Since the current and slew rate compete against each other, an efficient gradient design consists of two parts in which current and slew rate are pushed alternatively to their limits. Values for these types of gradients can be obtained by solving numerically the equation of motion for the spiral trajectory. This paper shows that simple but reasonable mathematical approximations deliver reliable analytical solutions. Images obtained using these analytical solutions do not show evident distortions when compared with images obtained with numerical solutions.     

Moving cylindrical structures in pinch discharges

Moving cylindrical current structures in plasma are described in a simple model using the Davydov–Zakharov formalism. Numerical calculations confirm the existence of solutions with tangential discontinuities and the discontinuities in which the magnetic field changes its direction to opposite. Both subsonic and supersonic solutions are obtained.     

Dual solutions and stability analysis of flow and heat transfer of Casson fluid over a stretching sheet

The aim of the current study is to find out the dual solutions of the two-dimensional magnetohydrodynamic (MHD) flow of Casson fluid and heat transfer over the stretching sheet. The focus of the study is to examine the linear thermal radiation effects on dual solutions for both the steady and unsteady flow of Casson fluid over the stretching sheet under the influence of uniform magnetic field. The governing equations are formed as system of partial differential equations (PDEs). Using suitable transformations, the system of PDEs are converted into favorable nonlinear system of ordinary differential equations (ODEs). Simulations are performed in Maple 2015 to form the dual solutions in order to achieve the velocity, temperature, skin friction and heat transfer profiles of the Casson fluid over the stretching sheet. It is concluded that the dual solutions for the corresponding model are numerically stable. Furthermore, the upper branch solutions of the Casson fluid profiles are numerically stable as compared to the lower branch solutions. Results indicate that positive Eigen values of the MHD flow of Casson fluid provide stable profiles as compared to the negative Eigen values. It is believed that the current study would provide a base for the dual solution of the other types of the non-Newtonian fluid flows over various categories of surfaces.     

On the self-consistent states of a planar vacuum diode with an electron beam

The self-consistent stationary solutions for a planar vacuum diode with a monoenergetic electron beam are fully classified. Formulas are presented to calculate potential distributions of all types and the maximum electric current that can pass through the diode under steady-state conditions at an arbitrary applied voltage. The stability of the solutions is studied.     

Current transitions of superconducting whiskers

In long one-dimensional superconductors, such as whiskers, new, current-carrying states above the critical current were found that are due to spatially periodic solutions of the orderparameter and spatially periodic super and normal transport currents in parallel. These solutions lead to voltage steps in the DC voltage-current characteristic and are in good agreement with experiments.     

螺旋型爆磁压缩发生器初始电性能的高频分析

 从电流扩散方程和磁扩散方程出发，研究了在瞬态过程中螺旋型爆磁压缩发生器(HMFCG)的电流密度在螺线管导线中的分布以及感应电流密度在金属套筒中的分布情况，分析计算了爆磁回路初始充电过程中频率对HMFCG电感和电阻的影响，计算结果与实验测量吻合；这为进一步完善校正程序，更好地描述爆磁压缩过程奠定了基础。     

Asymmetrical solutions and role of thermal fluctuations in dc current driven extended Josephson junction

Extended Josephson junction driven by dc bias current is studied numerically. Two types of solutions, symmetrical and asymmetrical, are found. The current–voltage characteristic (IVC) is calculated. The symmetrical solutions form main hysteretic IVC and asymmetrical ones create an additional branch. Depending on the bias current value periodic, quasiperiodic and chaotic modes of the junction motion was observed. Dynamics of the junction affected by thermal fluctuations was analyzed. Stability of different states of the junction is discussed.     

On the structure of the hadronic neutral current

The coupling constants of the hadronic neutral current are determined independently of any gauge models. Essentially two solutions emerge from this analysis: either the isovector neutral current is predominantly vector and the isoscalar component predominantly axial-vector or vice versa.     

磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合

本文采用Hasegawa-Wakatani方程组研究磁化等离子体中静电漂移波和剪切阿耳芬波的非线性耦合。求得非线性方程组的偶极涡旋解。这些解属于本性电磁涡旋,对应的扰动磁场和纵向电流在涡旋边界上是连续的。 关键词：     

Tokamak equilibria with reversed current density

Observations of nearly zero toroidal current in the central region of tokamaks (the "current hole") raises the question of the existence of toroidal equilibria with very low or reversed current in the core. The solutions of the Grad-Shafranov equilibrium equation with hollow toroidal current density profile including negative current density in the plasma center are investigated. Solutions of the corresponding eigenvalue problem provide simple examples of such equilibrium configurations. More realistic equilibria with toroidal current density reversal are computed using a new equilibrium problem formulation and computational algorithm which do not assume nested magnetic surfaces.     

Near field of a loaded circular toroidal antenna

In this paper a special toroidal coordinate system is introduced in order to derive general solutions for the electric and magnetic fields from a toroidal antenna. These solutions depend on the current distribution on the toroid and are in integral forms. Some Fourier expansion techniques have been used in order to simplify these integral equations. The surface current is found under the assumption that the thickness of the toroid is thin compared to the wavelength, which leads to an analytic solution for the fields at the center. Many uniform loading impedances are used with the purpose of producing a plane-wave-like field at the center of the toroid.     

Note on Similarity Solutions for Electric Field Penetration into a Plasma with Current Saturating Conductivity

Approximate similarity solutions are given for the problem of electric field penetration into a plasma with a nonlinear current saturating conductivity.