Magnetic helicity tensor for an anisotropic turbulence

The evolution of the magnetic helicity tensor for a nonzero mean magnetic field and for large magnetic Reynolds numbers in an anisotropic turbulence is studied. It is shown that the isotropic and anisotropic parts of the magnetic helicity tensor have different characteristic times of evolution. The time of variation of the isotropic part of the magnetic helicity tensor is much larger than the correlation time of the turbulent velocity field. The anisotropic part of the magnetic helicity tensor changes for the correlation time of the turbulent velocity field. The mean turbulent flux of the magnetic helicity is calculated as well. It is shown that even a small anisotropy of turbulence strongly modifies the flux of the magnetic helicity. It is demonstrated that the tensor of the magnetic part of the alpha effect for weakly inhomogeneous turbulence is determined only by the isotropic part of the magnetic helicity tensor.     

Measuring the 9-component magnetic permeability tensor of ferrites

The magnetic permeability tensor of ferrite monocrystals can, in the general case, be represented as consisting of nine components [1]. In [2] the 6-component magnetic permeability tensor was obtained for a triaxial ferrite monocrystal with low magnetic anisotropy energy magnetized by a constant field in the crystallographic plane (110). In the general case of magnetization in an arbitrary crystallographic direction the tensor becomes a 9-component tensor [3]. In the context of the increasing application of ferrite monocrystals in microwave engineering the question of measuring such a tensor is of current scientific and practical interest. In the present article we propose a method for measuring the 9-component tensor for ferrite materials at microwave frequencies.     

Dielectric tensor elements for the description of waves in rotating inhomogeneous magnetized plasma spheroids

The dielectric permittivity tensor elements of a rotating cold collisionless plasma spheroid in an external magnetic field with toroidal and axial components are obtained. The effects of inhomogeneity in the densities of charged particles and the initial toroidal velocity on the dielectric permittivity tensor and field equations are investigated. The field components in terms of their toroidal components are calculated and it is shown that the toroidal components of the electric and magnetic fields are coupled by two differential equations. The influence of thermal and collisional effects on the dielectric tensor and field equations in the rotating plasma spheroid are also investigated. In the limiting spherical case, the dielectric tensor of a stationary magnetized collisionless cold plasma sphere is presented.     

An invariant theory of the constitutive parameters of a plasma and a ferrite

Under the influence of a constant magnetic field, the electric property of a plasma and the magnetic property of a ferrite are anisotropic. In this paper, the general coordinatefree invariant forms of the dielectric tensor of a plasma and the permeability tensor of a ferrite are obtained. The tensors are expressed explicitly as a sum of three tensors: a unit tensor, a symmetric tensor and an antisymmetric tensor, each of which is weighted by different constants. The symmetric and antisymmetric tensors are related to the unit vector of the constant magnetic field. The invariant forms in terms of the sum of the projectors of the tensors are also derived. When a Cartesian coordinate system is introduced, the invariant forms are easily reduced to the commonly used matrix representations. The invariant forms clearly show the effects of the constant magnetic field on the anisotropies of the media. Moreover, they effectuate and simplify the deduction of the general solutions of problems involving wave propagation and excitation in plasma and ferrite and thus facilitate interpretations of the final results.     

Gravitational Waves Interacting with a Spinning Charged Particle in the Presence of a Uniform Magnetic Field

The equations which determine the response of a spinning charged particle moving in a uniform magnetic field to an incident gravitational wave are derived in the linearized approximation to general relativity. We verify that 1) the components of the 4-momentum, 4-velocity and the components of the spinning tensor, both electric and magnetic moments, exhibit resonances and 2) the co-existence of the uniform magnetic field and the GW are responsible for the resonances appearing in our equations. In the absence of the GW, the magnetic field and the components of the spin tensor decouple and the magnetic resonances disappear.     

Oscillations of the kinetic coefficients in a two-dimensional electron system with the spin-orbit interaction in an alternating magnetic field

The response of a two-dimensional electron system with the spin-orbit interaction to a measuring direct-current electric field is investigated for the case in which the system is disturbed from the equilibrium by a microwave alternating magnetic field. Point nonmagnetic impurities are considered as scattering sources. It is demonstrated that the combined transitions occurring under the action of an alternating magnetic field lead to new oscillations of the diagonal components of the electrical conductivity tensor of the two-dimensional electron gas.     

Low-energy relation for the trace of the energy–momentum tensor in QCD and the gluon condensate in a magnetic field

The nonperturbative QCD vacuum in a magnetic field has been studied. A low-energy relation for the trace of the energy–momentum tensor in the magnetic field has been obtained. It has been shown that the derivatives of the quark and gluon contributions to the trace of the energy–momentum tensor with respect to the magnetic field coincide with each other. The magnetic field dependence of the gluon condensate has been calculated in the limits of strong and weak fields.     

磁性颗粒膜法拉第转角的研究

在外磁场作用下,复合介质的法拉第磁光效应依赖于颗粒膜电介质张量。而复合介质的电介质张量的计算相当复杂。运用了有效介质近似理论,利用非均匀复合介质的有效电场等于单个颗粒中局域场的平均值的自恰条件,由电介质张量εe方程及自洽条件导出了计算磁性颗粒膜系统磁光法拉第转角的解析公式。并应用导出的关系,以Cu金属颗粒为例,讨论了颗粒膜中金属颗粒含量及对应的基质、离子浓度、颗粒形状对法拉第转角的影响,结果表明,利用有效介质近似理论计算的结果与实验结果一致。     

Magnetic field focusing of hyperfine interaction in hydrogen

We find a new correction to hyperfine splitting in the ground state of hydrogen atom in magnetic field. The physical basis for this effect is the reduction of the size of the electron orbit in magnetic field. As a result, the value of the wavefunction at the origin increases which can be called magnetic focusing. Another magnetic-field-induced effect is the appearance of field dependent tensor forces.     

General magnetostatic shape-shape interaction forces and torques

Expressions for the magnetostatic interaction force and torque between two magnetic objects of arbitrary shape are derived within the shape amplitude formalism. A generalized force is derived as the gradient of the magnetometric tensor field, which is the convolution of the cross-correlation of the object shapes with the dipolar tensor field. Expressions for the mechanical and magnetic torques are also derived in terms of the magnetometric tensor field. Expressions suitable for numerical evaluation are given as finite Fourier summations. Example computations are given for the interactions between pairs of uniformly magnetized spheres (for which analytical results are compared to numerical results), cubes, octahedra, tetrahedra, and cuboctahedra. The accuracy of the derived numerical relations for energy, force, and torques is of the order of 0.1% for object spacings smaller than the object dimensions.     

Dispersion of multi-stream instability in quantum magnetized hot plasmas

Using the quantum hydrodynamic (QHD) equations with magnetic field on the Wigner-Maxwell system, the general dielectric tensor and dispersion equation for quantum plasmas were derived. Dispersion relations of one-, two-stream and beam-plasma instabilities in uniform quantum magnetized plasmas are investigated through the new dielectric tensor. The magnetic field which is parallel to the fluid velocity does not work on stream instabilities. The quantum and thermal effects have remarkable impact on two-stream instability. The critical wave number for beam-plasma instability with quantum effects correction is given too.     

High-frequency magnetic permeability of nanocomposite film

The high-frequency magnetic permeability of nanocomposite film consisting of the single-domain spherical ferromagnetic particles in the dielectric matrix is studied. The permeability is assumed to be determined by rotation of the ferromagnetic inclusion magnetic moments around equilibrium direction in AC magnetic field. The composite is modeled by a cubic array of ferromagnetic particles. The magnetic permeability tensor is calculated by solving the Landau–Lifshits–Gilbert equation accounting for the dipole interaction of magnetic particles. The permeability tensor components are found as functions of the frequency, temperature, ferromagnetic inclusions density and magnetic anisotropy. The obtained results show that nanocomposite films could have a rather high value of magnetic permeability in the microwave range.     

On space-time permeated by the perfect magnetofluid

A space-time permeated by the self-gravitating perfect fluid with infinite electrical conductivity and constant magnetic permeability (perfect magnetofluid) is investigated. For aC space defined as the space in which the divergence of conformal curvature vanishes, it is proved that the rotation explicitly depends on the magnetic field. In aJ space characterized by the vanishing of the divergence of Petrov space-matter tensor, the invariance of the energy density, the isotropic pressure, and the magnitude of the magnetic field along the divergence-free magnetic lines is established. It is found that if the stress-energy tensor of the perfect magnetofluid is a Killing tensor, the energy density, the isotropic pressure, and the magnitude of the magnetic field are constant. Moreover it is shown that the stream lines are expansion-free and the magnetic lines are divergence-free. It is proved that the complexion of the field of the perfect magnetofluid remains invariant along the magnetic lines if and only if these lines are normal to the lines of vorticity.     

Nonlinear optical and magneto-optical effects in non-spherical magnetic granular composite

The magnetization-induced nonlinear optical and nonlinear magneto-optical properties in a magnetic metal-insulator composite are studied based on a tensor effective medium approximation with shape factor and Taylcr-expansion method. There is a weakly nonlinear relation between electric displacement D and elcctric field E in the composite. The results of our studies on the effective dielectric tensor and the nonlinear susceptibility tensor in a magnetic nanocomposite are surveyed. It is shown that such a metal-insulator composite exhibits the enhancements of optical and magneto-optical nonlinearity. The frequencies at which the enhancements occur, and the amplitude of the enhancement factors depend on the concentration and shape of the magnetic grains.     

Isometric motion in relativistic magnetohydrodynamics

It is shown that if the flow of a plasma coupled to a frozen-in magnetic field is isometric, the velocity field, the vorticity tensor and the four-vector magnetic field are invariant under the group of motions. A generalization of Ferraro's theorem of isorotation and of the Bernoulli's theorem for force-free fluids is found.     

The double duals and gauges of the Lanczos tensor

It is shown that: i) the Weyl tensor can be expressed in terms of the sum of a tensor and its double dual, where the tensor is constructed from the covariant derivatives of the Lanczos tensor, ii) a similar expression does not exist for the Riemann tensor in electromagnetic theory, iii) the electromagnetic field cannot be identified with the differential gauge freedom of the Lanczos tensor, iv) the symmetries of Einstein Maxwell theory and the Lanczos tensor do not prohibit the identification of the electromagnetic field with the algebraic gauge freedom of the Lanczos tensor, these symmetries require a differential equation relating the electromagnetic field tensor to the algebraic gauge vector and this is given.     

舰船感应磁场预测的一种新方法

提出一种基于磁化强度的舰船感应磁场预测法.首先证明了一个基于磁化观点的铁磁物体内部磁场强度计算公式,随后通过该公式导出了点函数去磁张量的概念并证明了它的一些性质,最后利用此公式构造了一个预测非均匀外场中舰船感应磁场的新方法——磁化强度法,且在该方法中用到了点函数去磁张量.与传统的舰船感应磁场预测方法相比,磁化强度法具有计算量小、精度高、物理意义明显等特点.船模数值试验验证了本方法.     

Photon dispersion in a strong magnetic field

In an external magnetic field analytical properties are studied of the photon polarization tensor calculated as the electron-positron loop in the Furry picture. The polarization tensor is reexpressed as a sum over singular contributions coming from e⁺e^?-pair photocreation in semidiscrete Landau states. The solutions of the photon dispersion equation (i.e., the one for the poles of the photon propagator) are described. The shape of the photon dispersion curve obtained is responsible for the effect of photon deflection by a strong magnetic field. No physically reliable solutions, apart from spurions, are found for the longitudinal photon mode. An infinite number of solutions with complex space-momentum are found, with no apparnet ghosts among them. An attempt is made to interprete the former in terms of possible bound and quasibound states of electron and positron pairs.     

电磁场的复张量表述

在电磁场的三维复矢量表述基础之上获得对应的四维复张量表述形式,同时又考虑磁荷流密度并引入双势法,将电磁场复张量表述推广到同时包含电荷与磁荷流密度的情形并获得了复张量麦克斯韦方程组.     

Optical properties of a polarizable linear magneto-cosserat fluid

General optical properties of polarizable linear magneto-Cosserat fluids are investigated. The constitutive dielectric tensor is generalized to include the effects of magnetic field and rotation vector, and the general expression for the refractive index is obtained. If the optical effects of the magnetic field and rotation vector are negligible, the fluid shows the same birefringent phenomena as a stokesian fluid and if the effect of magnetic field or rotation vector is dominant, the fluid shows double circular refraction. The coupling effect of the magnetic field and rotation vector is considered and special cases of slow motion and low conductivity are also discussed.