The Dynamo-Driven Magnetic Helicity Transport

In this paper, a new set of the evolution equations for the helicity of the mean magnetic field and the mean helicity of the fluctuating magnetic field is derived from the Maxwell equations and the generalized Ohm's law with the dynamo action. It is shown that there exist two kinds of the dynamo-driven magnetic helicity transport. One of them makes the mean magnetic field helicity transfer to the fluctuating magnetic field, yielding an anomalous loop voltage. The other makes the fluctuating magnetic field helicity transfer to the mean magnetic field, which provides a convincing evidence for the existence of the dynamo current. Therefore, the two kinds of the magnetic helicity transport describe the mutual conversion between the regular and irregular motions. The formulas of the loop voltage and the dynamo current are given. In particular, we give out the formula of the dynamo current-generated equilibrium magnetic field which provides a concrete mode of the magnetic field creation and maintenance in both astrophysical and laboratory (e.g., reversed-field pinch) plasmas.     

New dynamical mean-field dynamo theory and closure approach

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.     

Plane Waves Propagating in Chiral Plasma and Chiral Ferrite Media

Plane wave propagation in chiral plasma and chiral ferrite media is studied in kDB coordinate system. General wave equations and characteristic equations of plane waves propagating along an arbitrary direction in chiral plasma and in chiral ferrites are derived in simple formulations respectively. Four wavenumbers and their corresponding dispersion characteristics are resulted for propagation both along and normal to the biasing magnetic field. When plane wave with negative helicity propagates along the biasing magnetic field in chiral ferrites, backward waves emerge. However backward waves occur with both positive and negative helicities when propagating along the biasing magnetic field in chiral plasma.     

读“等效的磁荷观点”有感

文章在假想的“磁荷世界”中修改了麦克斯韦方程组和洛伦兹力公式.由磁的库仑定律出发,并根据磁荷与电荷产生的电磁场的等效性,得到真空中静磁场的高斯定理和环路定理.仿照“电荷世界”中的电流定义了磁流强度,又根据磁场的相对论变换,由毕奥—萨伐尔定律和法拉第电磁感应定律得到稳恒电场D的高斯定理和环路定理.     

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.     

Hybrid helicity and magneto-vorticity flux conservation in superdense npe-plasma

In this paper, it is shown that the magnetic helicity dissipation per unit volume, coupled with the longitudinal conductivity, causes enhancement of the kinematic rotation of the electric (and magnetic) lines if the npe-plasma vorticity vector aligns with the electric (or the magnetic) field. In the case of a rigidly rotating npe-plasma under the influence of a strong magnetic field, the electric lines are rotating faster than the magnetic lines. It is deduced that the orthogonality of the electric and magnetic fields is an essential condition for the conduction current to remain finite in the limit of infinite electric conductivity of the npe-plasma. In this case, the magnetic field is not frozen into the npe-plasma, but the magnetic flux in the magnetic tube is conserved. The hybrid helicity is conserved if the “magneto-vorticity” vector is tangent to the level surfaces of constant entropy per baryon. The “magneto-vorticity” lines are rotating on the level surfaces of constant entropy per baryon due to the electromagnetic energy flow in the direction of the npe-plasma vorticity and the chemical potential variation locked with the kinematic rotation of the npe-plasma flow lines. In the case of an isentropic npe-plasma flow, there exists a family of timelike 2-surfaces spanned by the “magneto-vorticity” lines and the npe-plasma flow lines. In this case, the electric field is normal to such a family of timelike 2-surfaces. Maxwell like equations satisfied by “magneto-vorticity” bivector field are solved in axially symmetric stationary case. It is shown that the npe-plasma is in differential rotation in such a way that its each plasma shell (i.e., plasma surface spanned by “magneto-vorticity” lines) is rotating differentially without continually winding up “magneto-vorticity” lines frozen into the npe-plasma. It is also found that gravitational isorotation and Ferraro’s law of isorotation are intimately connected to each other because of coexistence of both the plasma vorticity and the magnetic field due to interaction between the electromagnetic field and npe-plasma flows.     

大学生对麦克斯韦方程组的理解研究

本研究通过收集麦克斯韦方程组概念测试题的课堂讨论录音及书面回答,获得物理专业大学生对麦克斯韦方程组的错误理解,总结出学生常见的错误概念为不清楚方程式来源、对电场和磁场的相互关系理解有误、将电场和磁场进行不恰当类比、不能正确理解平行板间电磁场的来源、对感生电场和位移电流理解不到位等,对此提出有针对性的教学建议,为电磁学教学提供参考.     

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.     

Mathematical Foundation of Kapitsa's Hypothesis About the Origin and Structure of Ball Lightning

This paper is devoted to the mathematical rationale of the Kapitsa's hypothesis about interference nature of the phenomenon known as ball lightning. It is shown that (i) there are exact solutions of the free Maxwell equations in vacuum describing closed spherical magnetic surfaces (with a tangential time dependent magnetic field, and without an electric field) and (ii) ring-like formations with tangential time-dependent electric field (and with a zero magnetic field everywhere on the ring). It is concluded that the form of these spheres and rings does not suffer changes with time.     

Quantization of the Maxwell field and extensions of zero mass representations of Poincaré group

It is proved that the only covariant quantizations of the Maxwell field associated with representations of Poincaré group built by extension on the direct sum of four unitary zero-mass representations with helicities 0, +1, -1 and 0, are the quantizations defined in the so-called generalized Lorentz gauges. They are explicitly related to the equivalence classes of extensions of the representation with helicity zero by itself.     

Formal Similarity Between Mathematical Structures of Electrodynamics and Quantum Mechanics

Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that the Schrödinger equation admits an analogous treatment. We present a Lagrangian theory of a real scalar field φ whose equation of motion turns out to be equivalent to the Schrödinger equation with time independent potential. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics. The field φ is in the same relation to the real and imaginary part of a wave function as the vector potential is in respect to electric and magnetic fields. Preservation of quantum-mechanics probability is just an energy conservation law of the field φ.     

Numerical upscaling for the eddy-current model with stochastic magnetic materials

This paper deals with the upscaling of the time-harmonic Maxwell equations for heterogeneous media. We analyze the eddy-current approximation of Maxwell’s equations to describe the electric field for heterogeneous, isotropic magnetic materials. The magnetic permeability of the materials is assumed to have random heterogeneities described by a Gaussian random field. We apply the so-called Coarse Graining method to develop a numerical upscaling of the eddy-current model. The upscaling uses filtering and averaging procedures in Fourier space which results in a formulation of the eddy-current model on coarser resolution scales where the influence of sub-scale fluctuations is modeled by effective scale- and space-dependent reluctivity tensors. The effective reluctivity tensors can be obtained by solving local partial differential equations which contain a Laplacian as well as a curl–curl operator. We present a computational method how the equation of the combined operators can be discretized and solved numerically using an extended variational formulation compared to standard discretizations. We compare the results of the numerical upscaling of the eddy-current model with theoretical results of Eberhard [J.P. Eberhard, Upscaling for the time-harmonic Maxwell equations with heterogeneous magnetic materials, Physical Review E 72 (3), (2005)] and obtain a very good agreement.     

Field theory onR×S 3 topology. IV: Electrodynamics of magnetic moments

The equations of electrodynamics for the interactions between magnetic moments are written on R×S³ topology rather than on Minkowskian space-time manifold of ordinary Maxwell's equations. The new field equations are an extension of the previously obtained Klein-Gordon-type, Schrödinger-type, Weyl-type, and Dirac-type equations. The concept of the magnetic moment in our case takes over that of the charge in ordinary electrodynamics as the fundamental entity. The new equations have R×S³ invariance as compared to the Lorentz invariance of Maxwell's equations. The solutions of the new field equations are given. In this theory the divergence of the electric field vanishes whereas that of the magnetic field does not.Research supported in part by the Colgate Research Council and by the Center for Theoretical Physics, University of Maryland.     

Maxwell’s Equations as the One-Photon Quantum Equation

Maxwell's equations (the Faraday and Ampère-Maxwell laws) can be presented as a three-component equation in a way similar to the two-component neutrino equation. However, in this case, the electric and magnetic Gauss laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.     

Indecomposable representations of Poincaré group and quantization of weak gravitational and electromagnetic fields

In this paper a quantization procedure of the electromagnetic and the weak gravitational fields, in an indefinite (but non-negative) metric space of states, is presented. We show that the covariance axiom can only be formulated with non-unitary representations (of the Poincaré group) whose restrictions to the one-particle states are indecomposable. In the gravitational case the corresponding indecomposable representation describes six states of helicity for gravitons. The quantized field appears as six interacting massless fields of helicities 2, ?2,1, ?1,0 and 0. These six values of helicity correspond to the six modes of polarization in the most general metric theory of gravity. For the electromagnetic field one obtains an indecomposable representation of the Poincaré group with helicities 1, ?1 and 0 corresponding to transverse and longitudinal photons.     

平面横电磁波模的初值问题

经典理论所描述的电场和磁场处处同相的平面电磁波模并不存在.Maxwell方程组的解依赖于 电磁场的初始值或边界条件,根据不同的初始条件解得的平面电磁波模是不同的.结果表明 ,平面电磁波是横波,在不同的位置,由变化的电场激发的磁场或由变化的磁场激发的电场 振幅不同,电场与磁场的相位差也不同. 关键词： Maxwell方程组 最优微分方程 初始条件 平面电磁波     

Complex Maxwell's equations

A unified complex model of Maxwell’s equations is presented.The wave nature of the electromagnetic field vector is related to the temporal and spatial distributions and the circulation of charge and current densities.A new vacuum solution is obtained,and a new transformation under which Maxwell’s equations are invariant is proposed.This transformation extends ordinary gauge transformation to include charge-current as well as scalar-vector potential.An electric dipole moment is found to be related to the magnetic charges,and Dirac’s quantization is found to determine an uncertainty relation expressing the indeterminacy of electric and magnetic charges.We generalize Maxwell’s equations to include longitudinal waves.A formal analogy between this formulation and Dirac’s equation is also discussed.     

Energy fluxes in helical magnetohydrodynamics and dynamo action

Renormalized viscosity, renormalized resistivity, and various energy fluxes are calculated for helical magnetohydrodynamics using perturbative field theory. The calculation is of firstorder in perturbation. Kinetic and magnetic helicities do not affect the renormalized parameters, but they induce an inverse cascade of magnetic energy. The sources for the large-scale magnetic field have been shown to be (1) energy flux from large-scale velocity field to large-scale magnetic field arising due to non-helical interactions and (2) inverse energy flux of magnetic energy caused by helical interactions. Based on our flux results, a primitive model for galactic dynamo has been constructed. Our calculations yield dynamo time-scale for a typical galaxy to be of the order of 10⁸ years. Our field-theoretic calculations also reveal that the flux of magnetic helicity is backward, consistent with the earlier observations based on absolute equilibrium theory.     

On the boundary-value problems and the validity of the Post constraint in modern electromagnetism

We recall that the theory of electromagnetism consists of three building blocks: (a) the inhomogeneous Maxwell equations for the electric and magnetic excitations (D,H) (which reflects charge conservation), (b) the homogeneous Maxwell equations for the electric and magnetic field strengths (E,B) (which reflects flux conservation), and (c) the constitutive relation between (D,H) and (E,B). In the recent paper [A. Lakhtakia, Boundary-value problems and the validity of the Post constraint in modern electromagnetism, Optik 117 (2006) 188-192], Lakhtakia proposed to change the standard boundary conditions in electrodynamics in order to exclude certain constitutive parameters. We show that this is inadmissible both from the macroscopic and the microscopic points of view.     

Orthonormal tetrads and the charged fluid in general relativity

A space-time filled with the self-gravitating charged fluid with constant electric permitivity and constant magnetic permeability is investigated. On expressing the stress-energy tensor in terms of an orthonormal tetrad, the equations of motion and Maxwell equations are formulated. In case of the geodesic flow, the conditions for divergence-free electric and magnetic fields are obtained. It is shown that the space-time permeated by the charged fluid with the electric field orthogonal to the magnetic one is embedded in 5-dimensional flat class-one space-time if and only if the electromagnetic energy flux vector vanishes.