Showing papers on "Maxwell's equations published in 1978"
TL;DR: In this paper, a new class of numerical algorithms for computer simulation of low frequency electromagnetic and electrostatic phenomena in magnetized plasma is presented, which are solved in the limits of quasineutrality and negligible transverse displacement current (Darwin's model).
92 citations
TL;DR: In this paper, the physics, spectra and damping rates of high and low-frequency surface waves in semi-infinite and cylindrical plasmas are studied.
Abstract: The physics, spectra and damping rates of high- and low-frequency surface waves in semi-infinite and cylindrical plasmas are studied. The boundary conditions (both macroscopic and microscopic) imposed on the plasma fluid/particles are discussed. The solution of the Vlasov-Maxwell set of equations for semi-infinite and cylindrical plasmas assuming mirror reflection of plasma particles at the boundary is given. The dispersion relations are derived and analysed. The dispersion properties obtained from the kinetic model are compared with those derived from the fluid model.
72 citations
TL;DR: In this article, a solution for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes.
Abstract: A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.
59 citations
TL;DR: In this paper, current density profiles in several types of interplanetary magnetic holes were calculated assuming that the currents flow in planar sheets and that the magnetic field varies only in the direction normal to the sheet.
Abstract: Current density profiles in several types of interplanetary magnetic holes were calculated assuming that the currents flow in planar sheets and that the magnetic field varies only in the direction normal to the sheet. The planarity was verified in four holes which were observed by two suitably spaced spacecraft. The structure of the current sheets ranges from very simple in some holes to very complex in others. The observed structures are found to be qualitatively consistent with models based on self-consistent solutions of Vlasov's equation and Maxwell's equations. Examples of complex, irregular magnetic holes are also presented, and they are shown to contain multiple, current sheets in which currents flow parallel to one another.
50 citations
TL;DR: In this article, the authors presented two new solutions to the classical Yang-Mills field equations in the presence of a localized external source, which totally screen the charge of the source.
Abstract: We present two new solutions to the classical Yang-Mills field equations in the presence of a localized external source. These solutions totally screen the charge of the source. They have lower energy than the corresponding Coulomb solution.
43 citations
TL;DR: In this paper, the static, spherically symmetric, pure electric, source-free solutions to the most general second-order vector-tensor theory of gravitation and electromagnetism were investigated.
Abstract: In this paper I investigate the static, spherically symmetric, pure electric, source-free solutions to the most general second-order vector-tensor theory of gravitation and electromagnetism which is such that its field equations are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, (iii) in agreement with Einstein's equations in the absence of electromagnetic fields, and (iv) compatible with Maxwell's equations in a flat space. These solutions (which are given in series form) bear a strong resemblance to the Reissner-Nordstroem solution (of the Einstein- Maxwell field equations) in the asymptotic domain; however, they differ quite radically from the Reissner-Nordstroem solution in the vicinity of the source. In addition it appears as though many of these solutions are only compatible with electric monopoles of finite extent.
37 citations
TL;DR: In this paper, the classical foundations of the bag picture for hadrons are established in n space-time dimensions, and the associated Maxwell equations are solved exactly, which induces a pressure term in the energy-momentum tensor identical to that introduced by hand in the MIT bag model.
31 citations
TL;DR: In this article, Teukolsky's equations are expressed directly in terms of the basic derivative operators of the theory and a preferred gauge in which two of the components of the Weyl tensor are governed by the same equations as a Maxwell field is suggested.
Abstract: As a preliminary towards a complete integration of the Newman-Penrose equations governing the gravitational perturbations of the Kerr black hole, the perturbations in the spin coefficients and in the components of the Weyl tensor, which vanish in the stationary state, are considered. The manner of treatment of the basic equations yields Teukolsky's equations expressed directly in terms of the basic derivative operators of the theory and, further, suggests a preferred gauge in which two of the components of the Weyl tensor are governed by the same equations as a Maxwell field. Various identities and relations that are needed in subsequent work are assembled. In two appendixes, the solution of Maxwell's equations in Kerr geometry and the perturbations of the charged Kerr-Newman black hole are considered.
30 citations
TL;DR: In this article, a set of fluid-like equations is derived which describes the stability of a diffuse, high β, arbitrary, near-ϑ pinch configuration, simultaneously including geometric effects which drive ideal magnetohydrodynamic instabilities and kinetic effects which give rise to finite Larmor radius stabilization.
Abstract: A set of fluid‐like equations is derived which describes the stability of a diffuse, high β, arbitrary, near‐ϑ pinch configuration. The equations simultaneously include geometric effects which drive ideal magnetohydrodynamic instabilities and kinetic effects which give rise to finite Larmor radius stabilization. A simple heuristic procedure is given for determining these equations in addition to a full derivation starting from basic principles.
29 citations
TL;DR: In this paper, it was shown that laser fields in plasmas, in addition to the usual ponderomotive force in the center-of-mass momentum equation, give rise to significant modifications of the material stresses and additional terms in the Ohm's law and equation for the heat flow vector.
Abstract: It is shown that laser fields in plasmas, in addition to the usual ponderomotive force in the center‐of‐mass momentum equation, give rise to significant modifications of the material stresses and additional terms in the Ohm’s law and equation for the heat flow vector. These are evaluated explicitly for the case of a single geometric optics field assuming that the slowly varying part of the electron distribution function is collision dominated, that the equation for the high frequency part can be linearized, and that the effective charge number Z≫1. The new terms are all roughly proportional to the energy density in the high‐frequency field. They are thus comparable in magnitude with conventional ponderomotive forces.
26 citations
TL;DR: In this article, a direct variational formulation for the electromagnetic field in terms of the field vectors is presented. But this formulation is based on a canonical approach, and it is not suitable for the case of electromagnetic fields.
Abstract: Using a canonical approach, we present a direct variational formulation for the equations of the electromagnetic field in terms of the field vectors.
TL;DR: In this article, the solution of Maxwell's equations for toroidal systems has been reduced to the scalar Helmholtz equation, and the eigenfunctions and corresponding electromagnetic fields have been calculated analytically.
Abstract: The solution of Maxwell's equations for toroidal systems has been reduced to the solution of the scalar Helmholtz equation. The eigenfunctions and the corresponding electromagnetic fields have been calculated analytically. The dispersion relation was formulated. Three different types of eigenmodes were obtained for each frequency. The structure of the electromagnetic field of the m= 0,1,2, and 3 modes is analyzed.
TL;DR: The analysis and results given in this paper show that boundary layer dynamics obeys very useful scaling laws which permit one solution of the basic equations to hold for many cases, and a single solution suffices for all pulse parameters for a given shape of the electron energy spectrum.
Abstract: The analysis and results given here show that boundary layer dynamics obeys very useful scaling laws which permit one solution of the basic equations to hold for many cases. In particular, during the time that the X-ray pulse is linearly rising, or when the pulse time history changes slowly after a rapid rise, (or when the pulse behaves as any power of time), the equations scale completely, and a single solution suffices for all pulse parameters for a given shape of the electron energy spectrum. Detailed solutions for the time-dependent structure of the boundary layer for two cases of interest were presented in the previous two sections. In both cases the emission electron spectrum was assumed to be exponential with an arbitrary average energy E, and the angular distribution was taken to be proportional proportional to cos ?. The material yield Y is arbitrary. In the first case the incident X-ray flux is taken to rise linearly in time at an arbitrary rate, while in the second case the flux is taken to be a step function turned on at t = 0 and then held constant at an arbitrary value. Useful scaling laws are apparent from the equations in the previous two sections. For example, for a linearly rising pulse, the surface electric field varies only as the cube root of the yield, or the electron average energy, or the flux rise rate, Equation 43.
TL;DR: In this article, the scattering from dielectric-slab-optical waveguides having refractive-index inhomogeneities in the core region has been studied by solving the Maxwell equations together with the use of a stationary phase method.
Abstract: The scattering from dielectric-slab-optical waveguides having refractive-index inhomogeneities in the core region has been studied by solving the Maxwell equations together with the use of a stationary phase method. The scattering phenomenon is of interest since it provides the radiation pattern in the far-field region which is characterized by the statistical scale of inhomogeneities in a waveguide. The anisotropic fluctuations of the refractive index in the directions parallel and perpendicular to the axis of light propagation have been assumed in the analysis. It is found that the strong multiple peaks in the forward direction occur in the substrate region when the correlation length of refractive-index inhomogeneities in the axial direction is much greater than the wavelength of light.
TL;DR: In this paper, the relativistic corrections to the ponderomotive force for a general transverse plane wave of arbitrary polarization lead to an approximately twenty percent reduction in the single particle ponderOMotive forces for 10.6 μm CO2 light at 1016 W/cm2.
Abstract: The relativistic corrections to the ponderomotive force for a general transverse plane wave of arbitrary polarization lead to an approximately twenty percent reduction in the single particle ponderomotive force for 10.6 μm CO2 light at 1016 W/cm2. The recent nonrelativistic derivation of laser‐induced plasma profiles is extended to the relativistic regime by including the relativistic corrections to the ponderomotive force in the fluid equations. Specifically, analytic results are obtained which facilitate relating the number densities and flow velocities to the electric field strength at the sonic point; in addition, these relations allow the complete self‐consistent steady state structure of the profile to be determined numerically. Several detailed comparisons of nonrelativistic and relativistic results are discussed.
TL;DR: In this paper, the general nonlinear differential equations describing the interaction of finitely deformable, polarizable, heat conducting intrinsic n-type semiconductors with the quasi-static electric field are transformed from the unknown present coordinate description to the known reference coordinate description, which is the form needed in the treatment of problems.
Abstract: The general nonlinear differential equations describing the interaction of finitely deformable, polarizable, heat conducting intrinsic n-type semiconductors with the quasi-static electric field are transformed from the unknown present coordinate description to the known reference coordinate description, which is the form needed in the treatment of problems. For the differential form of each balance equation in the reference coordinate description, the associated integral form is obtained. The resulting integral forms turn out as expected with the exception of the one due to the balance of linear momentum for the semiconducting fluid, in which an important change in and simplification from the form used heretofore is introduced. More importantly, the previous existing integral form of the equation of the balance of energy in the present coordinate description is transformed to a different form, which is equivalent to the original form only when the field variables are differentiable. The revised integral form in the present coordinate description is then transformed to the reference coordinate description, from which an energetic jump condition across a moving non-material surface of discontinuity is obtained which is consistent with all the other jump conditions obtained from the other integral forms. In addition, the expression for the quasi-static electric Poynting vector in the reference coordinate description is determined.
TL;DR: In this paper, a formulation of electrodynamics with both electric and magnetic charges is obtained without introduction of a metric structure into the space-time arena, without constitutive assumptions through use of extensions of the calculus of exterior forms.
TL;DR: In this paper, a systematic procedure generalized to derive the variational expressions for electromagnetic and/or acoustic field problems is proposed, based on the simple and basic principle of least action point of view.
Abstract: A systematic procedure generalized to derive the variational expressions for electromagnetic and/or acoustic field problems is proposed. It is shown that the variational expressions useful to treat the systems involving electromagnetic waves or acoustic waves or both can be formulated systematically all from the simple and basic principle of least action point of view.
TL;DR: In this article, the authors considered solutions of the Einstein-Maxwell field equations satisfying the conditions Fij;k+lk=fFij+, Fij,k+nk=gFij+ where Fij+ is the self-dual Maxwell bivector and li and ni are the principal null vectors of Fij+.
Abstract: The author considers solutions of the Einstein-Maxwell field equations satisfying the conditions Fij;k+lk=fFij+, Fij;k+nk=gFij+ where Fij+ is the self-dual Maxwell bivector and li and ni are the principal null vectors of Fij+. The fields are algebraically general and the most general solution is found in closed form when li and ni have non-zero twist. Several twist-free solutions are also obtained. Vacuum space-times admitting a test Maxwell field are also considered. In all cases the metric admits a three-parameter group of motions acting transitively on three-dimensional orbits. Fields satisfying the dual conditions with li and ni replaced by mi and mi are also investigated and similar results are obtained.
TL;DR: In this article, the relation of orbital excitations to critical curves in the initial data (l, E )-plane of classical equations of motions is pointed out, and it is shown that the string motion with the linear trajectory J = α ′ m 2 corresponds to a degenerate solution of the inhomogeneous Maxwell equations.
TL;DR: In this paper, the complete solution, applying both inside and outside the sources, is given, where Harmonic time dependence is assumed, and the solution is extended to vector spherical harmonics.
Abstract: Conventional expansions of solutions to Maxwell’s equations in vector spherical harmonics apply only outside the sources. The complete solution, applying both inside and outside the sources, is given here. Harmonic time dependence is assumed.
01 Mar 1978
TL;DR: The theory presented in this article represents a different approach toward unification of the various branches of physics, and provides predictions that may be experimentally investigated, such as a limiting rate of mass conversion, reduced pressures in electromagnetically contained plasmas, increased viscous effects in shocked materials, a finite self-energy for a charged particle, and the possible creation of particles with velocities greater than the speed of light.
Abstract: The theory presented represents a different approach toward unification of the various branches of physics. The foundation of the theory rests upon generalizations of the classical laws of thermodynamics, particularly Caratheodory's abstract statement of the second law. These adopted laws are shown to produce, as special cases, current theories such as Einstein's General and Special Relativity, Maxwell's electromagnetism, classical thermodynamics, and quantum principles. In addition to this unification, the theory provides predictions that may be experimentally investigated. Some of the predictions are a limiting rate of mass conversion, reduced pressures in electromagnetically contained plasmas, increased viscous effects in shocked materials, a finite self-energy for a charged particle, and the possible creation of particles with velocities greater than the speed of light. 8 figures.
TL;DR: In this article, a five-parameter solution of the combined Einstein-Maxwell equations is given that describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds and angular momentum.
Abstract: A scheme is presented by which we can obtain static electrovac exterior solutions from the stationary gravitational fields given by Kerr and Tomimatsu and Sato. A five-parameter solution of the combined Einstein-Maxwell equations is given that describes a source containing mass, electric charge, magnetic dipole, higher multipole moments of all three kinds and angular momentum. These are generated by using Kinnersley's method from Wang's electrovac solutions, which, in turn, were generated from the gravitational fields of Tomimatsu and Sato for δ=2–3. All the solutions are asymptotically flat.
TL;DR: In this article, the equivalence of the interior and exterior scattering problems to the Ewald-Oseen extinction theorem and boundary conditions is proved for nonmagnetic media, and a hypothesis was put forward according to which these non-local boundary conditions completely and uniquely specify the solution of interior-scattering problems.
Abstract: It has been shown in the past that the Ewald-Oseen extinction theorem can be generalized into a nonlocal boundary-value problem and that the scattering of an electromagnetic wave on a medium of arbitrary response can be described in terms of this boundary-value problem. The scattered field inside the medium (the interior-scattering problem) is determined, without any reference to the scattered field outside the medium, by solving a set of coupled partial differential equations, subject to certain nonlocal boundary conditions which are generalizations of the Ewald-Oseen extinction theorem. Once the field on the boundary of the medium is known, the exterior field (the exterior-scattering problem) is evaluated by direct integration. Moreover, a hypothesis was put forward according to which these nonlocal boundary conditions completely and uniquely specify the solution of the interior-scattering problem. In this paper it is shown that this hypothesis is true. The equivalence of the interior- and exterior-scattering problems to Maxwell’s equations and boundary conditions is proven. For simplicity, the proof is confined to nonmagnetic media. Thus, if Maxwell’s equations and boundary conditions have a unique solution, the interior-scattering problem will also have a unique solution, namely, that obtained from the former. Some illustrative examples are presented in the special case of a linear medium.
TL;DR: In this paper, it was shown that neglecting displacement currents entirely may reduce the space dimension of the problem and yields the magnetic and electric fields in the conducting regions accurately, but the electric field in the air regions is very inaccurate, and the charge distribution resulting on the conducting surfaces is absent in the standard solution, which neglects displacement currents and longitudinal field variations.
Abstract: Eddy current problems are commonly solved by neglecting displacement current. This assumption reduces Maxwell's equations to a parabolic partial differential equation [1]. It is shown that neglecting displacement currents entirely may reduce the space dimension of the problem and yields the magnetic and electric fields in the conducting regions accurately. However, the electric fields in the air regions are very inaccurate, and the charge distribution resulting on the conducting surfaces is absent in the standard solution, which neglects displacement currents and longitudinal field variations. The standard solution is found to yield the proper value of skin depth over a very wide range of conductivity, permeability, and frequency.
TL;DR: In this article, a system of equations which describes the behavior of magnetized or polarized dispersive media in electromagnetic fields in the diffusion approximation was derived, which includes terms related to the nonequilibrium nature of the process (velocity derivatives, difference of pressure, chemical potentials, and temperatures of the different phases).
Abstract: A system of equations, which describes the behavior of magnetized or polarized dispersive media in electromagnetic fields in the “diffusion approximation,” is derived. It is assumed that the medium consists of several phases and components, each of which is generally magnetized or polarized according to its own law and has its own temperature. A formula for the force acting on such a medium due to the presence of the electromagnetic field is derived, which includes terms related to the nonequilibrium nature of the process (velocity derivatives, difference of pressure, chemical potentials, and temperatures of the different phases). The part of the force which is proportional to the differences of the pressures, chemical potentials, and the temperatures of the phases occurs in the equations of motion even in the case when the medium does not interact with the electromagnetic field or when there is no electromagnetic field. The terms associated with the magnetization or polarization occur in this part of the force through the difference of pressures and the chemical potentials of the different phases. The equations for the diffusion fluxes and heat flux, the equations for the rate change of the mass of the α-phase (component) and entropy of the α-phase (component), and also the equation for the rate of change of the volume concentration of the α-phase (component) are written with the use of the methods of thermodynamics of irreversible processes. In the “diffusion approximation” these equations for the rate of change of entropy replace the more unwieldy energy equation usually used in the hydrodynamics of multiphase media. It should be particularly noted that the proposed method permits one to obtain equations for the change of volume concentration of the phases. Instead of these equations, usually a Rayleigh-type equation for the oscillations of the bubble is used for closing the complete system in liquid —gas bubble mixtures, which differs from the equation obtained in this work, and within the framework of the assumptions used here it does not follow from the general formalism of thermodynamics of irreversible processes. The obtained results and their corollaries are compared with the results of other authors. The basic premises discussed in [1, 2] are used in the derivation of the equations.
TL;DR: In this article, a new family of asymptotically flat solutions to the Einstein-Maxwell equations with static source m of axial symmetry and charge l is presented in closed form.
TL;DR: In this paper, a vector variational principle in terms of electric and magnetic field vectors for lossy media is developed, and the natural interface and boundary conditions associated with the principle are investigated and further modifications needed to implement more required conditions.
Abstract: Some of the basic developments in the variational treatment of electromagnetic field problems in anisotropic inhomogeneous media are reviewed. The field is assumed to be time harmonic and satisfies appropriate Maxwell's equations. A vector variational principle in terms of electric and magnetic field vectors for lossy media is developed. The natural interface and boundary conditions associated with the principle are investigated and further modifications needed to implement more required conditions are presented. The results extend the class of problems for which the variational approach is useful in addition to facilitating the computations involved.