Showing papers on "Maxwell's equations published in 1981"
TL;DR: In this article, augmented electric and magnetic field integral equations are introduced to eliminate the spurious resonances from the exterior solution of the original integral equations, which preserve the basic simplicity, solution capability, and pure electric-and magnetic-field character of Maue's original integral equation.
Abstract: Augmented electric- and magnetic-field integral equations, which preserve the basic simplicity, solution capability, and pure electric- and magnetic-field character of Maue's original integral equations, are introduced to eliminate the spurious resonances from the exterior solution of the original integral equations. The exact dependence of the original and augmented integral equations on the geometry of the principal area (self patch) which excludes the singularity of their kernels is also determined, and alternate forms for the integral equations are provided that avoid integrals dependent upon the geometry of the principal area. Numerical results obtained for scattering from the perfectly conducting cube, sphere, and infinite circular cylinder confirm the theoretically predicted result that the augmented integral equations eliminate the spurious resonances for all perfectly conducting scatterers except the sphere.
113 citations
TL;DR: In this article, the three dimensional magnetic vector potential (m.v.p.) variational formulation for magnetostatic field problems with ideal current carrying conductors is given, and an appropriate functional is chosen for this class of problems, which is shown to be stationary whenever the partial differential equations, the Neumann, and the specified Dirichlet boundary conditions are satisfied, within and on the boundary of the volume under investigation, respectively.
Abstract: The three dimensional magnetic vector potential (m.v.p.) variational formulation for magnetostatic field problems, with ideal current carrying conductors is given. An appropriate functional was chosen for this class of problems. Variational techniques were used to prove that the chosen functional is stationary whenever the partial differential equations, the Neumann, and the specified Dirichlet boundary conditions are satisfied, within and on the boundary of the volume under investigation, respectively. The finite element method is used to obtain a numerical approximation of the stationary point of the functional. A three dimensional discretization scheme involving first order tetrahedral elements was used to implement the method. The m. v. p. at each of the four tetrahedral vertices (nodes) has three degrees of freedom (or components) in the x, y and z directions due to the three dimensional nature of the field.
83 citations
TL;DR: In this article, the atmospheric propagation of a sequence of short intense electromagnetic pulses and their creation of a low density channel in the beam vicinity are considered, and a Lagrangian as well as Eulerian description of the electromagnetic pulses is developed to solve Maxwell's equations in t he paraxial approximation.
Abstract: The atmospheric propagation of a sequence of short intense electromagnetic pulses and their creation of a low density channel in the beam vicinity are considered. A Lagrangian as well as Eulerian description of the electromagnetic pulses is developed to solve Maxwell’s equations in t he paraxial approximation. The hydrodynamic response of the atmosphere is considered in the adiabatic approximation. After a scaling of the electromagnetic and hydrodynamic variable three dimensionless parameters, the pressure parameter, the focusing parameter and the diffraction parameter, emerge which describe the interaction of the pulse with the atmosphere in a convenient way. The electromagnetic equations are solved using the finite‐difference method as well as the Fourier transform technique. For the latter method a fast Hankel transform algorithm is used. An explicit inclusion of end‐corrections in the Hankel transform algorithm makes our propagation code fast and accurate. We discuss the numerical results and their de...
75 citations
TL;DR: In this paper, conditions are given when such abstract Hilbert space-solutions represent differentiable regular functions which satisfy Maxwell's equations, boundary conditions, and transmission conditions in the classical sense, where the Hilbert space operators have been very powerful in the past to achieve uniqueness and existence results for the equations.
Abstract: Methods using the theory of distributions and Hilbert space operators have been very powerful in the past to achieve uniqueness and existence results for Maxwell's equations. In this paper conditions are given when such abstract “Hilbert space”-solutions represent differentiable “regular” functions which satisfy Maxwell's equations, boundary conditions, and transmission conditions in the classical sense.
71 citations
70 citations
TL;DR: Instead of using the uniform warm plasma dispersion relation with an inverse Fourier transform to form the mode conversion−tunneling equation, the equation is developed directly from the Vlasov equation and Maxwell's equations as discussed by the authors.
Abstract: Instead of using the uniform warm plasma dispersion relation with an inverse Fourier transform to form the mode conversion‐tunneling equation, the equation is developed directly from the Vlasov equation and Maxwell’s equations The plasma is assumed uniform parallel to B0 The expansion parameters are the Larmor orbit and the scale length, keeping terms to order ρ2L and L−1 = (1/ωc)(dωc/dx) For the special case with ω≃2ωc in a single species plasma, the asymptotic form of the mode conversion‐tunneling equation is unchanged, but localized third and first derivative terms appear even as absorption vanishes
60 citations
TL;DR: In this paper, the relevant Maxwell's equations, boundary conditions, and constitutive equations for axes in linear sinusoidal motion are derived for reflections from a perfectly conducting plane in sinusoid vibration.
Abstract: The signal scattered by a moving object is traditionally evaluated by the quasistationary method. This method is not relativistically correct, although it yields satisfactory results in most practical cases. A correct approach implies solution of the problem in the accelerated reference system in which the object is at rest. The relevant Maxwell's equations, boundary conditions, and constitutive equations are derived for axes in linear sinusoidal motion. As a first application the reflections from a perfectly conducting plane in sinusoidal vibration are evaluated.
58 citations
TL;DR: In this article, the magnetic field, current density, and energy of an arbitrary array of curved or straight flux lines in a type II superconductor with a planar surface are calculated from the London theory.
Abstract: The magnetic field, current density, and energy of an arbitrary array of curved or straight flux lines in a type II superconductor with a planar surface are calculated from the London theory. The general expressions and their expansion with respect to displacements from the equilibrium flux-line positions are given. The elastic energy of the distorted flux-line lattice near a planar surface is presented and discussed. The equilibrium configuration becomes unstable to the growth of helical perturbations if a current exceeding a critical value is applied parallel to the external magnetic field.
54 citations
TL;DR: In this article, the spontaneous and induced emission from a free-electron laser is treated for the case in which an axial magnetic field is imposed in addition to the helical, axially periodic wiggler magnetic field.
Abstract: The spontaneous and induced emission from a free-electron laser is treated for the case in which an axial magnetic field is imposed in addition to the helical, axially periodic wiggler magnetic field. The classes of possible single-particle trajectories in this configuration are discussed, and the results are applied to a calculation of the incoherent radiation from a beam of relativistic electrons in the system. The coherent radiation is treated by solving the Vlasov-Maxwell equations for the linear gain in the tenuous-beam limit, where the beam plasma frequency is much less than the radiation frequency and self-field effects can be ignored.
51 citations
TL;DR: In this paper, the relationship between the periodicity constraints imposed by the geometry, magnetic shear, and the spatial structure of eigenmodes is investigated by exploiting the radial translational invariance and the poloidal periodicity of the gyrokinetic and Maxwell equations.
Abstract: Low‐frequency waves with high toroidal mode numbers in an axisymmetric toroidal configuration are studied. In particular, the relationship between the periodicity constraints imposed by the geometry, magnetic shear, and the spatial structure of eigenmodes is investigated. By exploiting the radial translational invariance and the poloidal periodicity of the gyro‐kinetic and Maxwell equations, the two‐dimensional problem can be converted into a one‐dimensional one, and the mode structure can be expressed in terms of a single extended poloidal variable. This representation is used in the description of electromagnetic modes with phase velocities larger than the ion thermal velocity and with frequencies below the ion gyro‐frequency. Trapped particle, curvature, and compressional effects are retained. The dispersion equations for drift modes and Alfven‐type modes are given in general geometry and simplified solutions are presented in the configuration of a double periodic plane slab.
TL;DR: In this paper, the relationship between Maxwell's equations and radiative-transport theory is studied for isotropic, nondispersive media that have arbitrary permittivity variations, and it is demonstrated that the postulates of transport theory are consistent with Maxwell's equation if the characteristics of the medium and the fields are such that the field-correlation tensor possesses certain properties and if the relative permittivities fluctuations in the medium are small in comparison with unity and have correlation lengths that satisfy appropriate requirements.
Abstract: The relationship between Maxwell’s equations and radiative-transport theory is studied for isotropic, nondispersive media that have arbitrary permittivity variations. It is demonstrated that the postulates of transport theory are consistent with Maxwell’s equations if the characteristics of the medium and the fields are such that the field-correlation tensor possesses certain properties and if the relative permittivity fluctuations in the medium are small in comparison with unity and have correlation lengths that satisfy appropriate requirements.
TL;DR: In this paper, the existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies, by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable.
Abstract: The existence of a unique solution to Maxwell's equations defined in an exterior domain with impedance boundary condition is established for all frequencies. This is accomplished by reducing this problem to that of solving a system of singular integral equations and then regularizing this system such that the Riesz theory is applicable. We also consider the inverse problem in which it is desired to determine the impedance from a knowledge of the far field pattern. By restricting the impedance to lie a priori in a compact set results are obtained on the existence, uniqueness, and stability of the solution to this inverse scattering problem.
TL;DR: In this article, the dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder parallel to the axis.
Abstract: The dynamic effects of an alternating magnetic field on containers of conducting fluid are investigated in two special cases: (i) an infinitely long circular cylinder in a uniform magnetic field normal to the generators; (ii) a truncated circular cylinder in a uniform magnetic field parallel to the axis. Neglecting the motion effects in Maxwell's equations, the problem is conveniently decoupled into electromagnetic and dynamic parts. Using either analytical or numerical solutions of the electromagnetic equations, the electromagnetic forces are calculated and introduced in the motion equations. In the first case, asymptotic solutions of the Navier–Stokes equations valid for high frequencies are calculated and compared with numerical solutions obtained for the same geometry. The second case has been studied numerically, and the solutions are presented and interpreted.
TL;DR: In this paper, a coupled-wave theory describing diffraction from a volume grating is developed, which applies to planar diffraction geometries with the electric field polarized normal to the plane of incidence.
Abstract: A simple but accurate coupled-wave theory describing diffraction from a volume grating is developed, which applies to planar diffraction geometries with the electric field polarized normal to the plane of incidence. Modulation of the dielectric and the absorption properties of the medium are considered, and the analysis is developed for gratings nonuniform with depth and for composite (multiplexed) gratings. The theory is based axiomatically on Maxwell's equations, and no approximations or simplifying assumptions other than those requisite to the scalar wave formulation of the theory enter into the analysis (except that for computational applications, only a finite number of diffracted orders may be retained in the analysis).
TL;DR: In this article, the authors considered the continuous spectrum of radiation modes along open-boundary dielectric waveguides of arbitrary cross-section shape and established the orthogonality of the spectral components of these radiation modes in a general manner.
Abstract: The continuous spectrum of radiation modes along open-boundary dielectric waveguides of arbitrary cross-section shape is considered. Orthogonality of the spectral components of these radiation modes is established in a general manner. This development is based on the Lorentz reciprocity theorem, and it is demonstrated that orthogonality is a direct consequence of (1) satisfaction of Maxwell’s equations by spectral-component fields and (2) satisfaction of the radiation condition by total radiation-mode fields. The amplitude spectrum of continuous radiation modes, maintained by impressed excitatory electric currents immersed in either the waveguide core or cladding regions, is determined. These results are of general use in the study of discontinuities along open-boundary dielectric waveguides.
TL;DR: In this article, it was shown that in the magnetohydrodynamic approximation, neglecting pressure terms, the transverse wave fields in a uniform medium with a uniform magnetic field can be derived from linear combinations of scalar potentials of the form ϕ±(x, y, z±V At) where VA is the Alfven speed.
Abstract: It is shown that in the magnetohydrodynamic approximation, neglecting pressure terms, the transverse wave fields in a uniform medium with a uniform magnetic field can be derived from linear combinations of scalar potentials of the form ϕ±(x, y, z±V At) where VA is the Alfven speed; guidance by the magnetic field is thus perfect. It is further shown that in the ray approximation, strong guidance still exists even if the medium and the magnetic field are not quite uniform provided that the component perpendicular to the magnetic field of the propagation vector is much greater than the parallel component. If the reciprocal of the parallel component is not much greater than the spatial scale on which the medium and the magnetic field vary, then the ray approximation is only valid in the perpendicular direction. The differential equations of wave propagation along the magnetic field are derived under these conditions directly from Maxwell's equations. An alternative derivation, using an analogy to transmission lines, is also given. These equations must then be applied to each perpendicular Fourier component of a source; differently oriented Fourier components propagate differently. The resulting imperfections in guiding will be investigated elsewhere in detail.
TL;DR: In this paper, a self-consistent analysis is presented to describe the behavior of the radiation field and the modulation of the electron beam in free-electron lasers, where the motion of electrons is governed by the Lorentz force equations in the presence of a radiation field.
Abstract: In free-electron lasers, the motion of electrons is governed by the Lorentz force equations in the presence of a radiation field. The variation of the radiation field then follows from Maxwell equations in which the modulated electron current acts as a source. A self-consistent analysis, which completely incorporates these two concepts, is presented to describe the behavior of the radiation field and the modulation of the electron beam. In this analytical study, we consider the space-charge effect as well as high interaction strength in the small-signal limit so that the result can be compared directly with the traveling-wave tube theory. It is found that the well-known three-wave solution is essentially applicable to the electron beam only. The variation of the radiation field is much more complicated. According to the analysis, there are only three controlling parameters: the pumping strength, the electron density, and the electron energy detuning. For different choices of those parameters, the field can be in a stable regime where its growth is limited or in an unstable regime where it grows exponentially. The boundary between these two regimes is defined quantitatively. The effect of the plasma resonance is observed at high electron densities as a natural result of maximum single-pass gains. The traveling-wave tube is then analyzed as a special example.
TL;DR: In this article, an algorithm of single masking in the Maxwell equations for electromagnetic particle simulation is discussed, and the absorbing boundary condition is analyzed in the light of the Budden turning point condition.
TL;DR: In this article, it was shown that the permittivity and permeability profiles of a lossless plane stratified medium can be uniquely determined from the reflection coefficient due to transverse electric plane waves at two angles of incidence and all the frequencies.
Abstract: It is shown that the permittivity and permeability profiles of a lossless plane stratified medium can be uniquely determined from the reflection coefficient due to transverse electric plane waves at two angles of incidence and all the frequencies. The inverse scattering problem at oblique incidence is transformed to an equivalent inverse scattering problem at normal incidences. The latter is transformed to an inverse scattering problem for the one‐dimensional Schrodinger equations, the solution of which is obtained by the Gel’fand–Levitan theory.
TL;DR: In this paper, the long-distance properties of pure gauge theories are described by thin strings, and quantum fluctuations induce a long-range spin-spin potential between widely separated heavy quarks This potential falls off as the fifth power of the distance between the quarks.
Abstract: If the long-distance properties of pure gauge theories are described by thin strings, then quantum fluctuations induce a long-range spin-spin potential between widely separated heavy quarks This potential falls off as the fifth power of the distance between the quarks and may be important in heavy-quark phenomenology
TL;DR: In this paper, a macroscopic theory for bulk superconductors is developed in the framework of the theory for other magnetic materials, where ''magnetization'' current is separated from ''free'' current on the basis of scale.
Abstract: A macroscopic theory for bulk superconductors is developed in the framework of the theory for other magnetic materials, where ''magnetization'' current is separated from ''free'' current on the basis of scale. This contrasts with the usual separation into equilibrium and nonequilibrium currents. In the present approach magnetization, on a large macroscopic scale, results from the vortex current, while the Meissner current and other surface currents are surface contributions to the Maxwell j. The results are important for the development of thermodynamics in type-II superconductors. The advantage of the description developed here is that magnetization becomes a local concept and its associated magnetic field can be given physical meaning.
TL;DR: In this paper, the equations of motion for a free-electron laser (FEL) with an electromagnetic pump field and a static axial electric field were derived using a Hamiltonian formalism.
Abstract: The equations of motion for a free-electron laser (FEL) with an electromagnetic pump field and a static axial electric field are derived using a Hamiltonian formalism. Equations governing the energy transfer between the electron beam and each of the electromagnetic fields are given, and the phase shift for each of the electromagnetic fields is derived from a linearized Maxwell wave equation. The relation between the static axial electric field and the resonant phase is given. Laser gain and the fraction of the electron energy converted to photon energy are determined using a simplified resonant particle model. These results are compared to those of a more exact particle simulation code.
TL;DR: In this article, the general problem of coupled heat and mass transfer in n component mixtures is formulated using a generalization of the Maxwell-Stefan equations and approximate and rigorous methods for obtaining the mass and energy fluxes are developed under the assumptions of steady one dimensional transfer.
TL;DR: In this paper, the effects of a magnetic field on wave and pulse propagation in a shearing plasma are investigated, where the wave fields are derived from the Minkowski relations for an anisotropic medium, when the magnetic field is parallel to the shearing velocity.
Abstract: Effects of a magnetic field on wave and pulse propagation in a shearing plasma are investigated. Equations for the wave fields are derived from Maxwell's equations and the Minkowski relations for an anisotropic medium, when the magnetic field is parallel to the shearing velocity. The independent propagation modes are elliptically polarized in the stationary frame and vary with the velocity of the medium. Numerical calculations are presented which show the propagation of waves and pulses through a plane-parallel shearing plasma in the case of weak and strong fields. It is found that in a weak field, propagation effects are very similar to those previously found in field-free models: the transmitted pulses acquire temporal modulations whose period is frequency dependent. In a strong field, the period of the temporal modulations is independent of frequency. Transmitted pulses can also undergo polarization changes as a result of phase differences between modes. These results are discussed in relation to their significance to propagation in a pulsar magnetosphere and, in particular, to a model for pulse microstructure.
TL;DR: In this article, a new class of separable variables is found which allows one to find an approximate analytical solution of the Maxwell equations for axial symmetric waveguides with slow (but not necessarily small) varying boundary surfaces.
Abstract: A new class of separable variables is found which allows one to find an approximate analytical solution of the Maxwell equations for axial symmetric waveguides with slow (but not necessarily small) varying boundary surfaces. Two examples of the solution are given. Possible applications and limitations of this approach are discussed.
TL;DR: In this paper, a rotational coordinate system xi, Theta, psi was introduced, where the field vector components F/sub xi/F/sub Theta/ may be expressed by F/Sub psi/This component can be obtained from a two-dimensional Hehlmholtz equation.
Abstract: After introducing a new method to solve Maxwell's equations using a complex electromagnetic field vector F, a rotational coordinate system xi, Theta, psi is introduced. In this coordinate system, the field vector components F/sub xi/, F/sub Theta/ may be expressed by F/sub psi/. This component can be obtained from a two-dimensional Hehlmholtz equation. Specifying xi, Theta by cylindrical coordinates r, z the complex Maxwell equation curl F= gamma F is solved for the axisymmetric case (/spl part///spl part/psi = 0) and for the nonsymmetric case. The differential equations for magnetic field lines are solved and surfaces on which the normal component of B and the tangential components of E vanish are recognized as metallic walls of toroidal resonators of various arbitrary cross sections. In the Appendix the results of the new method are compared with well known results for circular cylindrical waveguides.
TL;DR: In this paper, a generalized expression for relaxation entropy, Δs r, including momentum transfer in incompressible fluids and relaxation coefficient matrices, is given for the second-sound wave moving with speed c 0 and relationships describing diffusive fluxes of mass J and energy J vs concentration and enthalpy increments in wave front are found.