Showing papers on "Maxwell's equations published in 1972"

Solutions of the Einstein-Maxwell equations with many black holes

Abstract: In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G1/2m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.

Theorems of bianisotropic media

Abstract: Theorems concerning electromagnetic fields in linear nonconducting bianisotropic media are investigated. After establishing their symmetry properties, the constitutive relations are examined under time reversal and spatial inversion transformations. Conditions under which the image method and the reciprocity relationships can be applied are discussed. Dyadic Green's functions and duality relations are also derived. With a postulated Lagrangian density, Maxwell's equations are obtained from Hamilton's principle, and energy momentum tensors are obtained from Noether's theorem. Introducing a quantum postulate in addition to the Maxwell's equations, electromagnetic fields in bianisotropic media are quantized.

Analytical model for a polarizable medium at radio and lower frequencies

Abstract: The Maxwell equations are written and discussed in the frequency domain for a medium exhibiting electrical polarization at radio and lower frequencies, in the range of linearity between current density and electric-field intensity. A complex function of frequency is proposed for the conductivity, which is able to describe all the families of available experimental curves for rock samples in the natural state, showing the effect of polarization. Such a function is a constitutive relation for the polarizable medium in the frequency domain. The concept of ‘abnormal’ dielectric constant for rocks is discussed in the context of the physical mechanisms responsible for the effect of electrical polarization at radio frequencies and below. Such a concept, always possible theoretically, only introduces confusion in the understanding of the basic physical mechanisms involved. As an alternative the extensive use of the concept of a total current complex conductivity is suggested.

Instabilities and Induced Scattering Due to Nonlinear Landau Damping of Longitudinal Plasma Waves in a Magnetic Field

Abstract: The matrix elements for nonlinear wave‐particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov‐Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k⊥≫k‖, the symmetry relations for mode‐mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss‐cone modes. In additi...

Models of static, cylindrically symmetric solutions of the einstein-maxwell field

Abstract: Models of static, cylindrically symmetric solutions of the combined Einstein-Maxwell field equations are given. These models consist of extended distributions of matter with surface electric currents and magnetic fields outside the matter. The electric currents serve as sources of the magnetic fields; the distribution of matter as well as the magnetic fields serve as sources of the gravitational field. The magnetic lines of force may be parallel to the axis or circular and centered on the axis. The matter distribution is cylindrically symmetric and may be contained within a central cylinder or a tube centered about the axis. All ordinary physical and geometric requirements are satisfied by the models.

Self‐Consistent Electromagnetic Waves in Relativistic Vlasov Plasmas

Abstract: It is shown that the treatment of relativistic superluminous waves can be simplified by making a Lorentz transformation to a new frame in which the spatial variable no longer appears. Self‐consistent solutions of the relativistic Vlasov‐Maxwell equations can be constructed in the new frame. These solutions correspond to nonlinear traveling waves in a finite temperature plasma, and reduce to the usual linear results in the small‐amplitude limit. A particular example is considered in which the nonlinear waves propagate through a relativistic Maxwellian plasma, and it is shown that pure transverse waves cannot exist in such a case, but that a coupled longitudinal field necessarily appears. For this case the nonlinear effects are evaluated correct to second order in the transverse field amplitude, thus obtaining a nonlinear dispersion relation and a measure of the coupling. In addition, solutions involving pure longitudinal waves can be found, and are also investigated. In limiting cases the results agree closely with previous calculations based on hydrodynamic models.

Lagrangian studies of plasma wave interactions. I

Abstract: A study of wave-wave interactions in plasmas is made using a lagrangian formulation developed by Low. Coupled mode equations are derived. The method offers distinct advantages over the conventional approach starting from the Vlasov- Maxwell equations. Two examples of the lagrangian method are considered: (i) the nonlinear interaction of transverse waves in a warm field-free plasma to produce plasma oscillations and (ii) the interaction of three- electromagnetic waves in a cold magnetized plasma. Its application to waves in warm magnetized plasmas and to explosive instabilities is considered in part II.

On the presentation of Maxwell's theory

Abstract: Maxwell's original work on electromagnetic theory is reviewed. All the general equations prominently displayed by the scientist in his two important works have been cast in modern notation with particular emphasis on the connotation. The relationship between two integral forms of the Faraday-Maxwell and the Ampere-Maxwell laws has been examined in detail, all within the framework of Maxwell's theory, and using the conventional concepts of space and time. An example is given to show the exact nature of the integral form of the Faraday-Maxwell equation based on the Special Theory of Relativity. Some typical ambiguities found in many presentations of Maxwell's theory are pointed out and two unconventional presentations are commented on.

Equilibrium configurations of Vlasov plasmas carrying a current component along an external magnetic field.

Abstract: A model of equilibrium configurations of Vlasov plasmas is considered which represents a combination of the models of Harris (1962) and Nicholson (1963). These plasma configurations carry a current component along an external magnetic field. The considered slab model contains a diamagnetic current and a field-aligned current for an arbitrary ratio of particle pressure to magnetic pressure of the applied constant field. For a fixed pressure ratio and field-aligned current, the model admits a family of equilibrium solutions in which the diamagnetic currents range from zero to a maximum value. The amount of diamagnetic current flowing in a machine depends on the width of the machine, the field-aligned current and other plasma parameters.

Conformal Invariance of Maxwell's Equations

Abstract: A self-contained derivation of the conformal invariance of Maxwell's equations is presented.

Equilibrium and Stability of Large‐Amplitude Magnetic Bernstein‐Greene‐Kruskal Waves

Abstract: The stability of transverse magnetic Bernstein‐Greene‐Kruskal waves to small‐amplitude perturbations is analyzed within the framework of the Vlasov‐Maxwell equations. The Vlasov‐Maxwell equations are linearized about an equilibrium state which supports (self‐consistently) a spatially‐periodic finite‐amplitude transverse electromagnetic wave. An external magnetic field, B0 = B0ez, is included in the analysis, and spatial variations in equilibrium and perturbed quantities are taken to be in the z direction. A matrix dispersion relation is obtained that relates the (complex) oscillation frequency ω and wavenumber k of the perturbation; stability criteria are obtained for a monochromatic circularly polarized equilibrium wave. As an example, a trapped electron distribution is considered which is isotropic and monoenergetic in the plane perpendicular to the propagation direction of the equilibrium wave, and cold parallel to the propagation direction. The ions are assumed to form a cold neutralizing background. ...

Magnetic dipole moment determination by near-field analysis

Abstract: A method for determining the magnetic moment of a spacecraft from magnetic field data taken in a limited region of space close to the spacecraft. The spacecraft's magnetic field equations are derived from first principles. With measurements of this field restricted to certain points in space, the near-field equations for the spacecraft are derived. These equations are solved for the dipole moment by a least squares procedure. A method by which one can estimate the magnitude of the error in the calculations is also presented. This technique was thoroughly tested on a computer. The test program is described and evaluated, and partial results are presented.

A Decoupled Formulation of the Vector Wave Equation in Orthogonal Curvilinear Coordinates, with Application to Ferrite-Filled and Curved Waveguides of General Cross Section

Abstract: The introduction of a double complex-number system and the combining of the transverse field components into a compact composite structure enable the wave equation to be expressed in a form in which certain mathematical combinations of field components appear as entities completely decoupled from each other. Hence the equations can be solved for these combinations and ultimately for the components themselves. The method appears limited to guides of constant cross section and of either 1) isotropic medium and curved axis, or 2) axially anisotropic nonreciprocal medium and straight axis.

Dual symmetry of quantum electrodynamics

Abstract: Thus, the introduction of a magnetic charge into electrodynamics from the point of view of dual symmetry arguments is not only justified but necessary. In this case one achieves mutual consistency between the symmetry of the Maxwell equations with sources and the free Maxwell equations. However, Maxwell's equations can be symmetrized without introducing a new type of particle (Dirac monopole). Treating the known particles as doubly-charged particles is selfconsistent and does not contradict experimental data if there is a universal ratio of the electric and the magnetic charges for all particles [5, 21–23]; the corresponding single-charge formulation of electrodynamics corresponds to a definite choice of the “dual” gauge.

Instability of Electromagnetic Cyclotron Harmonic Waves in Plasmas

Abstract: The stability of electromagnetic ion cyclotron harmonic waves propagating normal to an external magnetic field is studied for plasmas whose ions possess loss cone type velocity distributions. It is found that, if the ions are stationary, no instability develops except in the extreme case when the ratio of parallel to perpendicular "temperatures" of the ions is of the order mi/me, where mi and me are the ion and electron masses respectively. However, for the case of two counterstreaming ion beams in a neutralizing background of electrons, instability at zero frequency and near the first several ion cyclotron harmonics can occur if the streaming velocity is of the order of the electron thermal speed.

Unification of field and circuit theories of electrical machines

Abstract: The field in the airgap of an idealised model induction motor is derived from Maxwell's equations, and the result is extended to give the stator and rotor field equations of the practical machine. It is shown that, if each term of the voltage equation of the machine, referred to stationary axes, be multiplied by the quantity K = (1/2k1N1?) sin p?1 where N1 is the number of primary terms per phase, k1 is the distribution factor, ? is the axial length, in metres, and p is the number of pole pairs, each term of the field equation will be obtained. Since the voltage equation concerned applies generally to all types of machine, the unification also appears to be general. As an illustration of its consequences, the commutator (Park's) transformation of circuit theory is shown to be equivalent to the Lorentz transformation of field theory.

Relativistic Solution of Maxwell's Equations in a Class of Conservative Flow Fields

Abstract: Maxwell's equations are solved in spherically and cylinderically symmetric regions containing a dielectric medium moving radially with constant velocity. The solutions are correct to all orders in v/c and are obtained by appropriate modification of the corresponding solutions for zero velocity.

On coupled fields in warm stratified plasmas

Abstract: This paper deals with small-amplitude coupled electromagnetic and electron acoustic waves, as described by Maxwell's equation and single-fluid hydrodynamics, in a horizontally stratified, continuously varying, warm electron plasma. First-order coupled wave equations are used to investigate the fields in a coupling region, and the results are compared with those obtained from second-order coupled wave equations. All field components are found to be finite in the coupling region.

Computer study of convection of weakly ionized plasma in a nonuniform magnetic field.

Abstract: A weakly ionized plasma in a strong and nonuniform magnetic field exhibits an instability analogous to the flute instability in a fully ionized plasma. The instability sets in at a critical magnetic field. To study the final state of the plasma after the onset of the instability, the plasma equations are integrated numerically assuming a certain initial spectrum of small disturbances. In the regime studied, numerical results indicate a final steadily oscillating state consisting of a single finite amplitude mode together with a time‐independent modification of the original equilibrium. These results agree with the analytic results obtained by Simon in the slightly supercritical regime. As the magnetic field is increased further, the wavelength of the final oscillation becomes nonunique. There exists a subinterval in the unstable wave band. Final stable oscillation with a wavelength in this subinterval can be established if the initial disturbance has a sufficiently strong component at the particular wavelength.

Kinetic theory of scattering by a plasma cylinder.

Abstract: The kinetic theory of scattering by a circular homogeneous isotropic plasma cyclinder is treated for plane wave incidence parallel to the axis of the cylinder. The relativistic form of the Vlasov equation is inverted, subject to the specular boundary condition, expressing the electronic distribution function in terms of the electric field intensity. After inverting Maxwell's equations and eliminating the distribution function, a set of Fredholm integral equations of the second kind are obtained for the angular Fourier components of the electric field. Since for low temperature the Neumann series converges, the low temperature solution is easily obtained. The first order temperature corrections are thus derived for the reflection coefficients associated with the Fourier components.