Showing papers on "Maxwell's equations published in 1988"

Nonlinear gyrokinetic theory for finite‐beta plasmas

Abstract: A self‐consistent and energy‐conserving set of nonlinear gyrokinetic equations, consisting of the averaged Vlasov and Maxwell’s equations for finite‐beta plasmas, is derived. The method utilized in the present investigation is based on the Hamiltonian formalism and Lie transformation. The resulting formulation is valid for arbitrary values of k⊥ρi and, therefore, is most suitable for studying linear and nonlinear evolution of microinstabilities in tokamak plasmas as well as other areas of plasma physics where the finite Larmor radius effects are important. Because the underlying Hamiltonian structure is preserved in the present formalism, these equations are directly applicable to numerical studies based on the existing gyrokinetic particle simulation techniques.

Calculations of the dispersive characteristics of microstrips by the time-domain finite difference method

Abstract: A direct time-domain finite-difference method is used to recharacterize the microstrip. Maxwell's equations are discretized both in time and space and a Gaussian pulse is used to excite the microstrip. The frequency-domain data are obtained from the Fourier transform of the calculated time-domain field values. Since this method is completely independent of all the above-mentioned investigations, the results can be considered as an impartial verification of the published results. The comparison of the time-domain results and those from the frequency-domain methods has shown the integrity of the time-domain computations. This method is very general and can be applied to model many other microwave components. >

Global existence for the relativistic Vlasov-Maxwell system with nearly neutral initial data

Abstract: Global classical solutions to the initial value problem for the relativistic Vlasov-Maxwell equations are obtained in three space dimensions. The initial distribution of the various species may be large, provided that the total positive charge nearly cancels the total negative charge.

Three-dimensional finite, boundary, and hybrid element solutions of the Maxwell equations for lossy dielectric media

Abstract: Finite, boundary, and hybrid element approaches are presented as numerical methods for computing electromagnetic (EM) fields inside lossy dielectric objects. These techniques are implemented as computer algorithms for solving the Maxwell equations in heterogeneous media in three dimensions. Algorithm verification takes the form of comparisons of test cases with analytic solutions. Computed results for each technique are in good agreement with exact solutions, especially in light of the coarse computational grid resolutions used. Implementation was in FORTRAN on a moderate-sized computer (MicroVax II). The basic problem formulation is quite general; however, it has direct application in hyperthermia as a cancer therapy where the EM fields produced inside the patient by external sources are of interest. An example of the application of these numerical methods in a three-dimensional clinical setting is shown. >

An error‐based approach to complementary formulations of static field solutions

Abstract: The constitutive relationship between fields in electromagnetic media is cast in error form. For well-posed static problems, the error splits systematically into complementary functionals. Error minimization provides a universal variational principle that generates complementary and dual solution formulations. The error, which is wholly attributed to the numerical constraints in approximate solutions, is always defined and computable locally and globally.

Calculation of self and mutual impedances for coils on ferromagnetic cores

Abstract: By means of integral transform techniques, the paper establishes a new set of self- and mutual-impedance formulas relating to coils on ferromagnetic cores of circular cross-section. If the core is straight and infinitely long, the formulas are expressed in terms of convergent integrals that may be evaluated numerically. In the case of closed cores, e.g. toroidal cores, the formulas formally reduce to convergent series that may be truncated according to the degree of accuracy required. The formulas follow directly from the solution of Maxwell's equations and therefore offer the ultimate in accuracy.

Radiation from oscillating dipoles embedded in a layered system

Abstract: Maxwell’s equations are solved for the radiation due to a source consisting of an oscillating point dipole located in a layered system. Solutions are developed first for the related problem of the fields generated in the system by a distant dipole source, and the problem of interest is then solved by application of the Lorentz reciprocity theorem. The effects of extremely thin layers are considered in detail. Some of the results are illustrated by calculations of the emission from dipoles located in, or near, a film covering a plane‐bounded silver metal substrate. It is found that the surface selection rule for absorption, emission, or Raman scattering is not valid for molecules contained in this film.

Force calculation using magnetizing currents

Abstract: An application of the finite-element method to force calculations is proposed. The force is determined by utilizing the magnetizing currents and flux densities on the line-forming elements. The method has been applied to a model of a permanent-magnet-type synchronous motor. Theoretical and test values of the model are shown to be well matched, demonstrating that this method is effective for highly accurate calculations of force and torque. The method has the additional advantage that the force distribution acting on the object is obtained. >

Magnetohydrodynamic equations for systems with large Larmor radius

Abstract: A set of one‐fluid, modified magnetohydrodynamic (MHD) equations is developed that describes magnetized plasmas for which the relevant scale lengths are intermediate between the electron and ion Larmor radii, and the relevant time scales are intermediate between the electron and ion cyclotron frequencies. It is shown that the momentum equation is the same as that of conventional MHD but that the evolution of the magnetic field is strongly affected. The implications of the modified MHD system on the ‘‘frozen‐in’’ theorem, magnetosonic waves, Alfven waves, and the interchange instability are examined.

Transient analysis of a magnetized plasma in three-dimensional space

Abstract: The time-domain formation, in terms of unified nodal equations, of a magnetized cold plasma in three-dimensional space using the Bergeron method is described. The validity of this treatment is shown by simulations of both transverse propagation and longitudinal propagation. In the formulation of the characteristic equation in the time domain, the authors introduce variables corresponding to the first and second derivates of the electric polarization. Thus the iterative computation can be performed by using only the values obtained at the previous time step. This procedure very closely matches the architecture for high-speed computation in the vector processor of a supercomputer. This property can render practical the simulation of three-dimensional fields involving gyroelectric anisotropic media and expand the generality of the numerical vector analysis method in the time domain. >

Spherically symmetric solutions of the non-minimally coupled Einstein-Maxwell equations

Abstract: The four-dimensional Einstein-Maxwell action is modified by introducing a 'non-minimal coupling' between the electromagnetic field strength and the spacetime curvature. This is partly motivated by recent results on dimensional reduction of higher-dimensional unified theories. The authors study the corresponding field equations in the case of static and spherically symmetric field configurations, and classify the solutions without magnetic charge according to their global properties. It is shown that asymptotically flat black hole solutions have positive ADM mass and satisfy similar relations between mass and charge as the Reissner-Weyl-Nordstrom solution (1918) of the minimally coupled Einstein-Maxwell equations.

On a surface integral representation for homogeneous anisotropic regions: two-dimensional case

Abstract: A mathematical statement of the Huygen's principle for an electromagnetic field in an anisotropic region is obtained by a linear mapping of the original anisotropic region into a complex isotropic region using the material permeability and permittivity tensors. The original field equations are reduced to canonical form so that they resemble Helmholtz equations in transform space. This allows the use Huygen's principle in the transform space, after which the result is mapped back into real space; here the resulting contour quantities can be expressed in terms of tangential field quantities, using Maxwell's equations. The field representation is found to be polarization-dependent. In this two-dimensional analysis, each polarization has a different representation and is therefore treated both separately and using duality. Some elementary applications to scattering are presented and discussed in detail. >

Flow fields in electromagnetic stirring of rectangular strands with linear inductors: Part I. theory and experiments with cold models

Abstract: A model is presented to compute the electromagnetic force fields and fluid flow fields in electromagnetic stirring of continuously cast strands with rectangular cross-section. The model involves the solution of the Maxwell equations, the Navier-Stokes equations, and the transport equations for the turbulence characteristicsk and e. The procedure of depth-averaging is applied in the treatment of several three-dimensional flows. Experiments were performed to check the computations using mercury as fluid. The spatial distribution of the magnetic induction and of the force density was determined for the laboratory inductor used in the stirring experiments. The flow velocity was measured photographically or with a drag probe, respectively. The agreement between experimental and theoretical data was found to be within 25 pct. It is concluded that the theory is sufficiently reliable to predict the flow fields in electromagnetic stirring of steel strands. In Part II of this paper the model is applied to analyze stirring situations in continuous casting of steel.

An update on the circuit approach to calculate shielding effectiveness

Abstract: The shielding effectiveness of an enclosure at low frequencies can be computed using a circuit approach. Not only does this technique include the effects of the properties of the shield material, but it also includes the details of the geometry of the enclosure. This approach allows a nonempirical consideration of mesh enclosures and the effects of resistive seams in enclosure walls. By working with the circuit analogue, penetration by transient fields can be computed. Essentially the enclosure is viewed as an antenna. In the case of magnetic shielding effectiveness, the enclosure is viewed as a short-circuited loop antenna. In the case of electric-field penetration, the enclosure is viewed as a fat electric dipole. Using this characterization and exact solutions where available, the current distribution on the outside of the enclosure is determined. Based on the current distribution, the penetrating fields are computed. The equations are developed in such a way as to preserve a lumped circuit analogue for the low-frequency region. The basic circuit equations for magnetic field penetration are rederived from a rigorous solution. Rules to estimate the rise time, fall time, and peak magnitudes of transient penetrating fields are developed. The electric shielding effectiveness is developed in a similar manner. >

On a family of solutions of the Einstein-Maxwell equations

Abstract: A family of axisymmetric asymptotically flat solutions of the Einstein-Maxwell field equations is presented. In a particular case we obtain a magnetostatic solution which reduces to the well-known Schwarzschild metric in the absence of a magnetic field and describes the exterior gravitational field of a massive magnetic dipole moment.

Consequences of the Maxwell relation for anti-plane shear deformations of an elastic solid

Abstract: Previous numerical work has predicted chaotic distributions of phases in certain deformations of an elastic solid whose stress-strain relation in simple shear is nonmonotone. The present work provides an interpretation of these results making use of elastic stability considerations. For a specific material, a conformal mapping technique is shown to generate the totality of all deformations satisfying the Maxwell relation. It is shown that some boundary value problems have no solutions which obey the Maxwell relation. Such problems may have associated with them an infinite sequence of deformations (corresponding to a minimizing sequence in variational calculus) which satisfies the Maxwell relation in the sense of a limit. The properties of such sequences are examined in detail, and it is shown that the chaotic numerical solutions may be interpreted as terms in this sequence.

Analysis of electromagnetic scattering from dielectrically coated conducting cylinders using a multifilament current model

Abstract: A method of moments solution is presented for the problem of transverse magnetic scattering from dielectrically coated conducting cylinders. The solution uses fictitious filamentary electric sources of yet unknown currents to simulate both the field scattered by the cylinder and the field inside the dielectric coating. The simulated fields obey the boundary conditions, namely, the continuity of the tangential components of the electric and magnetic fields across the air-dielectric interface and the vanishing of the tangential component of the electric field at the perfect conductor, at selected sets of points on these respective surfaces. The result is a matrix equation that is readily solved for the unknown current. The currents can be used to determine approximate values for the fields and field-related parameters of interest. The procedure is simple to implement and is general in that cylinders of smooth but otherwise arbitrary shape and coating of arbitrary complex permittivity can be handled. Illustrative examples are considered and compared with available data, demonstrating the efficiency of the solution. >

Calculation of 3D eddy current problems by finite element method using either an electric or a magnetic vector potential

Abstract: The authors review the theories that they have used to develop two finite-element software packages. One uses a magnetic vector potential combined with an electric scalar potential in conducting regions and only the magnetic vector potential elsewhere. The second formulation is based on an electric vector potential and a magnetic scalar potential whereby only the latter is used in conducting regions. A way to obtain unique solutions by satisfying the divergence condition of the vector potentials is shown. Calculations for several problems are reported, showing the efficiency of the codes. The pros and cons of both formulation are discussed. >

An exterior boundary-value problem for the Maxwell equations with boundary data in a Sobolev space

Abstract: We treat the time-harmonic Maxwell equations in an exterior domain with prescribed boundary data [n, E] in the Sobolev space of square integrable tangential fields with square integrable surface divergence. By using boundary integral equation methods, existence and uniqueness results are established. Furthermore, we investigate the completeness of electric and magnetic dipoles distributed on an inner surface in this Sobolev space.

On the local power dissipation of h.f. waves in hot inhomogeneous plasmas

Abstract: In a medium with spatial dispersion the power Pabs dissipated per unit volume by an electro-magnetic wave differs from (J.E) by the divergence of a vector which is interpreted as the correction delta Skin to the Poynting flux due to the coherent particle motion in the field. The authors obtain expressions for Pabs and delta Skin in hot, inhomogeneous, weakly collisional plasmas by evaluating the time-averaged rate of change of the total kinetic energy density of charged particles, generalizing a method suggested by McVey et al. (Phys. Rev. Lett. vol.55, p.507, 1985). The authors prove that these expressions are consistent with the time averaged Poynting theorem for Maxwell equations. By specializing them to uniform and plane-stratified geometries, they derive some interesting properties of wave-plasma energy exchanges, and they check that the well known expressions for Pabs and delta Skin in the case of a plane wave propagating in an infinite homogeneous plasma are recovered in the appropriate limit.

The separability of Maxwell’s equations in type‐D backgrounds

Abstract: It is shown that in a type‐D space‐time that admits a two‐index Killing spinor a differential operator can be constructed that maps a solution of the Maxwell equations into another solution. By considering as a background the Plebanski–Demianski metric, which includes all the vacuum type‐D metrics, this operator is used to obtain all the components of the electromagnetic field and the vector potential. The separated functions appearing in the solutions are shown to obey identities of the Teukolsky–Starobinsky type and the separable solutions are shown to be eigensolutions of a certain differential operator with the ‘‘Starobinsky constant’’ as the eigenvalue.

Leading order hard edge fringe fields effects exact in (1 + δ) and consistent with Maxwell's equations for rectilinear magnets

Abstract: In a circular machine, where the linear lattice functions ({alpha}, {beta},{gamma}) and a phase advance can be defined, one expects the fringe field effects to be negligible if the change in these functions is small through the element. However, this may not always be the case. In such situations, it is useful to have a leading order result which is adapted to tracking and analytical analysis. In this paper, we provide such a result for the quadrupole and we also provide a general formula for the effect of an arbitrary rectilinear multipole. Starting from the standard multipole expansion for the B field of a 2(n + 1)-pole (n {ge} 1), we compute the missing terms in the vector potential expansion consistent with the puree 2(n + 1)- pole symmetry. We then compute the leading effects of the fringing fields of a multipole on the dynamics. Finally, we apply this result to quadrupoles and reproduce the original results of Graham Lee-Whiting, Matsuda, and Wollnik. For the quadrupole, we show how to write a symplectic (canonical) integrator for the dynamics which can be used in a standard circular machine kick code. For higher order multipoles, we display the implicit characteristic function solutionmore » as first proposed by Dragt. 12 refs.« less

lightning‐related fields in the ionosphere

Abstract: Lightning-related transient electric fields and conduction current densities due to the redistribution of charge by the return stroke, but not directly associated with the high-intensity current channel, are investigated via a simulation of Maxwell's equations. The investigation presents evidence to suggest that the lightning-related charge redistribution and subsequent relaxation, rather than the high intensity current, is the source of the major component of the transient field and energy coupled to the ionosphere. A time domain finite element analysis is employed in the simulation, using a conductivity profile obtained simultaneously with electric field measurements which agree, in general terms, with the simulations. It is concluded that prior depictions of these phenomena underestimate the fraction of the total energy that couples to and dissipates within the ionosphere and magnetosphere.

A liquid‐metal magnetohydrodynamic acoustic transducer

Abstract: The properties of a liquid‐metal magnetohydrodynamic acoustic power transducer have been both calculated and measured. The calculations are based on linearized Navier–Stokes and Maxwell’s equations, and include Ohmic and viscous dissipation in the liquid metal. The measurements were made with liquid sodium at frequencies of about 1 kHz in a channel much larger than the viscous penetration depth but comparable in size to the electromagnetic skin depth. Calculated and measured quantities are in good agreement, indicating a quantitative understanding of this transducer. It converts acoustic power to electric power with 45% efficiency; substantially higher efficiencies appear possible with a slightly modified design.

Electric and magnetic four-vectors in classical electrodynamics

Abstract: Following the pro('edure customarily used to define the four- spin, we define clectric and magnetic ficld four-\'ectors and use them to write Maxwell equations in a manifestly Lorentz covariant formo \Ve prove that these equations are physically equivalent to the standard co- variant formulation oCMaxwel1 <,quations. \Ve th('n 5how how to develop covariant electrodynamics from our set of equations.

Theoretical study of the folded waveguide

Abstract: A three-dimensional (3-D) algorithm for solving Maxwell's equations is applied to the analysis of folded waveguides used for fusion plasma heating at the ion cyclotron resonance frequency (ICRF). In this method a finite-difference method is used with a successive overrelaxation (SOR) convergence scheme and a method of treating boundaries that allows the cavity to have an arbitrary shape. A rigorous analysis of the magnetic-field structure in the folded waveguide is presented. The results are compared with experimental measurements in vacuum. To study breakdown problems, a much simpler two-dimensional (2-D) model is adopted. It is found from the 2-D analysis that the geometry, shape, and thickness of the vanes play an important role in avoiding voltage breakdown problems. >

Theoretical electric field distributions produced by three types of regional hyperthermia devices in a three-dimensional homogeneous model of man

Abstract: A boundary-element formulation of the Maxwell equations is used to solve for the electric field in a three-dimensional homogeneous model of man. The boundary element grid is constructed from cross-sectional slices of the body in such a way that the contour of the body surface is preserved, but the interior heterogeneity is not taken into account. By using the method in conjunction with a homogeneous three-dimensional model, only the body surface and the source are discretized; hence, the computational resolution required for detailed three-dimensional modeling is reached within the constraints of moderate computing power (MicroVax II). Electromagnetic source arrangements simulating three types of regional noninvasive hyperthermia systems are examined, namely magnetic induction devices, annular array applications, and capacitive heating systems. Results indicate that the longitudinal extent of the electric fields produced by the annular array and capacitive heating models can be significant, suggesting that three-dimensional simulation of these types of devices may be required to fully understand their capabilities. >