On the electromagnetic pulse produced by nuclear explosions

The electromagnetic pulse (EMP) produced by the gamma rays from nuclear explosions is discussed. The gamma rays produce a current of Compton recoil electrons, and these electrons produce further ionization so that the air becomes conducting. The Compton current leads to the generation of electromagnetic fields according to Maxwell's equations. The conductivity tends to limit the magnitude of the fields. Approximate methods of solving the equations are described by considering time regimes in which various terms in the equations are negligible, e.g., either the conduction current or the displacement current can be dropped. Further advantage is obtained by replacing the transverse fields by outgoing and ingoing waves; outgoing waves are dominant at early times. Features of the solutions are described for nuclear bursts at the ground surface and at high altitude. The history of EMP is reviewed briefly.     

A vector diagram of Maxwell's equations

A vector diagram illustrating Maxwell's equations is derived. Upon equating various components of vectors in the diagram, a number of common relationships between field quantities are obtained. The potentials and their relationships to field quantities may also be represented. Justification of the procedure used to construct the diagram is based on Fourier transformation of Maxwell's equations. While the diagram is mostly of interest for its novelty, it has found use in clarifying certain gauge choices in dealing with electromagnetic potentials     

Impedance, bandwidth, and Q of antennas

To address the need for fundamental universally valid definitions of exact bandwidth and quality factor (Q) of tuned antennas, as well as the need for efficient accurate approximate formulas for computing this bandwidth and Q, exact and approximate expressions are found for the bandwidth and Q of a general single-feed (one-port) lossy or lossless linear antenna tuned to resonance or antiresonance. The approximate expression derived for the exact bandwidth of a tuned antenna differs from previous approximate expressions in that it is inversely proportional to the magnitude |Z'/sub 0/(/spl omega//sub 0/)| of the frequency derivative of the input impedance and, for not too large a bandwidth, it is nearly equal to the exact bandwidth of the tuned antenna at every frequency /spl omega//sub 0/, that is, throughout antiresonant as well as resonant frequency bands. It is also shown that an appropriately defined exact Q of a tuned lossy or lossless antenna is approximately proportional to |Z'/sub 0/(/spl omega//sub 0/)| and thus this Q is approximately inversely proportional to the bandwidth (for not too large a bandwidth) of a simply tuned antenna at all frequencies. The exact Q of a tuned antenna is defined in terms of average internal energies that emerge naturally from Maxwell's equations applied to the tuned antenna. These internal energies, which are similar but not identical to previously defined quality-factor energies, and the associated Q are proven to increase without bound as the size of an antenna is decreased. Numerical solutions to thin straight-wire and wire-loop lossy and lossless antennas, as well as to a Yagi antenna and a straight-wire antenna embedded in a lossy dispersive dielectric, confirm the accuracy of the approximate expressions and the inverse relationship between the defined bandwidth and the defined Q over frequency ranges that cover several resonant and antiresonant frequency bands.     

Application of a variational principle to systems with radiation loss

A variational principle for the frequency of electromagnetic systems with radiation is derived from Maxwell's equations. Expressions for the quality factorQare obtained in three illustrative examples: a leaky transmission line resonator, a grating coupler, and a curved slab waveguide. Extensive numerical results for theQof the grating coupler are presented in normalized form. By optimization of the variational expressions with respect to the amplitudes of the forward and backward waves, coupled-mode equations are derived for a grating structure. The variational formulas agree with results obtained from a perturbational analysis.     

Minimum entropy quantizers and permutation codes

Amplitude quantization and permutation encoding are two approaches to efficient digitization of analog data. It has been proven that they are equivalent in the sense that their optimum rate versus distortion performances are identical. Reviews of the aforementioned results and of work performed in the interim by several investigators are presented. Equations which must be satisfied by the thresholds of the minimum entropy quantizer that achieves a prescribed meanrth power distortion are derived, and an iterative procedure for solving them is developed. It is shown that these equations often have many families of solutions. In the case of the Laplacian distribution, for which we had previously shown that quantizers with uniformly spaced thresholds satisfy the equations whenr=2, other families of solutions with nonuniform spacing are exhibited. What had appeared to be a discrepancy between the performances of optimum permutation codes and minimum entropy quantizers is resolved by the resulting optimum quantizers, which span all entropy rates from zero to infinity.     

Semiempirical relation for curved optical waveguide design in theedge-guided mode regime

A semiempirical relation has been developed for determining the minimum allowable radius of curvature of a circular waveguide with an edge-guided fundamental mode. The specified parameters are the wavelength, the effective refractive index of the waveguide, the lateral index step, and the allowable radiation loss coefficient. This relation was fitted and verified against numerically evaluated solutions of Maxwell's equations in two dimensions for lateral index steps 0.01<ΔN<0.1, for effective indices of refraction 3xGa_1-xAs system), and for radiation losses of 10^-4 <α_r<100 cm^-1. The difference between the results of solving Maxwell's equations and the semiempirical relation over these parameter ranges was determined to be less than 2%     

The structure of the electromagnetic field as derived from first principles

The physical origin of the coupling between the electromagnetic field and electrically charged particles is rooted in quantum physics, and is thus not directly accessible to classical electrodynamics. We provide a physical discussion of the electromagnetic potentials that bridges this gap. Starting from an examination of the Aharonov-Bohm effect, we recognize the fundamental role of the electromagnetic potentials in the coupling process, and recover the mathematical origin of gauge invariance in electrodynamics. Then, we identify the dynamical components of the electromagnetic field, give an account of the concept of gauge fixing, and finally discuss solutions of Maxwell's equations in terms of gauge potentials.     

High-accuracy FDTD solution of the absorbing wave equation, and conducting Maxwell's equations based on a nonstandard finite-difference model

We previously introduced high-accuracy finite-difference time-domain (FDTD) algorithms based on nonstandard finite differences (NSFD) to solve the nonabsorbing wave equation and the nonconducting Maxwell equations. We now extend our methodology to the absorbing wave equation and the conducting Maxwell equations. We first derive an exact NSFD model of the one-dimensional wave equation, and extend it to construct high-accuracy FDTD algorithms to solve the absorbing wave equation, and the conducting Maxwell's Equations in two and three dimensions. For grid spacing h, and wavelength /spl lambda/, the NSFD solution error is /spl epsiv//spl sim/(h//spl lambda/)/sup 6/ compared with (h//spl lambda/)/sup 2/ for ordinary FDTD algorithms using second-order central finite-differences. This high accuracy is achieved not by using higher-order finite differences but by exploiting the analytical properties of the decaying-harmonic solution basis functions. Besides higher accuracy, in the NSFD algorithms the maximum time step can be somewhat longer than for the ordinary second-order FDTD algorithms.     

Capacity bound analysis for FIR Be/spl acute/zout equalizers in ISI MIMO channels

We provide a quantitative analysis for the capacity performance of zero-forcing equalizers, also known as Be/spl acute/zout equalizers, in a multiple antenna, frequency-selective fading environment with either parallel or sequential structure. The capacity upper bound of the equalizers, when there is no restriction on the filter length, is derived by directly extending the flat-fading results in a previous paper by the present authors. The parallel structure presents an inherent capacity loss quantified as a function of the channel couplings, which can be avoided by adopting an interference cancellation procedure in the sequential structure. For practical implementation, two approaches are investigated for finite impulse response (FIR) sequential equalizers-truncated LaBe/spl acute/st (Layered Be/spl acute/zout Space-Time) and perfect LaBe/spl acute/st equalizers. For truncated LaBe/spl acute/st equalizers, the percentage of achievable capacity is derived as a function of the filter length in analytical form, and the empirical optimum delay is also provided. For perfect LaBe/spl acute/st equalizers, we demonstrate that the filter choice that yields an optimum signal-to-noise ratio (SNR) can also asymptotically achieve the optimum infinite impulse response (IIR) capacity bound. Both of the two designs can approach the IIR capacity upper bound arbitrarily closely, provided there are an adequate number of FIR taps.     

Comments on `Riemann-Green function solution of transientelectromagnetic plane waves in lossy media'

In commenting on the above-named work by O.R. Asfar (see ibid., vol.EMC-32, no.3, p.228-31, Aug. 1990), the commenter notes that one can write infinitely many solutions for the associated magnetic field strength that will all satisfy Maxwell's equations, but Maxwell's equations cannot tell which one of these infinitely many solutions is the right one. It is further pointed out that the physical significance of the magnetic current density term used became clear when transients in lossy media were investigated with Lorentz's equations of electron theory, which allow for the fact that electric charges are always connected with particles having a mass, whereas Maxwell's original equations do not contain the concept of mass. A physical explanation for this is offered, and attention is given to the creation of the singularity in Maxwell's equations that make sit impossible to obtain the associated magnetic field strength without some limit process     

Computation of the Electromagnetic Fields and Induced Temperatures Within a Model of the Microwave-Irradiated Human Eye

The electromagnetic fields within a detailed model of the human eye and its surrounding bony orbit are calculated for two different frequencies of plane-wave irradiation: 750 MHz and 1.5 GHz. The computation is performed with a finite-difference algorithm for the time-dependent Maxwell's equations, carried out to the sinusoidal steady state. The heating potential, derived from the square of the electric field, is used to calculate the temperatures induced within the eyeball of the model. This computation is performed with the implicit alternating-direction (IAD) algorithm for the heat conduction equation. Using an order-of-magnitude estimate of the heat-sinking capacity of the retinal blood supply, it is determined that a hot spot exceeding 40.4/spl deg/C occurs at the center of the model eyeball at an incident power level of 100 mW/cm/sup 2/ at 1.5 GHz.     

Toroidal Resonators and Waveguides of Arbitrary Cross Section

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.     

Another language for describing motions of mechatronics systems: a nonlinear position-dependent circuit theory

Dynamics and control of nonlinear mechanical systems and advanced mechatronic systems can be investigated more vividly and efficiently by using corresponding nonlinear position-dependent circuits that describe Lagrange's equations of motions and interactions with objects or/and task environments. Such expressions of Lagrange's equations via nonlinear circuits are indebted to lumped-parameter discretization of mechanical systems as a set of rigid bodies through equations of motion due to Newton's second law. This observation is quite analogous to validity of electric circuits that can be derived as lumped parameter versions of Maxwell's equations of electromagnetic waves. Couplings of nonlinear mechanical circuits with electrical circuits through actuator dynamics are also discussed. In such electromechanical circuits the passivity should be a generalization of impedance concept in order to cope with general nonlinear position-dependent circuits and play a crucial role in their related motion control problems. In particular, it is shown that the passivity as an input-output property gives rise to a necessary and sufficient characterization of H/sub /spl infin//-tuning for disturbance attenuation of robotic systems, which can give another system theoretic interpretation of the energy conservation law.     

Nodal-based finite-element modeling of Maxwell's equations

Weak forms are derived for Maxwell's equations which are suitable for implementation on conventional C⁰ elements with scalar bases. The governing equations are expressed in terms of general vector and scalar potentials for the electric field intensity vector. Gauge theory is invoked to close the system and dictates the continuity requirements for the potentials at material interfaces as well as the blend of boundary conditions at exterior boundaries. Two specific gauges are presented, both of which lead to Helmholtz weak forms which are parasite-free and enjoy simple, physically meaningful boundary conditions. A general and numerically efficient procedure for enforcing the jump discontinuities on the normal components of vector fields at dielectric interfaces and boundary conditions on curved surfaces is also given     

Computer Analysis of Microwave Propagation in a Ferrite Loaded Circular Waveguide---Optimization of Phase-Shifter Longitudinal Field Sections

A theoretical analysis of the microwave propagation in a circular TE/sub 11/ waveguide partially or completely loaded with an axially magnetized ferrite rod is presented. This study is based upon an exact analytical treatment of the Maxwell's equations, together with an original numerical method of solving transcendental equations with a complex variable. The introduction of the complex propagation constant /spl Gamma/ = /spl alpha/ + j/spl beta/, taking in account the losses in the filling medium, had never been attempted because of the mathematical difficulties involved making essential the use of a large capacity computer. The developed program not only supplies all the propagation characteristics for a given structure but also enables us to optimize a phase-shift section in accordance with the user's requirements. This study is a first step towards the theoretical optimization of two types of reciprocal phasers: the dual mode phaser (DMP) and the polarization insensitive phaser (PIP), both widely used in array antenna systems. The computed results obtained for the basic section of such phasers operating at a central frequency of 9.5 GHz are given. Obviously, this work is still incomplete since it does not include the optimization of all the components of a practical phase shifter, for example, the polarizers. Moreover, we have assumed the ferrite partially magnetized by a continuously variable bias field, although the PIP and the DMP are normally operated in a latching configuration; we presently complete our study according to these practical considerations.     

The Maxwell's equations in the sense of distributions

It is well known that there is no direct one-to-one correspondence between the electromagnetic theory based on the physical laws and that based on the Maxwell's differential equations. For example, in order to derive the boundary conditions from the Maxwell's differential equations, one assumes that some integral identities derived from them are valid even when the field components (or material parameters) are discontinuous. This assumption violates, in a sense, the completeness of the theory of electromagnetism based on the Maxwell's differential equations. We will prove that if one postulates that the Maxwell's equations are valid in the sense of distributions, then this incompleteness will be removed and the boundary conditions will appear implicitly in the basic differential equations.     

An inverse scattering approach based on the differential E-formulation

An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated field values, while the Helmholtz wave equation is set as constraint. The Fre/spl acute/chet derivatives of the cost functional with respect to the scatterer properties are derived analytically by means of the calculus of variations. Edge elements are used for the numerical treatment of the problem.     

EMP Effects on the Performance of a Direct Sequence Spread-Spectrum Communication System

This paper presents an analysis of the performance of a direct sequence spread-spectrum communication (processor) system operating in a nuclear EMP environment. EMP-induced interference (conducted EMP) at the receiver is modeled by a damped sinusoid and the analysis of the system uses a frequency domain approach instead of the conventional time domain approach. However, the interference suppression factor derived using the frequency domain approach reduces to that obtained using a time domain approach for the tone jammer case, in which the damping factor in the conducted EMP interference model approaches unity. Using a Gaussian approximation to the interference, numerical results are presented to illustrate the significant EMP-induced interference effects on the system performance and its hardening design parameters.     

On the stability of the pulsewidth-modulated C/spl acute/uk converter

It has been observed that a stabilizing controller for the state-space-average model of a pulsewidth-modulated (PWM) DC-DC converter does not automatically imply a stabilizing controller for the DC-DC converter itself, especially in the case of the C/spl acute/uk converter. By applying multifrequency averaging as a generalization of the state-space averaging technique, the stationary periodic signals of the C/spl acute/uk converter can be obtained by solving a set of linear equations. Using these equations, we are able to analyze stability aspects of the open-loop and closed-loop PWM C/spl acute/uk converter. Simulations are included in open- and closed-loop situations.     

Use of the Lorentz condition for uncoupling scalar and vector potentials

The Lorentz condition, which specifies the divergence of a magnetic vector potential and which uncouples Maxwell's equations with mixed scalar and vector potentials, is considered for several media. Difficulties arising from position-dependent medium parameters are discussed.