Electromagnetic Energy Flow Research Articles

High-aperture focusing systems: control of light concentration in focal region by pupil filtering

Abstract The influence of various pupil filters on the field distribution in the neighbourhood of focus within the context of the vector diffraction theory is reviewed. The principal issue is with the focal depth via the calculations of integral parameters: encircled electric energy and encircled longitudinal electromagnetic energy flow along the optical axis. It is shown that in the case of filters which change the phase, the integral parameters for small radii attain their own maximum values not in the geometrical focal plane, but in the plane which is displaced from the latter by a certain distance. The encircled electric energy and the encircled longitudinal flux have maximum values in the focal plane only for large radii. For the optimum enhancement of focal depth the most suitable filter, from those under consideration, is the truncated Bessel filter.

High-aperture focusing systems: Control of light concentration in focal region by pupil filtering

The influence of various pupil filters on the field distribution in the neighbourhood of focus within the context of the vector diffraction theory is reviewed. The principal issue is with the focal depth via the calculations of integral parameters: encircled electric energy and encircled longitudinal electromagnetic energy flow along the optical axis. It is shown that in the case of filters which change the phase, the integral parameters for small radii attain their own maximum values not in the geometrical focal plane, but in the plane which is displaced from the latter by a certain distance. The encircled electric energy and the encircled longitudinal flux have maximum values in the focal plane only for large radii. For the optimum enhancement of focal depth the most suitable filter, from those under consideration, is the truncated Bessel filter.

The global morphology of wave Poynting flux: powering the aurora.

Large-scale, electric currents flowing along magnetic field lines into the polar regions of Earth are thought to be the main contributors of the energy that powers the ionospheric aurora. However, we have found evidence for global contributions from electromagnetic waves (Alfvén waves). Data that were collected from the Polar spacecraft over the course of 1 year show that the flow of wave electromagnetic energy at altitudes of 25,000 to 38,000 kilometers delineates the statistical auroral oval. The Poynting flux of individual events distributed along the auroral oval was larger than 5 ergs per square centimeter per second, which is sufficient to power auroral acceleration processes. This evidence suggests that in addition to magnetic field-aligned currents, the dayside and nightside aurora is globally powered by the energy flow of these high-altitude Alfvén waves.

Electromagnetic energy around Hertzian dipoles

This paper considers the behavior of electromagnetic energy around Hertzian dipoles. The method of causal surfaces (surfaces through which there is no net flow of electromagnetic energy) is used to partition and track the energy. A variety of examples, involving both transient and harmonic time dependence, are presented, to illustrate the way which static and/or reactive energy is converted to outgoing, uncoupled, energy around a Hertzian or point dipole. The principal conclusion is that although accelerating charge may be thought of as the source of the radiation fields, the source of the radiated energy lies the static and/or reactive field energy near an antenna, and not in or on an antenna itself.

Photonic crystal circuits

A theory is presented for the flow of electromagnetic energy in photonic crystal circuits. Photonic crystal circuits are waveguide networks in photonic crystals. The theory is based on a set of difference equations which describe the propagation of electromagnetic waves in particular types of photonic crystal waveguides. Solutions are given for the transmission and reflection of electromagnetic waves from barriers in an otherwise infinitely long straight photonic crystal waveguide, from a junction of an infinite and a semi-infinite photonic crystal waveguide, and from an optical switching circuit. The theory developed is applicable to extended circuits with complex topologies. It is applicable to circuits in two-dimensional and three-dimensional photonic crystals.

A propagation prediction tool for urban mobile radio systems

This paper presents a propagation prediction tool (PPT), developed mainly to facilitate the path loss computation in urban environments. Based on analytical methods-geometrical optics (GOs), physical optics (POs), and uniform theory of diffraction (UTD)-the tool incorporates an empirical factor, the path loss factor n, used in all unobstructed paths between two points to remedy the deficiencies of the analytical models. Ray tracing techniques were used to model the flow of electromagnetic energy from the transmitter to the receiver. The received field strength is computed by complex vector addition of the fields arriving at the receiver by any of the mechanisms utilized. Path loss results are given for line-of-sight (LOS) and non-line-of-sight (NLOS) cases, indicating the contribution from each mechanism. Finally, comparisons with measured data for DECT systems in urban sites are presented, in order to validate the prediction tool.

Use of the continuity equation for electromagnetic energy flow todescribe radiation transport

In the geometric-optics limit the electromagnetic (EM) continuityequation, which describes EM energy flow, reduces to the radiation transportequation, in which energy flow is described generically as the motion of light(or particle) rays along straight-line trajectories in the direction of a unitvector k̂. In practical applications k̂ is discretized, makingthe transport equation extremely difficult to implement computationally andgiving rise to `ray effect' distortions owing to the non-continuousdistribution of the energy over k̂. In this paper we solve the EMcontinuity equation directly in the transport regime, obtaining an energywhich is continuously distributed in k̂ and free of ray distortion.

Physical meaning of the Poynting vector and the resolution of paradoxes (basic concept 2)

In electrical and electronic engineering, the flow of electromagnetic energy is a fundamental physical quantity that is usually estimated by the Poynting vector. However, there have been several problems with this vector, and various attempts to resolve these problems have been carried out. In this paper, these problems are put forth in order and then the physical meaning of the Poynting vector is elucidated based on the concept clarified in the previous paper. In conclusion, this vector expresses the net electromagnetic energy flow density. If the plane wave expansion of the electromagnetic field and its orthogonality are noted, the paradox on this vector is naturally resolved so that its treatment becomes clear. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(10): 56–69, 1999

FDTD analysis of PBG waveguides, power splitters and switches

Finite two-dimensional photonic bandgap (PBG) structures were analyzed with a finite-difference time-domain (FDTD) full wave, vector Maxwell equation simulator. Removal of particular portions of these PBG structures lead to interesting sub-micron-sized waveguiding environments. Several waveguides and power dividers were designed and evaluated. By introducing further defects into the PBG waveguiding structures, control of the flow of electromagnetic energy in these nanometer-sized waveguides can be affected. This effect is demonstrated, and its use to achieve a micron-sized waveguide switch is shown.

Pi2 pulsations observed from the Akebono satellite in the plasmasphere

Magnetic field, electric field, and electron density measurements from the Akebono satellite are used to study the properties of two Pi2 pulsations that occurred in succession on February 13, 1990, when the satellite was in the plasmasphere at L = 2.4–3.8, 24°–40° magnetic latitude, and 22.5 hours magnetic local time. Magnetic pulsations with a nearly identical waveform were observed in the same time interval at three ground stations (Aedey, L ≈ 6.84; York, L ≈ 2.55; and Hermanus, L ≈ 1.83), which were located near midnight, confirming that the pulsations propagated to the ground. At the satellite the pulsations had comparable radial and azimuthal components in both the magnetic and electric fields. In contrast to the observations near the magnetic equator by the Active Magnetospheric Particle Tracer Explorers Charge Composition Explorer spacecraft [Takahashi et al., 1995], no compressional component was detected in the magnetic field. The orthogonal components of the electric and magnetic fields oscillated either in phase or 180° out of phase, a property of a propagating (rather than standing) wave. The Poynting flux of the Pi2 pulsations was parallel to the ambient magnetic field and directed toward the nearer ionosphere, with little indication of ionospheric reflection. This unidirectional flow of electromagnetic energy is consistent with the strong ionospheric damping of Alfvén waves estimated from a numerical calculation. It is significant that the measured Poynting flux could damp a cavity mode oscillation in ∼10 s, assuming that the previously reported equatorial compressional Pi2 pulsations represent the cavity mode. Since the transverse Pi2 pulsations at Akebono lasted ∼400 s, they cannot be due to a gradual energy leakage from a simple cavity mode oscillation. Consequently, if the observed energy flow is a general property of plasmaspheric Pi2 pulsations, a simple cavity mode oscillation excited by an impulsive source is not an appropriate model for Pi2 pulsations.

Dynamics of the inner magnetosphere near times of substorm onsets

The electrodynamics of the inner magnetosphere near times of substorm onsets have been investigated using CRRES measurements of magnetic and electric fields, energetic electron fluxes, in conjunction with ground‐based observations. Six events were studied in detail, spanning the 2100 to 0000 MLT sector and L values from 5 to 7. In each case the dawn‐dusk electric field was enhanced over typical background electric fields, and significant, low‐frequency pulsation activity was observed. The amplitudes of the pulsations were larger than the background electric fields. Dusk‐dawn excursions of the cross‐tail electric field often correlated with changes in currents and particle energies at CRRES and with ULF wave activity observed on the ground. Variations of the electric field and Poynting vectors with periods in the Pi 2 range are consistent with bouncing AlfVén waves that provide electromagnetic communication between the ionosphere and plasma sheet. Magnetic signatures of field‐aligned current filaments directed away from the ionosphere, presumably associated with the substorm current wedge, were observed during three orbits. In all cases, ground signatures of substorm expansion were observed at least 5 min before the injection of electrons at CRRES. Field‐aligned fluxes of counter‐streaming, low‐energy electrons were detected after three of the injections. We develop an empirical scenario for substorm onset. The process grows from ripples at the inner edge of the plasma sheet associated with dusk‐dawn excursions of the electric field, prior to the beginning of dipolarization. Energy derived from the braking of the inward plasma convection flows into the ionosphere in the form of Poynting flux. Subsequently reflected Poynting flux plays a crucial role in the magnetosphere‐ionosphere coupling. Substorms develop when significant energy (positive feedback?) flows in both directions, with the second cycle stronger than the initial. Pseudobreakups occur when energy flow in both directions is weak (negative feedback?). “Explosive‐growth‐phase” signatures occur after onset, early in the substorm expansion phase. Heated electrons arrive at the spacecraft while convection is earthward, during or at the end of electromagnetic energy flow away from the ionosphere.

The flow of electromagnetic energy in the decay of an electric dipole

In a typical dipole decay, the induction magnetic field and the radiation magnetic field are in opposing directions. The former is dominant close to the decay, and the latter is dominant far away. Thus, there exists a surface on which these two components cancel each other, so that the magnetic field reverses direction. Because the magnetic field changes direction, so also will the Poynting vector field, provided the electric field is reasonably well behaved. This defines a ‘‘causal surface,’’ within which electromagnetic energy will collapse, and outside which the electromagnetic energy will radiate away. I present a simple example, the decay of a point electric dipole, to argue that the radiated energy comes, not necessarily from the accelerating charges themselves, but from the energy stored in the far field.

Another Formula for Electromagnetic Energy Flow in Static Fields

Another Formula for Electromagnetic Energy Flow in Static Fields

Electromagnetic energy flow pattern on the axis of a circular disk by transient excitation

The exact energy flow pattern on the axis of a circular disk by transient excitation is presented in this paper. It has been shown that non-decaying region does not appear when the source is chosen to be a rectangular pulse, on the contrary, there exists a uprising region on the axis when the width of the pulse is less thana/c. After reaching its maximum value point, the energy decays slowly until the law ofr−2 is met. The scale of the uprising region is dependent upon the size of the antenna and the width of the pulse. It has also been shown that there exists a oscillatory region near the source for a harmonic excitation, and the amplitude is also uprising, which is quite different compared with the conclusion drawn by S. Silver (1949). Finally, the phenomenon of energy uprising in time domain is explained and some problems about the electromagnetic missiles are also expounded.

Instantaneous electromagnetic energy flow in remote-field eddy current testing : Journal of JSNDI, vol. 42, no. 11 (November 1993) p. 610 Koyama, Kiyoshi; Hoshikawa, Hiroshi

Instantaneous electromagnetic energy flow in remote-field eddy current testing : Journal of JSNDI, vol. 42, no. 11 (November 1993) p. 610 Koyama, Kiyoshi; Hoshikawa, Hiroshi

Mapping and energization in the magnetotail: 2. Particle acceleration

The selection of magnetic and electric field models specifies the rate at which charged particles must be accelerated throughout the magnetosphere during steady state conditions. This rate is estimated in the mid‐tail region (−60 RE < xsm < −10 RE) using the Tsyganenko (1989) magnetic field model and the assumption that E is approximately uniform in the plasma sheet. The uniform E assumption is found to be consistent with a projection of the Heppner and Maynard (1987) electric field model, and with observations in the magnetotail. The resulting energization rate decreases from 4 and 50 GW/RE at xsm = −10 RE to 0.8 and 5 GW/RE at xsm = −60 RE during quiet and disturbed times, respectively. The total energization rate throughout this entire tail region varies from 100 GW when Kp = 0 to 700 GW when Kp = 5. Ions carry most of the cross‐tail current, and therefore gain most of the kinetic energy within the plasma sheet. Electrons, which are responsible for most auroral phenomena, are primarily accelerated at lower altitudes. For quasi‐static conditions, the electromagnetic energy flow to low altitudes is controlled by the magnitude and location of Birkeland currents, even when the current‐carrying particles have negligible kinetic energy. The typical power deposited in the entire nightside auroral zone during steady conditions is approximately 15% to 20% of the Poynting flux entering the plasma sheet. Induced electric fields are known to produce most of the energetic ring current and radiation belt particles during substorm injection events. The energization rate goes well above 1000 GW during brief intervals. A simple injection model is used to compare the structure of induced and potential fields. This model shows plasma drifting earthward, equatorward, and toward midnight during a localized injection event.

Energy flow in remote field eddy current nondestructive testing

The electromagnetic energy flow is studied to elucidate the phenomena underlying remote-field eddy-current nondestructive testing of magnetic tubes. The flow intensity as well as its direction is obtained quantitatively. The energy travels through the tube wall from the outside into the inside of the tube in the remote field area, carrying the information on the tube wall thickness. This makes it possible to use this method to detect defects in ferromagnetic tubes. >

Measurement of transformer and shunt reactor load losses using a Poynting vector probe

The authors describe a novel method for the direct measurement of load losses in high-voltage transformers and shunt reactors using a Poynting vector probe. The probe measures the rate of flow of electromagnetic energy from the source supply to the load by sensing the electric and magnetic fields in a well-defined region. Unlike the complex bridge methods which are currently being used, the proposed method does not require any current or potential transformers, high-voltage capacitors, or current comparators. The integrated nature of the probe together with its light weight provides a simple and inexpensive method for measuring power losses in transformers, shunt reactors, and power capacitors in an industrial environment. Also, the very small number of components used in the probe and its electronic circuit ensures a minimum overall error and a high measurement accuracy. Design details and performance results are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Poynting vector probe for measuring power at extremely low power factor

The paper describes a new probe for the measurement of power flow from a source of supply to a load which is characterised by having an extremely low power factor. Power is measured by sensing the electric and magnetic fields in a defined region between the source and the load. A co-axial configuration is chosen to simplify the integration of the Poynting vector that represents the rate of flow of electromagnetic energy. This leads to a simple design that enables the measurement of voltage and current by sensing the corresponding electric and magnetic fields in an integrated structure incorporating both sensors. The new probe is particularly suitable for the measurement of load losses in large, high-voltage power transformers and shunt reactors in which the power factor is extremely low. A small experimental unit is described, together with the associated electronic circuit.

Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system

The mechanism by which unstable electron plasma waves are converted into electromagnetic waves in a uniform plasma is investigated. Electromagnetic radiation is generated upon injection of an electron beam (500 eV) into a collisionless quiescent magnetoplasma (ne ≲1012 cm−3, kTe ≊2 eV). The emission (ω0) is observed to peak near the plasma frequency (ωp) which is well above the cyclotron frequency (ωc ≪ωp≲ω0). It is shown that electromagnetic waves (ω0, k0) are produced by the scattering of electrostatic plasma waves (ωe, ke) off self-consistently produced ion-acoustic waves (ωi, ki). At low beam intensities the frequency and wave vector matching conditions are experimentally verified (ωe=ωi+ω0, ke=ki+k0≂ki). The emission is found to be polarized, negligible in intensity at ω0=2ωp, and its source is localized. The space-time evolution of the three-wave interaction is presented. Besides these nonlinear wave–wave interactions the wave–particle interactions are investigated. It is found that the strong Langmuir turbulence exhibits a three-dimensional character. Cross-correlation surfaces are measured, and their characteristic scale lengths are found to decrease with increasing wave intensity toward the Debye length (λD ≂20 μm) although the resolution is probe limited (Lmin ≂1 mm). The beam electrons are diagnosed using a novel directional velocity analyzer which is capable of resolving the true three-dimensional distribution function. After interacting with the intense Langmuir waves, the beam electrons are scattered in velocity space, both parallel and perpendicular to their injection velocity. The background electron distribution is observed to develop an energetic anisotropic tail (E≲50 eV, kTe ≂1 eV). The energization of the background electrons coincides with the strong damping of the Langmuir waves. The nonlinear damping is seen as an anomalous ac resistivity produced by large amplitude ion-density fluctuations (δni/ni ≂5%) in the electron beam region.