Analytical Expressions for Lightning Electromagnetic Fields With Arbitrary Channel-Base Current—Part I: Theory

In return strokes, the parameters that can be measured are the channel base current and the return stroke speed. For this reason, many return stroke models have been developed with these two parameters, among others, as inputs. Here, we concentrate on the current propagation type engineering return stroke models where the return stroke is represented by a current pulse propagating upwards along the leader channel. In the current propagation type return stroke models, in addition to the channel base current and the return stroke speed, the way in which the return stroke current attenuates along the return stroke channel is specified as an input parameter. The goal of this paper is to show that, within the confines of current propagation type models, once the channel base current and the return stroke speed are known, the measured radiation field can be used to evaluate how the return stroke current attenuates along the channel. After giving the mathematics necessary for this inverse transformation, the procedure is illustrated by extracting the current attenuation curve from the typical wave shape of the return stroke current and from the distant radiation field of subsequent return strokes. The derived attenuation curve is used to evaluate both the subsequent and first return stroke electromagnetic fields at different distances. It is shown that all the experimentally observed features can be reproduced by the derived attenuation curve, except for the subsidiary peak and long zero-crossing times. In order to obtain electromagnetic fields of subsequent return strokes that are in agreement with measurements, one has to incorporate the current dispersion into the model. In the case of first return strokes, both current dispersion and reduction in return stroke speed with height are needed to obtain the desired features.

Download Full-text

On the Transmittance of Metallic Superlattices in the Optical Regime and the True Refraction Angle

Photonics ◽

10.3390/photonics8030086 ◽

2021 ◽

Vol 8 (3) ◽

pp. 86

Author(s):

Pedro Pereyra

Keyword(s):

Electromagnetic Fields ◽

Systems Approach ◽

Periodic Systems ◽

Transmission Coefficients ◽

Parity Effect ◽

Optical Domain ◽

Induced Currents ◽

Analytical Expressions ◽

Flux Conservation ◽

Made In

Transmission of electromagnetic fields through (dielectric/metallic)n superlattices, for frequencies below the plasma frequency ωp, is a subtle and important topic that is reviewed and further developed here. Recently, an approach for metallic superlattices based on the theory of finite periodic systems was published. Unlike most, if not all, of the published approaches that are valid in the n→∞ limit, the finite periodic systems approach is valid for any value of n, allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown that, for frequencies below ωp, large metallic-layer thickness, and electromagnetic fields moving along the so-called “true” angle, anomalous results with an apparent parity effect appear. We show here that these results are related to the lack of unitarity and the underlying phenomena of absorption and loss of energy. To solve this problem we present two compatible approaches, both based on the theory of finite periodic systems, which is not only more accurate, but has also the ability to reveal and predict the intra-subband resonances. In the first approach we show that by keeping complex angles, above and below ωp, the principle of flux conservation is fully satisfied. The results above ωp remain the same as in Pereyra (2020). This approach, free of assumptions, where all the information of the scattering process is preserved, gives us insight to improve the formalism where the assumption of electromagnetic fields moving along the real angles is made. In fact, we show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach. The improved approach also allows one to evaluate the magnitude of the induced currents and the absorbed energy, as functions of the frequency and the superlattice parameters. We show that the resonant frequencies of intra-subband plasmons, which may be of interest for applications, in particular for biosensors, can be accurately determined. We also apply the approach for the transmission of electromagnetic wave packets, defined in the optical domain, and show that the predicted space-time positions agree extremely well with the actual positions of the wave packet centroids.

Download Full-text

An Algorithm for Evaluation of Lightning Electromagnetic Fields at Different Distances with respect to Lightning Channel

Mathematical Problems in Engineering ◽

10.1155/2014/925463 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Mahdi Izadi ◽

Mohd Zainal Abidin Ab Kadir ◽

Maryam Hajikhani

Keyword(s):

Electromagnetic Fields ◽

Time Domain ◽

Observation Point ◽

Geometrical Parameters ◽

Induced Voltage ◽

Base Current ◽

Lightning Channel ◽

The Time Domain

The analytical field expressions are proposed to estimate the electromagnetic fields associated with vertical lightning channel at an observation point directly in the time domain using current and geometrical parameters. The proposed expressions embrace a large number of channel base current functions and widely used engineering current models. Moreover, they can be joined with different coupling models for evaluation of lightning induced voltage when they provide different required field components directly in the time domain. The data from measured fields and simulated fields from previous works were employed to validate the proposed field expressions. The simulated results were compatible with both computed field values from previous studies and the measured fields.

Download Full-text

Layered and ion implantation specimens as possible reference materials for the electron-probe microanalysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100132893 ◽

1992 ◽

Vol 50 (2) ◽

pp. 1652-1653

Author(s):

G. Remond ◽

R.H. Packwood ◽

C. Gilles ◽

S. Chryssoulis

Keyword(s):

Ion Implantation ◽

Reference Materials ◽

Analytical Techniques ◽

Thin Film Deposition ◽

Film Deposition ◽

X Ray ◽

Spatially Resolved ◽

Analytical Expressions ◽

Original Approach ◽

Depth Concentration

Merits and limitations of layered and ion implanted specimens as possible reference materials to calibrate spatially resolved analytical techniques are discussed and illustrated for the case of gold analysis in minerals by means of x-ray spectrometry with the EPMA. To overcome the random heterogeneities of minerals, thin film deposition and ion implantation may offer an original approach to the manufacture of controlled concentration/ distribution reference materials for quantification of trace elements with the same matrix as the unknown.In order to evaluate the accuracy of data obtained by EPMA we have compared measured and calculated x-ray intensities for homogeneous and heterogeneous specimens. Au Lα and Au Mα x-ray intensities were recorded at various electron beam energies, and hence at various sampling depths, for gold coated and gold implanted specimens. X-ray intensity calculations are based on the use of analytical expressions for both the depth ionization Φ (ρz) and the depth concentration C (ρz) distributions respectively.

Download Full-text

A Simple Real-Space Channelling Theory for Electron Diffraction and HREM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100179075 ◽

1990 ◽

Vol 48 (1) ◽

pp. 64-65

Author(s):

D. Van Dyck

Keyword(s):

High Resolution ◽

Electron Diffraction ◽

Direct Method ◽

Real Space ◽

Zone Axis ◽

Phase Object ◽

High Resolution Images ◽

The Many ◽

Analytical Expressions ◽

Electron Wavefunction

The computation of the many beam dynamical electron diffraction amplitudes or high resolution images can only be done numerically by using rather sophisticated computer programs so that the physical insight in the diffraction progress is often lost. Furthermore, it is not likely that in this way the inverse problem can be solved exactly, i.e. to reconstruct the structure of the object from the knowledge of the wavefunction at its exit face, as is needed for a direct method [1]. For this purpose, analytical expressions for the electron wavefunction in real or reciprocal space are much more useful. However, the analytical expressions available at present are relatively poor approximations of the dynamical scattering which are only valid either for thin objects ((weak) phase object approximation, thick phase object approximation, kinematical theory) or when the number of beams is very limited (2 or 3). Both requirements are usually invalid for HREM of crystals. There is a need for an analytical expression of the dynamical electron wavefunction which applies for many beam diffraction in thicker crystals. It is well known that, when a crystal is viewed along a zone axis, i.e. parallel to the atom columns, the high resolution images often show a one-to-one correspondence with the configuration of columns provided the distance between the columns is large enough and the resolution of the instrument is sufficient. This is for instance the case in ordered alloys with a column structure [2,3]. From this, it can be suggested that, for a crystal viewed along a zone axis with sufficient separation between the columns, the wave function at the exit face does mainly depend on the projected structure, i.e. on the type of atom columns. Hence, the classical picture of electrons traversing the crystal as plane-like waves in the directions of the Bragg beams which historically stems from the X-ray diffraction picture, is in fact misleading.

Download Full-text