On the transmission line model for lightning return stroke representation (original) (raw)
Related papers
1999
Exact expressions for the electric and magnetic fields are derived for the case of a filamentary lightning current that flows in an extending channel. The treatment differs from those in the existing literature in that the expressions are found from fundamental principles applied to the appropriate bounded current rather than from the addition of an ex•a term in the radiation fields to account for the channel-tip discontinuity, the "turn-on" tenn. A different analytical form is obtained for the electrostatic field component, but this is found to be equivalent to existing relations. The radiation component of the magmetic field and a far-field expression for the electric field can each be expressed as a single expression in which the turn-on tem• from the clmnnel tip is an integral part. However, the far-field expression for E can only be represented in fids simple way if a term that arises from the induction field, the component that varies as ]/R 2 , is included with the remaining radiation terms, so that it is not a true radiation field. The Lorentz condition is shown to be equivalent to the continuity equation expressed in terms of the delayed time t-R/c. For a transmission line model with ch,-umel-tip speed v and current pulse propagation speed w, the same far-field expression is found for v=w as for v>w. The latter condition includes the case of a transmission-line current on a preexisting clmm•el.
IEEE Transactions on Electromagnetic Compatibility, 2021
The paper provides analytical expressions for the electromagnetic fields generated by a lightning return stroke characterized by a channel base current with arbitrary time waveform, in presence of either a perfectly conducting or a lossy ground, assuming the transmission line model for the current along the channel. In this second case, a time domain analytical expression for the Cooray-Rubinstein formula is presented. The main idea that leads to the derivation of analytical formulas consists of dividing the channel into intervals in which the distance between the field source point and the observation point can be approximated with a linear function of the time and of the spatial coordinates of both points. In the companion paper, a detailed comparison is proposed with the classical (numerical) approach highlighting excellent agreement both at close and far distances, considering all the values of practical interest for the ground conductivity. Moreover, the method guarantees a meaningful improvement in the computational performance.
Electromagnetic models of the lightning return stroke
Journal of Geophysical Research, 2007
1] Lightning return-stroke models are needed for specifying the source in studying the production of transient optical emission (elves) in the lower ionosphere, the energetic radiation from lightning, and characterization of the Earth's electromagnetic environment, as well as studying lightning interaction with various objects and systems. Reviewed here are models based on Maxwell's equations and referred to as electromagnetic models. These models are relatively new and most rigorous of all models suitable for computing lightning electromagnetic fields. Maxwell's equations are numerically solved to yield the distribution of current along the lightning channel. Different numerical techniques, including the method of moments (MoM) and the finite difference time domain (FDTD) method, are employed. In order to achieve a desirable current-wave propagation speed (lower than the speed of light in air), the channel-representing wire is embedded in a dielectric (other than air) or loaded by additional distributed series inductance. Capacitive loading has been also suggested. The artificial dielectric medium is used only for finding the distribution of current along the lightning channel, after which the channel is allowed to radiate in air. Resistive loading is used to control current attenuation with height. In contrast with distributed circuit and so-called engineering models, electromagnetic return-stroke models allow a self-consistent full-wave solution for both lightning-current distribution and resultant electromagnetic fields. In this review, we discuss advantages and disadvantages of four return-stroke channel representations: a perfectly conducting/resistive wire in air, a wire embedded in a dielectric (other than air), a wire in air loaded by additional distributed series inductance, and a wire in air having additional distributed shunt capacitance. Further, we describe and compare different methods of excitation used in electromagnetic return-stroke models: closing a charged vertical wire at its bottom with a specified grounded circuit, a delta-gap electric field source, and a lumped current source. Finally, we review and compare representative numerical techniques used in electromagnetic modeling of the lightning return stroke: MoMs in the time and frequency domains and the FDTD method. We additionally consider the so-called hybrid model of the lightning return stroke that employs a combination of electromagnetic and circuit theories and compare this model to electromagnetic models. Citation: Baba, Y., and V. A. Rakov (2007), Electromagnetic models of the lightning return stroke,
IEEE Transactions on Electromagnetic Compatibility, 2005
It is known from both theory and numerical simulations that a current pulse suffers apparent attenuation as it propagates along a vertical perfect conductor of uniform, nonzero thickness (e.g., a cylinder) above perfectly conducting ground, excited at its bottom by a lumped source. The associated electromagnetic field structure is non-transverse electromagnetic (TEM), particularly near the source region. On the other hand, it has been shown analytically by that no attenuation occurs and the electromagnetic field structure is pure transverse electromagnetic (TEM) if the conductor thickness and source size are assumed to be infinitesimal. The goal of this paper is to examine the mechanism of current attenuation as it propagates along a nonzero thickness conductor, based on the scattering theory and on a nonuniform transmission line approximation. In applying the scattering theory, we decompose the "total" current in the conductor into two components that we refer to as the "incident" and "scattered" currents. The "incident" current serves as a reference (no attenuation), specified disregarding the interaction of resultant electric and magnetic fields with the conductor, while the "scattered" current, found here using the finite-difference time-domain (FDTD) method, can be viewed as a correction to account for that interaction. The scattered current modifies the incident current so that the resultant total current pulse appears attenuated. Thus, the current attenuation is likely to be due to field scattering that does not occur in the case of zero thickness conductor. The attenuation of the total current pulse is accompanied by the lengthening of its tail, such that the total charge transfer is independent of height. Approximation of the vertical conductor above ground by a nonuniform transmission line whose characteristic impedance increases with increasing height is shown to reasonably reproduce the current pulse attenuation predicted by the scattering theory. In this approximation, the apparent current attenuation with height can be attributed to waves reflected back to the source. The results have important implications for development and interpretation of lightning models.
The Electromagnetic Fields of an Accelerating Charge: Applications in Lightning Return-Stroke Models
IEEE Transactions on Electromagnetic Compatibility, 2000
In the literature, three procedures have been used to calculate the electromagnetic fields from return strokes. In the first technique, the source is described only in terms of current density and the fields are expressed entirely in terms of the return-stroke current. In the second technique, the source is expressed in terms of the current and the charge densities and the fields are given in terms of both the current and the charge density. In the third technique, the fields are expressed in terms of the apparent charge density. The fields are connected to the source terms through the vector and scalar potentials. In this paper, the standard equations for the electromagnetic fields generated by an accelerating charge are utilized to evaluate the electromagnetic fields from lightning return strokes. It is shown that the total fields evaluated at any distance using these expressions are identical to those obtained using other techniques. However, the composition of the terms that vary as 1/R, 1/R 2 , and 1/R 3 of the total electric field is different from those of other formulations. In the case of the transmission-line model, where the return stroke is described as a current pulse propagating with uniform velocity, radiation emanates only from the bottom of the channel where current is generated. When the speed of propagation is equal to the speed of light, the total field throughout the entire space becomes radiation. The procedure is also applied here to obtain the electric fields of the traveling-current-source model. The electric fields obtained for this case, too, agree with the previous study. It is also shown how the equations can be applied rather conveniently to evaluate: 1) the electromagnetic fields generated by current pulses propagating along overhead power lines; and 2) the electromagnetic fields generated by vertical conductors and towers during lightning strikes.
Journal of Geophysical Research, 1988
The "transmission-line" model of return-stroke radiation, proposed by Uman and and invoked frequently thereafter to deduce peak currents from remote fields or to estimate propagation velocities from measured fields and currents, has never received a thorough experimental test. During the summer of 1985 at the Kennedy Space Center in Florida, we were able to measure peak currents (with a coaxial shunt), two-dimensional average propagation speeds (with a high-speed streak camera), and electric field waveforms (at 5.15-km range) for a number of subsequent return strokes in rocket-triggered lightning flashes. Because of the temporal ambiguity on the streak-camera films, it has not been possible to identify individual velocity measurements with particular strokes for which current and field data are available. Three multistroke flashes, however, each yielded a tight cluster of velocity measurements and a group of peak field to peak current ratios, though not necessarily for the same strokes. A further six flashes provided more current and field measurements for which no velocity information was obtained, and velocity measurements only are available for still other flashes. It is shown that these data indicate reasonable agreement between the propagation speeds measured with the streak camera and those deduced from the transmission-line model. The previously observed difference between current and radiation-field waveforms suggests a modification of the model, involving two wave fronts traveling upward and downward away from a junction point a short distance above the ground, which substantially improves the agreement between measured and inferred propagation speeds.
AN ANTENNA THEORY MODEL FOR THE LIGHTNING RETIJRN STROKE
A new approach, based on antenna theory, is used to evaluate the lightning return-stroke current as a fitnction of the and height. The lightning channel is modeled as a lossy, straight, attd vertical monopole antentla above a perfectly conducting ground, and is fed by a source voltage. The source voltage is a function of the assumed current at grotmd level and the input impedance of the tnonopole antenna. An electric field integral equation (EFIE) is employed to describe the electromagnetic behavior of the antetma. The mmterical solution of EFIE by the Method of Moments (MOM) in time domain provides the time-space distribution of the current along the lightning channel. This new atttennatheory model with specified current at the channel base requires only two adjustable parameters: the returttstroke propagation speed and the channel resistance per unit length. The new tnodel is compared to the tnost cotnmonly used lightning return-stroke models in terms of the temporal-spatial distribution of channel current and predicted electric fields.
Journal of Geophysical Research: Atmospheres, 2008
1] In this paper, the developed formulation, which we shall call the ''reference'' one, is used to assess the validity of the most popular simplified approach for the calculation of the lightning electromagnetic field over a conducting earth, namely, the Cooray-Rubinstein (CR) approximation. This formula provides a simple method to evaluate the radial component of the electric field which is the component most affected by the finite ground conductivity and which plays an important role within the Agrawal et al. (1980) field-to-transmission line-coupling model. Several configurations are examined, with different values for the ground conductivity and different field observation points. A thorough analysis of all the simulated field components is carried out and comparisons are also made with the ''ideal'' field, namely, the field that would be present under the assumption of perfectly conducting ground. It is shown that for channel base current typical of subsequent strokes and for very low conductivities, the CR formula exhibits some deviations from the reference one but it still represents a conservative estimation of the radial field component, since it behaves as un upper bound for the exact curve. The developed algorithm is characterized by fast performances in terms of CPU time, lending itself to be used for several applications, including a coupling code for lightning induced overvoltages calculations.