Return stroke transmission line model for stroke speed near and equal that of light

Thottappillil, Rajeev; Schoene, Jens; Uman, M. A.

doi:10.1029/2001gl013029

Cited by 56 publications

(68 citation statements)

References 22 publications

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“…Typical values of v are one-third to two-thirds of c (e.g., Rakov [23]). In this paper, we will assume that v = c, as done by Thottappillil et al [17], Kordi et al [9], [10]; and Baba and Rakov [7], in order to simplify the analysis aimed at identifying the mechanism of current attenuation with height. Baba and Rakov [7] showed numerically that a vertical phased current source array activated so as to satisfy (1) with v = c produced a spherical TEM wave [see Fig.…”

Section: Incident Currentmentioning

confidence: 99%

“…Note that (2) accounts for the electrostatic, induction, and radiation field components (Thottappillil et al [17], Fig. 2).…”

Section: Incident Currentmentioning

confidence: 99%

“…On the other hand, it has been shown analytically (Thottappillil et al [17], [18]) that no attenuation occurs and electromagnetic field structure is pure TEM if the conductor thickness and source size are assumed to be infinitesimal. This case corresponds to the so-called transmission line (TL) model (Uman and McLain [19]), not to be confused with distributed-circuit (R-L-C) models (e.g., Rakov and Uman 1998 [3]).…”

Section: Introductionmentioning

confidence: 99%

“…In view of the absence of ohmic losses, the observed current attenuation was attributed to "radiation losses" (e.g., Kordi et al [9], [10]; Baba and Ishii [11]). Thottappillil and Uman [20] suggested that a vertical cylinder above ground can support an unattenuated current if this cylinder is excited at its base by a circular ensemble of TEM wave sources. On the other hand, Baba and Rakov [7] have pointed out that the characteristic impedance of a vertical cylinder above ground varies with height, which implies that pulses propagating along such a cylinder in general cannot preserve their amplitude and shape.…”

Section: Introductionmentioning

confidence: 99%

“…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 Thottappillil et al (2001Thottappillil et al ( , 2004 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.…”

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confidence: 99%

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On the Mechanism of Attenuation of Current Waves Propagating Along a Vertical Perfectly Conducting Wire Above Ground: Application to Lightning

Baba

Rakov

2005

IEEE Trans. Electromagn. Compat.

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Abstract-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 Thottappillil et al. (2001Thottappillil et al. ( , 2004 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.

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Section: Incident Currentmentioning

confidence: 99%

“…Note that (2) accounts for the electrostatic, induction, and radiation field components (Thottappillil et al [17], Fig. 2).…”

Section: Incident Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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On the Mechanism of Attenuation of Current Waves Propagating Along a Vertical Perfectly Conducting Wire Above Ground: Application to Lightning

Baba

Rakov

2005

IEEE Trans. Electromagn. Compat.

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A study on the influence of corona on currents and electromagnetic fields predicted by a nonlinear lightning return‐stroke model

2014

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This paper investigates the influence of corona on currents and electromagnetic fields predicted by a return-stroke model that represents the lightning channel as a nonuniform transmission line with time-varying (nonlinear) resistance. The corona model used in this paper allows the calculation of corona currents as a function of the radial electric field in the vicinity of the channel. A parametric study is presented to investigate the influence of corona parameters, such as the breakdown electric field and the critical electric field for the stable propagation of streamers, on predicted currents and electromagnetic fields. The results show that, regardless of the assumed corona parameters, the incorporation of corona into the nonuniform and nonlinear transmission line model under investigation modifies the model predictions so that they consistently reproduce most of the typical features of experimentally observed lightning electromagnetic fields and return-stroke speed profiles. In particular, it is shown that the proposed model leads to close vertical electric fields presenting waveforms, amplitudes, and decay with distance in good agreement with dart leader electric field changes measured in triggered lightning experiments. A comparison with popular engineering return-stroke models further confirms the model's ability to predict consistent electric field waveforms in the close vicinity of the channel. Some differences observed in the field amplitudes calculated with the different models can be related to the fact that current distortion, while present in the proposed model, is ultimately neglected in the considered engineering return-stroke models.

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Differing current and optical return stroke speeds in lightning

Liang

Carlson

Lehtinen

et al. 2014

Geophys. Res. Lett.

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During the return stroke in downward negative cloud‐to‐ground lightning, a current wave propagates upward from the ground along the lightning channel. The current wave causes rapid heating of the channel and induces intense optical radiation. The optical radiation wave propagation speed along the channel has been measured to be between 15 and 23 of the speed of light. The current wave speed is commonly assumed to be the same but cannot be directly measured. Past modeling efforts treat either the thermodynamics or electrodynamics. We present the first model that simultaneously treats the coupled current and thermodynamic physics in the return stroke channel. We utilize numerical simulations using realistic high‐temperature air plasma properties that self‐consistently solve Maxwell's equations coupled with equations of air plasma thermodynamics. The predicted optical radiation wave speed, rise time, and attenuation agree well with observations. The model predicts significantly higher current return stroke speed.

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Return stroke transmission line model for stroke speed near and equal that of light

Cited by 56 publications

References 22 publications

On the Mechanism of Attenuation of Current Waves Propagating Along a Vertical Perfectly Conducting Wire Above Ground: Application to Lightning

On the Mechanism of Attenuation of Current Waves Propagating Along a Vertical Perfectly Conducting Wire Above Ground: Application to Lightning

A study on the influence of corona on currents and electromagnetic fields predicted by a nonlinear lightning return‐stroke model

Differing current and optical return stroke speeds in lightning

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