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NASA NTRS1983

Application of the Lienard-Wiechert solution to a lightning return stroke model

The electric and magnetic fields associated with the lightning return stroke are expressed as a convolution of the current waveform shape and the fields generated by a moving charge of amplitude one (i.e., the Lienard-Wiechert solution for a unit charge). The representation can be used to compute the fields produced by a current waveform of non-uniform velocity that propagates along a filament of arbitrary, but finite, curvature. To study numerically the effects of linear charge acceleration and channel curvature two simple channel models are used: the linear and the hyperbolic.

Meneghini, R.↗

NASA NTRS1984

Application of the Lienard-Wiechert solution to a lightning return stroke model

Meneghini, R.↗

NASA NTRS1988

Comparison of fast electric field changes from subsequent return strokes of natural and triggered lightning

Fast electric field changes from subsequent return strokes of natural and triggered lightning with propagation paths almost entirely over water are compared. Data were collected at the Kennedy Space Center, Florida. Comparisons have been made of the average shape, the rise time and the spectrum of the electric field changes. The electric field changes from the triggered flashes tend to rise to peak faster and decay faster than do their counterparts in natural cloud-to-ground flashes.

Le Vine, D. M.↗

NASA NTRS1989

Comparison of fast electric field changes from subsequent return strokes of natural and triggered lightning

Fast electric field changes from subsequent return strokes of natural and triggered lightning with propagation paths almost entirely over water are compared. Data were collected at the Kennedy Space Center, Florida, during the summer of 1987. Comparisons have been made of the average shape, the risetime, and the spectrum of the electric field changes. To a first approximation, the waveforms are very similar; however, the electric field changes from the triggered flashes tend to rise to peak faster and decay faster than do their counterparts in natural cloud-to-ground flashes.

Le Vine, D. M.↗

NASA NTRS1992

On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes

The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, nu, is a significant fraction of the speed of light, c, assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission-line model with a constant nu and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large nu is to increase the radiation fields by a factor of (1-beta-sq cos-sq theta) exp -1, where beta = nu/c and theta is measured from the vertical, and the Poynting vector by a factor of (1-beta-sq cos-sq theta) exp -2.

Krider, E. P.↗

NASA NTRS1988

Horizontal electric fields from lightning return strokes

An experiment to measure simultaneously the wideband horizontal and vertical electric fields from lightning return strokes is described. Typical wave shapes of the measured horizontal and vertical fields are presented, and the horizontal fields are characterized. The measured horizontal fields are compared with calculated horizontal fields obtained by applying the wavetilt formula to the vertical fields. The limitations and sources of error in the measurement technique are discussed.

Thomson, E. M.↗

NASA NTRS1976

A gated, wideband magnetic direction finder for lightning return strokes

A magnetic direction finder has been developed which utilizes only the initial few microseconds of wideband return stroke waveforms to provide accurate directions to the channel bases of lightning discharges to ground. Bearing errors are minimized because, near the ground, most channels tend to be straight and vertical with no large branches or horizontal sections. Tests on a number of lightning storms at distances of 10 to 100 km indicate the angular resolution is in the range 1-2 deg, with little or no systematic dependence on azimuth or distance.

Krider, E. P.↗

NASA NTRS1978

The influence of tortuosity on the spectrum of radiation from lightning return strokes

An investigation was made of the influence of tortuosity on the spectrum of radiation from lightning return strokes. The shape of the spectrum obtained by including effects of tortuosity was in keeping with data: The spectrum had a peak in the correct frequency regime followed by an initial decrease as the inverse of frequency. This spectrum was in better agreement with data than the spectrum predicted by the same model without tortuosity (i.e. the long straight channel), which decays at a rate proportional to 1/v squared.

Levine, D. M.↗

NASA NTRS1988

An experimental test of the 'transmission-line model' of electromagnetic radiation from triggered lightning return strokes

Peak currents, two-dimensional average propagation speeds, and electric field waveforms for a number of subsequent return strikes in rocket-triggered lightning flashes were measured in order to test the 'transmission-line model' of return-stroke radiation of Uman and McLain (1970). Reasonable agreement is found between the propagation speeds measured with the streak camera and those deduced from the transmission-line model. A modification of the model is proposed in which two wave fronts travel upward and downward away from a junction point a short distance above the ground.

Willett, J. C.↗

NASA NTRS1983

Variation in light intensity with height and time from subsequent lightning return strokes

Photographic measurements of relative light intensity as a function of height and time have been conducted for seven return strokes in two lightning flashes at 7.8 and 8.7 km ranges, using film which possesses an approximately constant spectral response in the 300-670 nm range. The amplitude of the initial light peak is noted to decrease exponentially with height, with a decay constant of 0.6-0.8 km. The logarithm of the peak light intensity near the ground is found to be approximately proportional to the initial peak electric field intensity, implying that the current decrease with height may be much slower than the light decrease. Absolute light intensity is presently estimated through the integration of the photographic signals from individual channel segments, in order to simulate the calibrated, all-sky photoelectric data of Guo and Krider (1982).

Jordan, D. M.↗

NASA NTRS1973

Electric radiation fields of lightning return strokes in three isolated Florida thunderstorms

Peak value and risetime distributions for the electric radiation fields produced by lightning strokes to ground in three isolated Florida thunderstorms are presented. The storm at 195 km produced about 1000 return strokes having an average peak radiation field (normalized to 100 km) of about 5.5 V/m, the storm at 110 km produced about 700 strokes having 2.0 V/m, and the storm within 10 km produced about 100 strokes having 15.0 V/m. For each storm the average peak radiation field for first strokes was only slightly greater than the average peak field for subsequent strokes. For the sample of three storms the average peak radiation field in a given storm was proportional to the number of subsequent strokes per flash in that storm. The field risetimes for the two distant storms have statistical properties which are essentially identical to those reported for distant storms in Pennsylvania, whereas the close Florida storm exhibited significantly faster risetimes.

Lin, Y. T.↗

NASA NTRS1991

Submicrosecond characteristics of lightning return-stroke currents

The authors describe the experimental results obtained during 1987 and 1988 triggered-lightning experiments in Florida. Seventy-four simultaneous submicrosecond time-resolved measurements of triggered return-stroke current (I) and current derivative (dI/dt) were made in Florida in 1987 and 1988. Peak currents ranged from about 5 to 76 kA, peak dI/dt amplitude from 13 to 411 kA/microsec and rise time from 90 to 1000 ns. The mean peak dI/dt values of 110 kA/microsec were 2-3 times higher than data from instrumented towers and peak I and dI/dt appear to be positively correlated. These data confirm previous experiments and conclusions supported by forty measurements. They are important in order to define, for example, standards for lightning protection. Present standards give a dI/dt maximum of 140 kA/microsec.

Leteinturier, Christiane↗

NASA NTRS1976

Test of the principle of operation of a wideband magnetic direction finder for lightning return strokes

The principle of operation of a wideband crossed-loop magnetic-field direction finder is studied by comparing the bearing determined from the NS and EW magnetic fields at various times up to 155 microsec after return stroke initiation with the TV-determined lightning channel base direction. For 40 lightning strokes in the 3 to 12 km range, the difference between the bearings found from magnetic fields sampled at times between 1 and 10 microsec and the TV channel-base data has a standard deviation of 3-4 deg. Included in this standard deviation is a 2-3 deg measurement error. For fields sampled at progressively later times, both the mean and the standard deviation of the difference between the direction-finder bearing and the TV bearing increase. Near 150 microsec, means are about 35 deg and standard deviations about 60 deg. The physical reasons for the late-time inaccuracies in the wideband direction finder and the occurrence of these effects in narrow-band VLF direction finders are considered.

Herrman, B. D.↗

NASA NTRS1991

First and subsequent return stroke properties of cloud-to-ground lightning

Lightning properties obtained by a network of magnetic direction finders and by electric field measurements for distances from 50 to 500 km are compared for three summer thunderstorms in Sweden. The data from direct field recordings indicate 31, 17, and 26 pcts. of negative subsequent return strokes with peak current (as inferred from the peak electric field) higher than the first. Electric fields from first strokes are compared with normalized amplitudes registered by the magnetic direction finding system. The efficiency of detection by the magnetic direction finding system is discussed in terms of the percentage of lightning flashes observed by electric field measurements that are not localized. Statistics of the number of strokes per flash and the interstroke time intervals are presented.

Namasivayam, S.↗

NASA NTRS1978

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

D M Le Vine↗

NASA NTRS1977

Simulation of radiation from lightning return strokes: The effects of tortuosity

A Monte Carlo simulation has been developed for the electromagnetic fields radiated from a tortuous lightning channel. This was done using a piecewise linear model for the channel and employing for each element the field radiated by a traveling wave on an arbitrarily oriented filament over a conducting plane. The simulation reproduces experimental data reasonably well and had been used to study the effects of tortuousity on the fields radiated by return strokes. Tortuosity can significantly modify the radiated waveform, tending to render it less representative of the current pulse and more nearly unipolar than one would expect based on the theory for a long straight channel. In the frequency domain the effect of tortuosity is an increase in high frequency energy as compared with an equivalent straight channel. The extent of this increase depends on the mean length of the elements comprising the channel and can be significant.

Levine, D. M.↗

NASA NTRS1978

Simulation of radiation from lightning return strokes - The effects of tortuosity

A Monte Carlo simulation has been developed for the electromagnetic fields radiated from a tortuous lightning channel. This was done using a piecewise linear model for the channel and employing for each element the field radiated by a traveling wave on an arbitrarily oriented filament over a conducting plane. The simulation reproduces experimental data reasonably well and has been used to study the effects of tortuosity on the fields radiated by return strokes. Tortuosity can significantly modify the radiated waveform, tending to render it less representative of the current pulse and more nearly unipolar than one would expect based on the theory for a long straight channel. In the frequency domain the effect of tortuosity is an increase in high frequency energy as compared with an equivalent straight channel. The extent of this increase depends on the mean length of the elements comprising the channel and can be significant.

Levine, D. M.↗

NASA NTRS1980

The RF spectra of first and subsequent lightning return strokes in the 1- to 200-km range

An experimental characterization of the frequency spectra of first and subsequent stroke electric fields are presented over a distance range from about 1 km, where the fields are primarily electrostatic, to 200 km, where they are primarily radiation. Spectra are presented to about 700 kHz for lightning within 12 km and to about 300 kHz for lightning at 50 and 200 km. It is shown that the return stroke ground wave spectrum beyond 50 km has a peak near 4 kHz but that within 10 km the spectrum shows a steady increase with decreasing frequency to 1 kHz. Frequency spectra at all ranges fall off roughly as 1/f for frequencies between 5 and 100 kHz, while the falloff above 100 kHz is faster as the distance to the stroke increases. From this high-frequency attenuation an RF conductivity for central Florida of between 0.002 and 0.005/ohm/m was determined.

Serhan, G. I.↗