The peak electromagnetic power radiated by lightning return strokes (original) (raw)
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On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes
Journal of Geophysical Research, 1992
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, v, 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 v and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large vis to increase the radiation fields by a factor of (1-/32 cos 2 0)-1 , where/3 = v/c and 0is measured from the vertical, and the Poynting vector by a factor of (1-/32 cos 2 0)-2. This increase is just a few percent or less at small/3, but when/3-0.67, the fields are about 80% larger at small 0 and 50% larger at 0 = 30 ø, and the power that is radiated is increased by 26%. When/3 = 0.5 and the peak current is 30 kA, typical values for negative first strokes, the peak power that is radiated into the upper hemisphere is 1.0 x 10 lø W. 1.
On remote measurements of lightning return stroke peak currents
Atmospheric Research, 2014
Return-stroke peak current is one of the most important measures of lightning intensity needed in different areas of atmospheric electricity research. It can be estimated from the corresponding electric or magnetic radiation field peak. Electric fields of 89 strokes in lightning flashes triggered using the rocket-and-wire technique at Camp Blanding (CB), Florida, were recorded at the Lightning Observatory in Gainesville, about 45 km from the lightning channel. Lightning return-stroke peak currents were estimated from the measured electric field peaks using the empirical formula of and the field-to-current conversion equation based on the transmission line model . These estimates, along with peak currents reported by the U.S. National Lightning Detection Network (NLDN), were compared with the ground-truth data, currents directly measured at the lightning channel base. The empirical formula, based on data for 28 triggered-lightning strokes acquired at the Kennedy Space Center (KSC), tends to overestimate peak currents, whereas the NLDNreported peak currents are on average underestimates. The field-to-current conversion equation based on the transmission line model gives the best match with directly measured peak currents for return-stroke speeds between c/2 and 2c/3 (1.5 and 2 × 10 8 m/s, respectively). Possible reasons for the discrepancy in the peak current estimates from the empirical formula and the ground-truth data include an error in the field calibration factor, difference in the typical return-stroke speeds at CB and at the KSC (considered here to be the most likely reason), and limited sample sizes, particularly for the KSC data. A new empirical formula, I = −0.66-0.028rE, based on data for 89 strokes in lightning flashes triggered at CB, is derived.
Electric field intensity of the lightning return stroke
Journal of Geophysical Research, 1973
Institute o] Atmospheric Physics, University o] Arizona, Tucson, Arizona 857•1 From an examination of about 1000 electric field wave forms produced by lightning return strokes in 16 storms at distances between 20 and 100 km from an observation site at the Kennedy Space Center, Florida, a typical return stroke current wave form is derived. For this current wave form, the electric field intensity at distances between 0.5 and 100 km is computed for three values of return stroke velocity. The resultant curves for close lightning • Now at
2014
In this paper detailed numerical results are presented for the estimation of the electric field generated by the first return stroke, in order to reproduce the main characteristics of field waveforms measured at distances beyond 50 km. The effect of parameters such as the lightning channel geometry, distance from the source, return-stroke current speed, its attenuation along the channel is discussed by comparing numerical and experimental results.
The Energy, Momentum, and Peak Power Radiated by Negative Lightning Return Strokes
Atmosphere
Electromagnetic radiation fields generated by return strokes transport both energy and momentum from the return stroke to outer space. The momentum transported by the radiation field has only a vertical or z component due to azimuthal symmetry (cylindrical symmetry) associated with a vertical return stroke. In this paper, the energy, momentum, and peak power radiated by return strokes as a function of the return stroke current, return stroke speed, and the zero-crossing time of the radiation fields are studied. The results obtained by numerical simulations for the energy, vertical momentum, and the peak power radiated by lightning return strokes (all parameters normalized by dividing them by the square of the radiation field peak at 100 km) are the following: A typical first return stroke generating a radiation field having a 50 μs zero-crossing time will dissipate field normalized energy of about (1.7–2.5) × 103 J/(V/m)2 and field-normalized vertical momentum of approximately (2.3–...
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.
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,
On the upper limit of peak current in return strokes of lightning flashes
2009
It is shown that the peak current in a return stroke is determined by the background electric field that exists between the cloud and the ground. Assuming 150 kV/m as the largest background electric field that can exist below thunderclouds, it is estimated that the largest negative first return stroke peak current that can exist in nature is about 300 kA in temperate regions and about 450 kA -500 kA in the tropics. Since corona discharges from trees, bushes and other protrusions and upward initiated discharges from tall structures limit the maximum electric field that can exist below thunderclouds over land, there is a high probability for these strong discharges to take place over the oceans.
Submicrosecond fields radiated during the onset of first return strokes in cloud-to-ground lightning
Journal of Geophysical Research, 1996
An experiment to measure the electric field E and dE/dr signatures that are radiated by the first return stroke in cloud-to-ground lightning was conducted on the eastern tip of Cape Canaveral, Florida, during the summer of 1984. At this site, there was minimal distortion in the fields due to ground wave propagation when the lightning struck within a few tens of kilometers to the east over the Atlantic Ocean. Biases that are introduced by a finite threshold in the triggered recording system were kept to a minimum by triggering this system on the output of a wideband RF receiver tuned to 5 MHz. Values of the peak dE/dr during the initial onset of 63 first strokes were found to be normally distributed with a mean and standard deviation of 39 _+ 11 V m-• /xs -• after they were normalized to a range of 100 km using an inverse distance relation. Values of the full width at half maximum (FWHM) of the initial half-cycle of dE/dr in 61 first strokes had a mean and standard deviation of 100 +_ 20 ns and were approximately Gaussian. When these results are interpreted using the simple transmission line model, after correcting for the effects of propagation over 35 km of seawater, the average value of the maximum current derivative, (dI/dt)p, and its standard deviation are inferred to be 115 + 32 kA/•s -•, with a systematic uncertainty of about 30%. The FWHM after correction for propagation is about 75 +_ 15 ns.
The optical and radiation field signatures produced by lightning return strokes
Journal of Geophysical Research, 1982
The optical signals radiated by Florida lightning in the 0.4-to 1.1-/zm wavelength interval have been recorded in correlation with wide-band electric field signatures. The initial light signal from a return stroke tends to be linear for about 15/zs and then rises more slowly to a peak that is delayed by about 60/zs from the electric field peak. The transition between the fast linear portion and the slower rise may be due to the return stroke entering the cloud base. A small percentage of the records indicate that two different branches of the same stepped leader can initiate separate return strokes. The light pulses from cloud discharges tend to be smaller and more slowly varying than those from return strokes. The total optical power radiated by first strokes in the 5-to 35-km range has a mean and standard deviation of 2.3 _+ 1.8 x 10 9 W at peak. Normal subsequent strokes produce 4.8 _+ 3.6 x 108 W at peak, and subsequent strokes preceded by a dart-stepped leader produce 5.4 _+ 2.2 x 108 W. The characteristic widths of 23 subsequent stroke signals range from 103 to 235/•s, with a mean and standard deviation of 158 _+ 33/•s. Analyses of the initial linear slopes of the light signals suggest that the space-and timeaveraged radiance of first strokes is about 1.0 _+ 0.9 x 10 6 W/m during the bright phase and that normal and dart-stepped subsequent strokes produce about 2.5 _+ 1.8 x 105 W/m and 4.3 _+ 3.1 x 105 W/m, respectively. Further analyses suggest that the dependence of the average radiance on the peak electric field, and probably the peak current, is neither linear nor quadratic.