Abstract
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 (2.3–3.1) × 10−6 Kg m/s/(V/m)2. A radiation field with a zero-crossing time of 70 μs will dissipate about (2.6–3.4) × 103 J/(V/m)2 in field-normalized energy and (3.2–4.3) × 10−6 Kg m/s/(V/m)2 in field-normalized vertical momentum. The results show that, for a given peak radiation field, the radiated energy and momentum increase with increasing zero-crossing time of the radiation field. The normalized peak power generated by a first return stroke radiation field is about 1.2 × 108 W/(V/m)2 and the peak power is generated within about 5–6 μs from the beginning of the return stroke. Conversely, a typical subsequent return stroke generating a radiation field having a 40 μs zero-crossing time will dissipate field-normalized energy of about (6–9) × 102 J/(V/m)2 and field-normalized vertical momentum of approximately (7.5–11) × 10−7 Kg m/s/(V/m)2. The field-normalized peak power generated by a subsequent return stroke radiation field is about 1.26 × 108 W/(V/m)2 and the peak power is generated within about 0.7–0.8 μs from the beginning of the return stroke. In addition to these parameters, the possible upper bounds for the energy and momentum radiated by return strokes are also presented.
Highlights
Electromagnetic fields generated by lightning play an essential role in lightning protection studies since they generate unwanted currents and voltages in electrical and electronic systems, causing them damage and disruptions [1]
One can deduce from the equations given in the previous section, that for a given current wave shape, the energy, momentum, and the peak power radiated by a return stroke is proportional to the square of the peak of the return stroke current
Using the proportionality as mentioned above, one can obtain the amount of energy, momentum, or peak power radiated by return strokes having other values of peak currents
Summary
Electromagnetic fields generated by lightning play an essential role in lightning protection studies since they generate unwanted currents and voltages in electrical and electronic systems, causing them damage and disruptions [1]. They can be utilized as a vehicle to study the terrain features by analyzing how these fields are modified when they travel along grounds of different configurations and electrical properties [2,3,4]. In physics-based return stroke models, the knowledge concerning the fraction of energy removed from the lightning channel by electromagnetic radiation is an essential parameter in evaluating the energy balance of the lightning return stroke [5]
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