Optical power and energy radiated by return strokes in rocket‐triggered lightning

Abstract

The broadband optical radiation covering the visible and near‐infrared (VNIR) spectral regions (0.4–1.0 μm) has been measured from 70 negative return strokes (RS) in rocket‐triggered lightning; 17 events were recorded in 2011, and 53 were recorded in 2012. The radiometers were calibrated, and all measurements were time‐correlated with currents measured at the channel base. The risetime and peak of an irradiance waveform are determined primarily by the RS current and by the geometrical growth and total length of channel that is in the field of view of the sensor. Following an initial peak, the irradiance decays faster than the current until there is a plateau or secondary maximum 20 to 40 μs (median of 22 μs) after the peak current, a time when the current itself is steadily decreasing. Estimates of the space‐ and time‐average optical power per unit length (ℓo) that is emitted at the source during onset of RS have been computed using the measured slopes of 70 irradiance waveforms together with an assumption that the initial speed of propagation is 1.2 × 108 m/s. The values range from 0.25 to 9.5 MW/m, with a mean and standard deviation of 2.4 ± 1.7 MW/m, and they are in good agreement with prior estimates of ℓo that were made by Quick and Krider (2013) for the subsequent return strokes in natural lightning that reilluminate a preexisting channel. The values of ℓo also agree with numerical estimates of the VNIR power per unit length that were computed by Paxton et al. (1986). Estimates of the peak optical power per unit length (ℓR) that is radiated at the source have been derived from the peaks of 53 irradiance waveforms, and the values range from 0.4 to 11 MW/m with a mean and standard deviation of 4.2 ± 2.5 MW/m. Both ℓo and ℓR are approximately proportional to the square of the peak current at the channel base. Estimates of the total optical energy per unit length, Jo, that is radiated in the VNIR have been computed by integrating the irradiance waveforms over 2 ms. The values of Jo have a mean and standard deviation of 150 ± 140 J/m, and they are proportional to the total charge that is transported to ground in that interval.

The Plasma Nature of Lightning Channels and the Resulting Nonlinear Resistance

“…The 0.1‐μs value is in excellent agreement with experimental results by Carvalho et al (, ) and Quick and Krider () who found delays of 0.09 ± 0.05 and 0.09 ± 0.06 μs, respectively. Differently than Quick and Krider (), Carvalho et al () recorded luminosity from a 3‐m‐long channel segment near the ground. From such a short segment, the luminosity rise time is not masked by the geometrical growth of the return stroke in the field of view.…”

“…Figure a shows the simulated temporal dynamics of visible power and electrical current in the channel, for conditions that resemble the aforementioned observations. The waveform is 0.5/50 μs with a 12‐kA peak current, similar to the median case in the data set (Quick & Krider, , Table 1). Figure b shows the first 3 μs of light emission, evidencing a 0.1‐μs delay between the rise of current and optical emissions in the channel.…”

“…We presented a detailed description of the light emission in a return stroke. We showed that the proposed model can reproduce the experimentally inferred direct relationship between peak current and peak radiated power and between charge transferred to ground and total energy radiated, as experimentally inferred by Quick and Krider (). The caveat is that the quadratic power law relationship between the two remains unexplained.…”

“…Perhaps the most pertinent is estimate #2, which is calculated by taking the ratio of vis in the visible range calculated by Cressault et al (2011, Figure 2) to in the total optical range calculated by (Naghizadeh-Kashani et al, 2002, Figure 13) for an optically thin plasma. This strategy places vis between 0.1% and 10% in the temperature range between 3,000 and 30,000 K. Within this range, we adopt the value of 3% because it yields a good agreement with experimental data from Quick and Krider (2017) discussed below. Figure 7 shows properties of return stroke light emission and comparison to rocket-triggered lightning data collected by Quick & Krider (2017, Figures 15 and 16).…”

Triggered Lightning Return Stroke Luminosity up to 1 km in Two Optical Bands

“…Luminosity waveforms emitted by natural and rocket‐and‐wire triggered lightning processes such as return strokes and M‐components have been studied to determine how such optical radiation varies with time and channel height (e.g., Carvalho et al, , ; Carvalho, Uman, Jordan, Hill, et al, ; Jordan & Uman, ; Schonland, ; Wang et al, , , , ), to measure return stroke speeds in both time and frequency domains (e.g., Carvalho et al, ; Carvalho, Uman, Jordan, Hill, et al, ; Carvalho, Uman, Jordan, & Moore, ; Chen et al, ; Mach & Rust, ; Olsen et al, ; Schonland, ; Wang et al, , , , ) to determine how luminosity relates to the electric current flowing through the lightning channel‐bottom (e.g., Carvalho et al, , ; Idone & Orville, ; Qie et al, ; Wang et al, ; Zhou et al, ), to determine the optical energy radiated (e.g., Guo & Krider, , ; Krider, ; Krider et al, ), to examine the efficiency with which the discharge converts input energy to light (e.g., Connor, ; Krider et al, ), and to examine the lightning optical spectra, including deriving physical properties of the lightning channel such as temperature, electron density, and pressure from analyzing lightning spectra (e.g., Krider, ; Orville & Uman, ; Orville, , , , ; Prueitt, ; Quick & Krider, ; Uman, ; Uman et al, ; Walker, ; Walker & Christian, ).…”