Reply to comments of Hill

Paxton, Alan H.; Baker, Louis C. W.; Gardner, R. L.

doi:10.1063/1.866100

Cited by 10 publications

(9 citation statements)

References 10 publications

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“…Similarly, Plooster (1971) and Paxton et al (1986) both avoided the use of an optimal return stroke current model in favor of a more simplified current source that had a linear rise to peak followed by an exponential decay.…”

Section: B Channel Currentmentioning

confidence: 97%

“…In other words, apart from cooling due to channel expansion, we neglect all other cooling mechanisms. Some of these mechanisms have been examined by other investigators: thermal conduction (Braginskii 1958), turbulent mixing (Picone et al 1981), and radiation (Paxton et al 1986). However, there is still debate in the literature as to which of these cooling mechanisms are most important (e.g., Hill 1987;Paxton et al 1987).…”

Section: Simplifying Assumptionsmentioning

confidence: 98%

“…Some of these mechanisms have been examined by other investigators: thermal conduction (Braginskii 1958), turbulent mixing (Picone et al 1981), and radiation (Paxton et al 1986). However, there is still debate in the literature as to which of these cooling mechanisms are most important (e.g., Hill 1987;Paxton et al 1987). These ancillary cooling mechanisms represent a loss of energy to the return stroke channel, so neglecting these mechanisms leads to overestimating the maximum channel radius attained.…”

Section: Simplifying Assumptionsmentioning

confidence: 98%

“…For example, a model that is applicable across both strong and weak shock domains and that employed an equation of state for air at high temperature was introduced (Plooster 1968(Plooster , 1970 and then directly applied to lightning return strokes (Plooster 1971). In addition, a detailed gas dynamic model introduced by Paxton et al (1986) included energy loss in the return stroke channel due to radiation.…”

Section: Introductionmentioning

confidence: 99%

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A Return Stroke NOx Production Model

Koshak

Solakiewicz

Peterson

2015

Journal of the Atmospheric Sciences

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A model is introduced for estimating the nitrogen oxides (NO x 5 NO 1 NO 2 ) production from a lightning return stroke channel. A realistic modified transmission line model return stroke current is assumed to propagate vertically upward along a stepped leader channel of 0.1-cm radius. With additional assumptions about the initial radial expansion rate of the channel, the full nonlinear differential equation for the return stroke channel radius r(z, t) is solved numerically using Mathematica V9.0.1.0. Channel conductivity and channel air density are adjustable constants, and the model employs typical atmospheric profiles of temperature, pressure, and density. The channel pressure is modeled by a dynamic pressure expression. Channel temperature is extracted from the pressure by a minimization technique that involves a generalized gas law appropriate for high temperatures where dissociation and ionization are important. The altitude and time variations of the channel energy density are also obtained. Three model runs, each with different input parameters, are completed. Channel radii at sea level range from about 1.7 to 6.0 cm depending on the model inputs and are in good agreement with other investigators. The NO x production from each 1-m segment of the channel is computed using conservation of energy and equilibrium freeze-out-temperature chemistry. Because the NO x per meter of channel is computed as a function of altitude, extensions of the results to tortuous and branched channels are possible and lead to preliminary estimates of total return stroke NO x . These estimates are found to be smaller than the return stroke NO x values obtained from the NASA Lightning Nitrogen Oxides Model (LNOM).

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Section: B Channel Currentmentioning

confidence: 97%

Section: Simplifying Assumptionsmentioning

confidence: 98%

Section: Simplifying Assumptionsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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A Return Stroke NOx Production Model

Koshak

Solakiewicz

Peterson

2015

Journal of the Atmospheric Sciences

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“…After the publication of Paxton et al [] on the optical radiation of lightning return strokes, criticisms from Hill [1987] were published, followed by a reply from Paxton et al []. The main critique of Hill [1987] is related to the fact that 69% of the total energy is radiated away by Paxton's model, which according to his analysis is certainly too high.…”

Section: Introductionmentioning

confidence: 97%

On the dynamics of hot air plasmas related to lightning discharges: 1. Gas dynamics

et al. 2014

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In this paper, we first study the dynamics of hot shocks in air in cylindrical geometry coupled to multiband radiation transport and detailed air chemistry. The wide energy and length scale ranges which are covered herein includes and exceeds the ones of first and subsequent return strokes happening during lightning discharges. An emphasis is put on the NO x production and the optical power emitted by strong shocks as the ones generated by Joule heating of the air from intense current flows. The production rate of NO x , which is useful for atmospheric global modeling, is found to be between 4.5 × 10 16 and 8.6 × 10 16 molecules/J for all computed cases, which is in agreement with the literature. Two different radiation transport methods are used to characterize the variability of the results according to the radiation transport method. With the exact radiation solver, we show that between 15 and 40% of the energy is lost by radiation, with a percentage between 20 and 25% for averaged lightning energies. The maximal visible peak is between 7 × 10 8 W/m and 3 × 10 7 W/m obtained for, respectively, a 19 kJ/cm and a 28 J/cm energy input. The mean radiated powers in the visible range are found between 9 × 10 6 W/m and 2 × 10 5 W/m for the energies just mentioned. We discuss the agreement of these values with previous studies.

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On the dynamics of hot air plasmas related to lightning discharges: 2. Electrodynamics

et al. 2014

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In this paper, we develop a model of electrical discharge in air for the simulation of some of the electrical processes involved in lightning discharges, as in lightning return strokes and dart leaders. The discharge is initiated by a vertical electrical field and modeled using a nonlinear R-L-C circuit model, with which we attempt to simulate initiation, growth, radial expansion, and decay of electrical discharges related to lightning. This gas dynamic type model includes also both detailed air chemistry and accurate air radiation transport, as described in the first part of this article. For certain parameter configurations, our first lightning-related discharge simulations compare well with lightning observations and actual knowledge in terms of chronology, charge and energy depleted, current created, electron concentration, temperature, pressure, and optical signature. We also discuss the difficulties to obtain fully consistent results due to the wide parameter variability, their uncertainty, and the complexity of the physics involved.

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Reply to comments of Hill

Cited by 10 publications

References 10 publications

A Return Stroke NOx Production Model

A Return Stroke NOx Production Model

On the dynamics of hot air plasmas related to lightning discharges: 1. Gas dynamics

On the dynamics of hot air plasmas related to lightning discharges: 2. Electrodynamics

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