Caitano L. da Silva

Dynamics of streamer‐to‐leader transition at reduced air densities and its implications for propagation of lightning leaders and gigantic jets

[1] In this paper we present modeling studies of air heating by electrical discharges in a wide range of pressures. The developed model is capable of quantifying the different contributions for heating of air at the particle level and rigorously accounts for the vibration-dissociation-vibration coupling. The model is validated by calculating the breakdown times of short air gaps and comparing to available experimental data. Detailed discussion on the role of electron detachment in the development of the thermal-ionizational instability that triggers the spark development in short air gaps is presented. The dynamics of fast heating by quenching of excited electronic states is discussed and the scaling of its main channels with ambient air density is quantified. The developed model is employed to study the streamer-to-leader transition process and to obtain its scaling with ambient air density. Streamer-to-leader transition is the name given to a sequence of events occurring in a thin plasma channel through which a relatively strong current is forced through, culminating in heating of ambient gas and increase of the electrical conductivity of the channel. This process occurs during the inception of leaders (from sharp metallic structures, from hydrometeors inside the thundercloud, or in virgin air) and during their propagation (at the leader head or during the growth of a space leader). The development of a thermal-ionizational instability that culminates in the leader formation and propagation is characterized by a change in air ionization mechanism from electron impact to associative ionization and by contraction of the plasma channel. The introduced methodology for estimation of leader speeds shows that the propagation of a leader is limited by the air heating of every newly formed leader section. It is demonstrated that the streamer-to-leader transition time has an inverse-squared dependence on the ambient air density at near-ground pressures, in agreement with similarity laws for Joule heating in a streamer channel. Model results indicate that a deviation from this similarity scaling occurs at very low air densities, where the rate of electronic power deposition is balanced by the channel expansion, and air heating from quenching of excited electronic states is very inefficient. These findings place a limit on the maximum altitude at which a hot and highly conducting lightning leader channel can be formed in the Earth’s atmosphere, result which is important for understating of the gigantic jet (GJ) discharges between thundercloud tops and the lower ionosphere. Simulations of leader speeds at GJ altitudes demonstrate that initial speeds of GJs are consistent with the leader propagation mechanism. The simulation of a GJ, escaping upward from a thundercloud top, shows that the lengthening of the leader streamer zone, in a medium of exponentially decreasing air density, determines the existence of an altitude at which the streamer zones of GJs become so long that they dynamically extend (jump) all the way to the ionosphere.

Physical mechanism of initial breakdown pulses and narrow bipolar events in lightning discharges

To date the true nature of initial breakdown pulses (IBPs) and narrow bipolar events (NBEs) in lightning discharges remains a mystery. Recent experimental evidence has correlated IBPs to the initial development of lightning leaders inside the thundercloud. NBE wideband waveforms resemble classic IBPs in both amplitude and duration. Most NBEs are quite peculiar in the sense that very frequently they occur in isolation from other lightning processes. The remaining fraction, 16% of positive polarity NBEs, according to Wu et al. (2014), happens as the first event in an otherwise regular intracloud lightning discharge. These authors point out that the initiator type of NBEs has no difference with other NBEs that did not start lightning, except for the fact that they occur deeper inside the thunderstorm (i.e., at lower altitudes). In this paper, we propose a new physical mechanism to explain the source of both IBPs and NBEs. We propose that IBPs and NBEs are the electromagnetic transients associated with the sudden (i.e., stepwise) elongation of the initial negative leader extremity in the thunderstorm electric field. To demonstrate our hypothesis a novel computational/numerical model of the bidirectional lightning leader tree is developed, consisting of a generalization of electrostatic and transmission line approximations found in the literature. Finally, we show how the IBP and NBE waveform characteristics directly reflect the properties of the bidirectional lightning leader (such as step length, for example) and amplitude of the thunderstorm electric field.

Infrasonic acoustic waves generated by fast air heating in sprite cores

Acceleration, expansion, and branching of sprite streamers can lead to concentration of high electrical currents in regions of space, that are observed in the form of bright sprite cores. Driven by this electrical current, a series of chemical processes take place in the sprite plasma. Excitation, followed by quenching of excited electronic states leads to energy transfer from charged to neutral species. The consequence is heating and expansion of air leading to emission of infrasonic acoustic waves. Results indicate that ≳0.01 Pa pressure perturbations on the ground, observed in association with sprites, can only be produced by exceptionally strong currents in sprite cores, exceeding 2 kA.

Mathematical constraints on the use of transmission line models to investigate the preliminary breakdown stage of lightning flashes

The initial stage of in-cloud lightning development is characterized by a series of initial breakdown pulses (IBPs), observed as abrupt electric field changes at a remote sensor. Recent studies have attributed this process to the stepwise elongation of a negative lightning leader channel and used transmission line (TL) models to interpret the observed electromagnetic emission. In these models a current pulse is injected at the base of the channel, propagates along it, and the current parameters are adjusted to fit the measured IBPs. In this paper we explore the limitations of TL models by comparing four of its variants: the classic TL (with no attenuation) and three modified transmission line models that have different current attenuation characteristics, i.e., following linear, exponential, and Gaussian functions. For a compact channel (less than a few hundred meters long) all four models tend to produce similar electromagnetic signatures, and nearly identical waveforms can be obtained by simply varying the channel length. It is impossible to simultaneously identify, with confidence, both channel length and the speed of current wave propagation at the source by matching a far-field waveform. The field-to-current conversion factor for in-cloud sources is not a constant and can vary by as much as 2 orders of magnitude depending on channel length and current pulse risetime. This conclusion contrasts with the assumption used by the National Lightning Detection Network, that the field-to-current conversion can be performed by a multiplicative constant, as it is done for return strokes in cloud-to-ground lightning.

Mechanism of fast air heating and infrasound generation by sprites

Summary form only given. Sprites are electrical discharges transversing the middle atmosphere, between 40-90 km altitude. They are generated by the the electric fields produced by cloud-to-ground lightning in underlying thunderstorms. Therefore, sprites represent optical evidences of the electrical coupling between troposphere and the mesosphere/lower ionosphere regions. In the last decade, another evidence of the above mentioned coupling has been discovered. Farges et al. [GRL, 32, L011813, 2005] have correlated optical observations with infrasound signatures produced by sprites. The main characteristics of infrasound from sprites are a chirp-inverted signature (at 0.1-9 Hz frequency range) and amplitudes of 0.01-0.1 Pa, as measured at ground at distances of the order of 400 km. Sprites manifest themselves as growing streamer tree discharges, where many individual streamers have a common origin point, that can be observed as a bright core [e.g., Li and Cummer, JGR, 116, A01301, 2011, Figure 2]. Although individual streamers transport low electrical current, the total electrical current flowing through the sprite body can be sufficiently large to produce Joule heating and excitation of vibrational states in nitrogen molecules. In this work, we introduce a first-principles model to quantify the air heating in sprites. The model describes the coupling between chemistry and gas dynamics in a nonequilibrium plasma. The model accounts for fast air heating due to quenching of excited electronic states of nitrogen molecules [Popov, JPD, 44, 285201, 2011]. We provide parametric dependences of air heating and pressure perturbation amplitudes on sprite characteristics, such as available current, electric field, and channel radius. This modeling study is the first step towards connecting the well-known optical [e.g., Stenbaek-Nielsen and McHarg, JPD, 41, 234009, 2008] and electrical [e.g., Cummer et al., GRL, 25, 8, 1998] properties of sprites to their infrasound signatures [e.g., Farges et al., 2005; de Larquier and Pasko, GRL, 37, L17804, 2010].