Victor P. Pasko

Sprites produced by quasi‐electrostatic heating and ionization in the lower ionosphere

Quasi-electrostatic (QE) fields that temporarily exist at high altitudes following the sudden removal (e.g., by a lightning discharge) of thundercloud charge at low altitudes lead to ambient electron heating (up to ∼5 eV average energy), ionization of neutrals, and excitation of optical emissions in the mesosphere/lower ionosphere. Model calculations predict the possibility of significant (several orders of magnitude) modification of the lower ionospheric conductivity in the form of depletions of electron density due to dissociative attachment to O2 molecules and/or in the form of enhancements of electron density due to breakdown ionization. Results indicate that the optical emission intensities of the 1st positive band of N2 corresponding to fast (∼ 1 ms) removal of 100–300 C of thundercloud charge from 10 km altitude are in good agreement with observations of the upper part (“head” and “hair” [Sentman et al., 1995]) of the sprites. The typical region of brightest optical emission has horizontal and vertical dimensions ∼10 km, centered at altitudes 70 km and is interpreted as the head of the sprite. The model also shows the formation of low intensity glow (“hair”) above this region due to the excitation of optical emissions at altitudes ∼ 85 km during ∼ 500 μs at the initial stage of the lightning discharge. Comparison of the optical emission intensities of the 1st and 2nd positive bands of N2, Meinel and 1st negative bands of , and 1st negative band of demonstrates that the 1st positive band of N2 is the dominating optical emission in the altitude range around ∼70 km, which accounts for the observed red color of sprites, in excellent agreement with recent spectroscopic observations of sprites. Results indicate that the optical emission levels are predominantly defined by the lightning discharge duration and the conductivity properties of the atmosphere/lower ionosphere (i.e., relaxation time of electric field in the conducting medium). The model demonstrates that for low ambient conductivities the lightning discharge duration can be significantly extended with no loss in production of optical emissions. The peak intensity of optical emissions is determined primarily by the value of the removed thundercloud charge and its altitude. The preexisting inhomogeneities in the mesospheric conductivity and the neutral density may contribute to the formation of a vertically striated fine structure of sprites and explain why sprites often repeatedly occur in the same place in the sky as well as their clustering. Comparison of the model results for different types of lightning discharges indicates that positive cloud to ground discharges lead to the largest electric fields and optical emissions at ionospheric altitudes since they are associated with the removal of larger amounts of charge from higher altitudes.

Electrical discharge from a thundercloud top to the lower ionosphere

For over a century, numerous undocumented reports have appeared about unusual large-scale luminous phenomena above thunderclouds and, more than 80 years ago, it was suggested that an electrical discharge could bridge the gap between a thundercloud and the upper atmosphere. Since then, two classes of vertically extensive optical flashes above thunderclouds have been identified—sprites and blue jets. Sprites initiate near the base of the ionosphere, develop very rapidly downwards at speeds which can exceed 107 m s-1 (ref. 15), and assume many different geometrical forms. In contrast, blue jets develop upwards from cloud tops at speeds of the order of 105 m s-1 and are characterized by a blue conical shape. But no experimental data related to sprites or blue jets have been reported which conclusively indicate that they establish a direct path of electrical contact between a thundercloud and the lower ionosphere. Here we report a video recording of a blue jet propagating upwards from a thundercloud to an altitude of about 70 km, taken at the Arecibo Observatory, Puerto Rico. Above an altitude of 42 km—normally the upper limit for blue jets and the lower terminal altitude for sprites—the flash exhibited some features normally observed in sprites. As we observed this phenomenon above a relatively small thunderstorm cell, we speculate that it may be common and therefore represent an unaccounted for component of the global electric circuit.

Spatial structure of sprites

A theory of the electrical breakdown (EB) above thunderstorms is developed. The streamer type of the EB is proposed for the explanation of recent observations of fine spatial structures and bursts of blue optical emissions associated with sprites.

Heating, ionization and upward discharges in the mesosphere due to intense quasi-electrostatic thundercloud fields

Quasi-electrostatic (QE) fields that temporarily exist at high altitudes following the sudden removal (e.g., by a lightning discharge) of thundercloud charge at low altitudes are found to significantly heat mesospheric electrons and produce ionization and light. The intensity, spatial extent, duration and spectra of optical emissions produced are consistent with the observed features of the Red Sprite type of upward discharges.

Efficient models for photoionization produced by non-thermal gas discharges in air based on radiative transfer and the Helmholtz equations

This paper presents formulation of computationally efficient models of photoionization produced by non-thermal gas discharges in air based on three-group Eddington and improved Eddington (SP3) approximations to the radiative transfer equation, and on effective representation of the classic integral model for photoionization in air developed by Zheleznyak et al (1982) by a set of three Helmholtz differential equations. The reported formulations represent extensions of ideas advanced recently by S´ egur et al (2006) and Luque et al (2007), and allow fast and accurate solution of photoionization problems at different air pressures for the range 0.1 <p O2 R< 150 Torr cm, where pO2 is the partial pressure of molecular oxygen in air in units of Torr (pO2 = 150 Torr at atmospheric pressure) and R in cm is an effective geometrical size of the physical system of interest. The presented formulations can be extended to other gases and gas mixtures subject to availability of related emission, absorption and photoionization coefficients. The validity of the developed models is demonstrated by performing direct comparisons of the results from these models and results obtained from the classic integral model. Specific validation comparisons are presented for a set of artificial sources of photoionizing radiation with different Gaussian dimensions, and for a realistic problem involving development of a double-headed streamer at ground pressure. The reported results demonstrate the importance of accurate definition of the boundary conditions for the photoionization production rate for the solution of second order partial differential equations involved in the Eddington, SP3 and the Helmholtz formulations. The specific algorithms derived from the classic photoionization model of Zheleznyak et al (1982), allowing accurate calculations of boundary conditions for differential equations involved in all three new models described in this paper, are presented. It is noted that the accurate formulation of boundary conditions represents an important task needed for a successful extension of the proposed formulations to two- and three-dimensional physical systems with obstacles of complex geometry (i.e. electrodes, dust particles, aerosols, etc), which are opaque for the photoionizing UV photons.

Energy and fluxes of thermal runaway electrons produced by exponential growth of streamers during the stepping of lightning leaders and in transient luminous events

[1] In the present paper, we demonstrate that the exponential expansion of streamers propagating in fields higher than the critical fields for stable propagation of streamers of a given polarity leads to the exponential growth of electric potential differences in streamer heads. These electric potential differences are directly related to the energy that thermal runaway electrons can gain once created. Using full energy range relativistic Monte Carlo simulations, we show that the exponential growth of potential differences in streamers gives rise to the production of runaway electrons with energies as high as ∼100 keV, with most of electrons residing in energy range around several tens of keVs. We apply these concepts in the case of lightning stepped leaders during the stage of negative corona flash. The computation of electric field produced by stepped leaders demonstrates for the first time that those energetic electrons are capable of further acceleration up to the MeV energies. Moreover, the flux of runaway electrons produced by streamers suggests that stepped leaders produce a considerable number of energetic electrons, which is in agreement with the number of energetic photons observed from satellites in terrestrial gamma ray flashes (TGFs). The results suggest that previously proposed process of relativistic runaway electron avalanche is difficult to sustain in the low‐electric fields observed in thunderclouds and is generally not needed for explanation of TGFs. The present work also gives insights on relations between physical properties of energetic electrons produced in streamers and the internal electrical properties of streamer discharges, which can further help development and interpretation of X‐ray diagnostics of these discharges.

Runaway electrons as a source of red sprites in the mesosphere

Large quasi-electrostatic (QE) fields above thunderclouds [Pasko et al., 1995] produce an upward traveling beam of ∼1 MeV runaway electrons which may contribute to the production of optical emissions above thunderclouds referred to as Red Sprites. Results of a one dimensional computer simulation model suggest that the runaway electrons can produce optical emissions similar in intensity and spectra to those observed in Red Sprites, but only for large QE fields produced by positive CG discharges lowering 250 C or more to ground from an altitude of at least 10 km. Differences in predicted optical spectra from that of other mechanisms suggest that the runaway electron mechanism can be readily tested by high resolution spectral measurements of Red Sprites.

VLF signatures of ionospheric disturbances associated with sprites

VLF perturbations on signals propagating along great-circle-paths (GCP) through electrically active midwest thunderstorms are associated with luminous high altitude glows (referred to as sprites) observed from aircraft or ground. The data constitutes the first evidence that the physical processes leading to sprites also alter the conductivity of the lower ionosphere.

VLF and LF signatures of mesospheric/lower ionospheric response to lightning discharges

New evidence is presented of disturbances of the electrical conductivity of the nighttime mesosphere and the lower ionosphere in association with lightning discharges. In addition to extensive documentation of the characteristics of a class of events heretofore referred to as early/fast VLF events [Inan et al., 1993], our data reveal a new feature of these events, consisting of a postonset peak that typically lasts for 1–2 s. We also report the observation of short-duration VLF or LF perturbations, in which the amplitude of the subionospheric signal exhibits a sudden change within 20 ms of the causative lightning discharge, and recovers back to its original level in < 3 s. These short-duration events have characteristics similar to the previously observed rapid onset, rapid decay VLF signatures [Dowden et al.., 1994]. Both the typical and rapidly recovering events are observed primarily when the causative lightning discharge is within ±50 km of the VLF or LF great circle propagation path, indicating that the scattering from the localized disturbance is highly collimated in the forward direction. The latter in turn implies that for the parameters in hand, the transverse extent of the disturbance must be at least ∼ 100–150 km. The measured VLF signatures are compared with the predictions of a three-dimensional model of subionospheric VLF propagation and scattering in the presence of localized ionospheric disturbances produced by electromagnetic impulses and quasi-electrostatic (QE) fields produced by lightning discharges. The rapidly recovering or short-duration events are consistent with the heating of the ambient electrons by quasi-static electric fields, in cases when heating is not intense enough to exceed the attachment or ionization thresholds. When no significant electron density changes occur, the conductivity changes due to heating alone last only as long as the QE fields, typically less than a few seconds. When heating is intense enough so that attachment or ionization thresholds are exceeded, reductions or enhancements in electron density can respectively occur, in which case the medium would relax back to the ambient conditions with the time scales of the local D region chemistry, typically 10–100 s.

Time resolved N2 triplet state vibrational populations and emissions associated with red sprites

Abstract The results of a quasi-electrostatic electron heating model were combined with a time dependent N2 vibrational level population model to simulate the spectral distributions and absolute intensities observed in red sprites. The results include both N2 excited state vibrational level populations and time profiles of excited electronic state emission. Due to the long atmospheric paths associated with red sprite observations, atmospheric attenuation has a strong impact on the observed spectrum. We present model results showing the effect of atmospheric attenuation as a function of wavelength for various conditions relevant to sprite observations. In addition, our model results estimate the variation in the relative intensities of a number of specific N2 emissions in sprites (1PG, 2PG, and VK) in response to changes in observational geometry. A recent sprite spectrum, measured from the Wyoming Infrared Observatory (WIRO) on Jelm Mountain, during July, 1996, has been analyzed and includes N2 1PG bands down to v′ = 1. In addition to N2 1PG, our analysis of this spectrum indicates the presence of spectral features which are attributable to N+2 Meinel emission. However, due to the low intensity in the observed spectrum and experimental uncertainties, the presence of the N+2(A2Πu) should be considered preliminary. The importance of both the populations of the lower levels of the N2(B3Πg) and the N2(B3Πg)/N+2(A2Πg) population ratio in the diagnosis of the electron energies present in red sprites is discussed. While the current spectral analysis yields a vibrational distribution of the N2(B3Πg) which requires an average electron energy of only 1–2 eV, model results do indicate that the populations of the lower levels of the N2(B3Πg) will increase with increases in the electron energy primarily due to cascade. Considering the importance of the populations of the lower vibrational levels, we are beginning to analyze additional sprite spectra, measured at higher resolution, which contain further information on the population of B(v = 1).