B. E. Carlson

Differing current and optical return stroke speeds in lightning

During the return stroke in downward negative cloud-to-ground lightning, a current wave propagates upward from the ground along the lightning channel. The current wave causes rapid heating of the channel and induces intense optical radiation. The optical radiation wave propagation speed along the channel has been measured to be between 15 and 23 of the speed of light. The current wave speed is commonly assumed to be the same but cannot be directly measured. Past modeling efforts treat either the thermodynamics or electrodynamics. We present the first model that simultaneously treats the coupled current and thermodynamic physics in the return stroke channel. We utilize numerical simulations using realistic high-temperature air plasma properties that self-consistently solve Maxwells equations coupled with equations of air plasma thermodynamics. The predicted optical radiation wave speed, rise time, and attenuation agree well with observations. The model predicts significantly higher current return stroke speed.

Modeling the relativistic runaway electron avalanche and the feedback mechanism with GEANT4

This paper presents the first study that uses the GEometry ANd Tracking 4 (GEANT4) toolkit to do quantitative comparisons with other modeling results related to the production of terrestrial gamma ray flashes and high-energy particle emission from thunderstorms. We will study the relativistic runaway electron avalanche (RREA) and the relativistic feedback process, as well as the production of bremsstrahlung photons from runaway electrons. The Monte Carlo simulations take into account the effects of electron ionization, electron by electron (Møller), and electron by positron (Bhabha) scattering as well as the bremsstrahlung process and pair production, in the 250 eV to 100 GeV energy range. Our results indicate that the multiplication of electrons during the development of RREAs and under the influence of feedback are consistent with previous estimates. This is important to validate GEANT4 as a tool to model RREAs and feedback in homogeneous electric fields. We also determine the ratio of bremsstrahlung photons to energetic electrons Nγ/Ne. We then show that the ratio has a dependence on the electric field, which can be expressed by the avalanche time τ(E) and the bremsstrahlung coefficient α(ε). In addition, we present comparisons of GEANT4 simulations performed with a “standard” and a “low-energy” physics list both validated in the 1 keV to 100 GeV energy range. This comparison shows that the choice of physics list used in GEANT4 simulations has a significant effect on the results. Key Points Testing the feedback mechanism with GEANT4 Validating the GEANT4 programming toolkit Study the ratio of bremsstrahlung photons to electrons at TGF source altitude

Relativistic electrons from sparks in the laboratory

Abstract Discharge experiments were carried out at the Eindhoven University of Technology in 2013. The experimental setup was designed to search for electrons produced in meter‐scale sparks using a 1 MV Marx generator. Negative voltage was applied to the high voltage (HV) electrode. Five thin (1 mm) plastic detectors (5 cm2 each) were distributed in various configurations close to the spark gap. Earlier studies have shown (for HV negative) that X‐rays are produced when a cloud of streamers is developed 30–60 cm from the negative electrode. This indicates that the electrons producing the X‐rays are also accelerated at this location, that could be in the strong electric field from counterstreamers of opposite polarity. Comparing our measurements with modeling results, we find that ∼300 keV electrons produced about 30–60 cm from the negative electrode are the most likely source of our measurements. A statistical analysis of expected detection of photon bursts by these fiber detectors indicates that only 20%–45% of the detected bursts could be from soft (∼10 keV) photons, which further supports that the majority of detected bursts are produced by relativistic electrons.

Time domain simulations of preliminary breakdown pulses in natural lightning

Lightning discharge is a complicated process with relevant physical scales spanning many orders of magnitude. In an effort to understand the electrodynamics of lightning and connect physical properties of the channel to observed behavior, we construct a simulation of charge and current flow on a narrow conducting channel embedded in three-dimensional space with the time domain electric field integral equation, the method of moments, and the thin-wire approximation. The method includes approximate treatment of resistance evolution due to lightning channel heating and the corona sheath of charge surrounding the lightning channel. Focusing our attention on preliminary breakdown in natural lightning by simulating stepwise channel extension with a simplified geometry, our simulation reproduces the broad features observed in data collected with the Huntsville Alabama Marx Meter Array. Some deviations in pulse shape details are evident, suggesting future work focusing on the detailed properties of the stepping mechanism. Key Points Preliminary breakdown pulses can be reproduced by simulated channel extension Channel heating and corona sheath formation are crucial to proper pulse shape Extension processes and channel orientation significantly affect observations

Meter-scale spark X-ray spectrum statistics

Abstract X‐ray emission by sparks implies bremsstrahlung from a population of energetic electrons, but the details of this process remain a mystery. We present detailed statistical analysis of X‐ray spectra detected by multiple detectors during sparks produced by 1 MV negative high‐voltage pulses with 1 μs risetime. With over 900 shots, we statistically analyze the signals, assuming that the distribution of spark X‐ray fluence behaves as a power law and that the energy spectrum of X‐rays detectable after traversing ∼2 m of air and a thin aluminum shield is exponential. We then determine the parameters of those distributions by fitting cumulative distribution functions to the observations. The fit results match the observations very well if the mean of the exponential X‐ray energy distribution is 86 ± 7 keV and the spark X‐ray fluence power law distribution has index −1.29 ± 0.04 and spans at least 3 orders of magnitude in fluence.

Constraints to do realistic modeling of the electric field ahead of the tip of a lightning leader

Abstract Several computer models exist to explain the observation of terrestrial gamma‐ray flashes (TGFs). Some of these models estimate the electric field ahead of lightning leaders and its effects on electron acceleration and multiplication. In this paper, we derive a new set of constraints to do more realistic modeling. We determine initial conditions based on in situ measurements of electric field and vertical separation between the main charge layers of thunderclouds. A maximum electric field strength of 50 kV/cm at sea level is introduced as the upper constraint for the leader electric field. The threshold for electron avalanches to develop of 2.86 kV/cm at sea level is introduced as the lower value. With these constraints, we determine a region where acceleration and multiplication of electrons occur. The maximum potential difference in this region is found to be ∼52 MV, and the corresponding number of avalanche multiplication lengths is ∼3.5. We then quantify the effect of the ambient electric field compared to the leader field at the upper altitude of the negative tip. Finally, we argue that only leaders with the highest potential difference between its tips (∼600 MV) can be candidates for the production of TGFs. However, with the assumptions we have used, these cannot explain the observed maximum energies of at least 40 MeV. Open questions with regard to the temporal development of the streamer zone and its effect on the shape of the electric field remain.

First simultaneous observations of optical lightning and terrestrial gamma flash from space

In this paper we present the very first simultaneous detection of a terrestrial gamma-ray flash (TGF) and the optical signal from lightning. By fortuitous coincidence two independent satellites passed less than 300 km from the thunderstorm system that produced a TGF that lasted 70 μs. Together with two independent measurements of radio emissions we have an unprecedented coverage of the event. We find that the TGF was produced inside the thundercloud at the initial stage of an intracloud (IC) lightning just before the leader reached the cloud top and extended horizontally. A strong radio pulse was produced by the TGF itself. This is the first time the sequence of radio pulses, TGF and optical emissions has been identified. Figure 1 shows the three data sets and illustrates our interpretation of this unique event.