A particle code has been developed to study the distribution and acceleration of electrons in electric discharges in air. The code can follow the evolution of a discharge from the initial stage of a ...single free electron in a background electric field to the formation of an electron avalanche and its transition into a streamer. The code is in 2D axi-symmetric coordinates, allowing quasi 3D simulations during the initial stages of streamer formation. This is important for realistic simulations of problems where space charge fields are essential such as in streamer formation. The charged particles are followed in a Cartesian mesh and the electric field is updated with Poisson’s equation from the charged particle densities. Collisional processes between electrons and air molecules are simulated with a Monte Carlo technique, according to cross section probabilities. The code also includes photoionisation processes of air molecules by photons emitted by excited constituents. The paper describes the code and presents some results of streamer development at 70km altitude in the mesosphere where electrical discharges (sprites) are generated above severe thunderstorms and at ∼10km relevant for lightning and thundercloud electrification. The code is used to study acceleration of thermal seed electrons in streamers and to understand the conditions under which electrons may reach energies in the runaway regime. This is the first study in air, with a particle model with realistic spatial dependencies of the electrostatic field. It is shown that at 1atm pressure the electric field must exceed ∼7.5 times the breakdown field to observe runaway electrons in a constant electric field. This value is close to the field where the electric force on an electron equals the maximum frictional force on an electron – found at ∼100eV. It is also found that this value is reached in a negative streamer tip at 10km altitude when the background electric field equals ∼3 times the breakdown field. At higher altitudes, the background electric field must be relatively larger to create a similar field in a streamer tip because of increased influence of photoionisation. It is shown that the role of photoionization increases with altitude and the effect is to decrease the space charge fields and increase the streamer propagation velocity. Finally, effects of electrons in the runaway regime on negative streamer dynamics are presented. It is shown the energetic electrons create enhanced ionization in front of negative streamers. The simulations suggest that the thermal runaway mechanism may operate at lower altitudes and be associated with lightning and thundercloud electrification while the mechanism is unlikely to be important in sprite generation at higher altitudes in the mesosphere.
In this paper we estimate the probability that cold electrons can be accelerated by an ambient electric field into the runaway regime, and discuss the implications for negative streamer formation. ...The study is motivated by the discovery of ms duration bursts of γ‐rays from the atmosphere above thunderstorms, the so‐called Terrestrial Gamma‐Ray Flashes. The radiation is thought to be bremsstrahlung from energetic (MeV) electrons accelerated in a thunderstorm discharge. The observation goes against conventional wisdom that discharges in air are carried by electrons with energies below a few tens of eV. Instead the relativistic runaway electron discharge has been proposed which requires a lower threshold electric field; however, seed electrons must be born with energies in the runaway regime. In this work we study the fundamental problem of electron acceleration in a conventional discharge and the conditions on the electric field for the acceleration of electrons into the runaway regime. We use particle codes to describe the process of stochastic acceleration and introduce a novel technique that improves the statistics of the relatively few electrons that reach high energies. The calculation of probabilities for electrons to reach energies in the runaway regime shows that even with modest fields, electrons can be energized in negative streamer tips into the runaway regime, creating a beamed distribution in front of the streamer that affects its propagation. The results reported here suggest that theories of negative streamers and spark propagation should be reexamined with an improved characterization of the kinetic effects of electrons.
Bursts of X‐rays and γ‐rays are observed from lightning and laboratory sparks. They are bremsstrahlung from energetic electrons interacting with neutral air molecules, but it is still unclear how the ...electrons achieve the required energies. It has been proposed that the enhanced electric field of streamers, found in the corona of leader tips, may account for the acceleration; however, their efficiency is questioned because of the relatively low production rate found in simulations. Here we emphasize that streamers usually are simulated with the assumption of homogeneous gas, which may not be the case on the small temporal and spatial scales of discharges. Since the streamer properties strongly depend on the reduced electric field E/n, where n is the neutral number density, fluctuations may potentially have a significant effect. To explore what might be expected if the assumption of homogeneity is relaxed, we conducted simple numerical experiments based on simulations of streamers in a neutral gas with a radial gradient in the neutral density, assumed to be created, for instance, by a previous spark. We also studied the effects of background electron density from previous discharges. We find that X‐radiation and γ‐radiation are enhanced when the on‐axis air density is reduced by more than ∼25%. Pre‐ionization tends to reduce the streamer field and thereby the production rate of high‐energy electrons; however, the reduction is modest. The simulations suggest that fluctuations in the neutral densities, on the temporal and spacial scales of streamers, may be important for electron acceleration and bremsstrahlung radiation.
Plain Language Summary
Bursts of X‐rays and γ‐rays are observed from electric discharges. They are bremsstrahlung from energetic electrons interacting with air molecules, but how do electrons achieve the necessary energies? Previous theories suggest that the enhanced electric fields of streamer discharges facilitate the acceleration; however, simulations found a relatively low production rate. Streamer simulations are usually performed in homogeneous air, which may not be realistic on the small temporal and spatial scales of discharges. Streamer properties depend not only on the electric field but also on the density of air; therefore, air perturbations may have a significant effect. To investigate the emission of X‐rays and γ‐rays in nonuniform air, we conduct simulations in a neutral gas with radial perturbations, for example, created by a previous discharge. We find that X‐radiation and γ‐radiation is enhanced when the on‐axis air density is reduced by more than ∼25%. The simulations suggest that perturbed air, on the temporal and spacial scales of streamers, is important for electron acceleration, bremsstrahlung radiation, and the production of X‐rays and γ‐rays emitted from discharges.
Key Points
Air perturbations significantly increase the velocity of streamer fronts
Air perturbations facilitate the emission of X‐rays from streamer discharges
Pre‐ionization moderately lowers the maximum energy of electrons and photons
Sprite streamers are bright atmospheric phenomena above thunderstorms powered by sufficiently high electric fields and free charges from inhomogeneities in the mesosphere or ionosphere. A common ...feature of recent simulations is that they model the streamer inception from spherical Gaussian electron‐ion patches. We here tackle the following question: How do the streamer inception time and streamer properties depend on the initial geometry? Therefore, we consider prolate (“cigar”) and oblate (“pancake”) electron‐ion patches aiming to understand the geometric influence on streamer inception speed, electric field evolution, branching time, and ohmic heating of streamers. We initiate patches of different geometry with fixed peak densities of 5·1011 m−3 or with a fixed total electron number of 9.40·1012 in ambient fields of 0.5 and 1.5 times the breakdown field and study the streamer evolution between 60 and 80 km altitude with a 2.5D cylindrical Monte Carlo particle code. We present the evolution of the electron density and of the electric field. In our simulations, the time for the electric field tips to develop into the regime where they can self sustain the discharge is shortest for streamers from prolate patches and longest for oblate patches. The branching time of negative fronts depends on the eccentricity and increases for oblate patches ranging from 5 to 8 μs. We observe ohmic heating with maximum temperature differences up to tens of kelvins depending on the eccentricity and density of the initial patch influencing the efficiency of plasma reactions in streamer channels.
Key Points
The speed of the streamer motion depends on the geometry of the initial electron‐ion patch
The development of the electric field in the early streamer stages is fastest for prolate patches
Ohmic heating is most significant for streamers from prolate patches and least significant for streamers from oblate patches
Blue LUminous Events (BLUEs) are transient corona discharges occurring in thunderclouds and characterized by strong 337.0 nm light flashes with absent (or weak) 777.4 nm component. We present the ...first nighttime climatology of BLUEs as detected by the Modular Multispectral Imaging Array of the Atmosphere‐Space Interaction Monitor showing their worldwide geographical and seasonal distribution. A total (land and ocean) of ∼11 BLUEs occur around the globe every second at local midnight and the average BLUE land/sea ratio is ∼7:4. The northwest region of Colombia shows an annual nighttime peak. Globally, BLUEs are maximized during the boreal summer‐autumn, contrary to lightning which is maximed in the boreal summer. The geographical distribution of nighttime BLUEs shows three main regions in, by order of importance, the Americas, Europe/Africa and Asia/Australia.
Plain Language Summary
Blue LUminous Events (BLUEs) are transient corona discharges occurring in thunderclouds and characterized by their distinct 337.0 nm light flashes with absent (or negligible) 777.4 nm component. We present the first two year nighttime climatology of BLUEs as detected by the Modular Multispectral Imaging Array of the Atmosphere‐Space Interaction Monitor on board the International Space Station that shows distinct worldwide geographical and seasonal distributions.
Key Points
The first nighttime two‐year climatology of streamer corona discharges (blue luminous events) in thunderclouds is presented
Globally, the rate of blue luminous events at local midnight is ∼11 per second
Zonal and meridional distributions of blue luminous events peak in the northern tropic and the Americas, respectively
Streamers are ionization filaments of electric gas discharges. Negative polarity streamers propagate primarily through electron impact ionization, whereas positive streamers in air develop through ...ionization of oxygen by UV photons emitted by excited nitrogen; however, experiments show that positive streamers may develop even for low oxygen concentrations. Here we explore if bremsstrahlung ionization facilitates positive streamer propagation. To discriminate between effects of UV and bremsstrahlung ionization, we simulate the formation of a double headed streamer at three different oxygen concentrations: no oxygen, 1 ppm O2 and 20% O2, as in air. At these oxygen levels, UV-relative to bremsstrahlung ionization is zero, small, and large. The simulations are conducted with a particle-in-cell code in a cylindrically symmetric configuration at ambient electric field magnitudes three times the conventional breakdown field. We find that bremsstrahlung induced ionization in air, contrary to expectations, reduces the propagation velocity of both positive and negative streamers by about 15%. At low oxygen levels, positive streamers stall; however, bremsstrahlung creates branching sub-streamers emerging from the streamer front that allow propagation of the streamer. Negative streamers propagate more readily forming branching sub-streamers. These results are in agreement with experiments. At both polarities, ionization patches are created ahead of the streamer front. Electrons with the highest energies are in the sub-streamer tips and the patches.
Terrestrial gamma ray flashes (TGFs) are beams of high‐energy photons associated to lightning. These photons are the bremsstrahlung of energetic electrons whose origin is currently explained by two ...mechanisms: energizing electrons in weak, but large‐scale thundercloud fields or the acceleration of low‐energy electrons in strong, but localized fields of lightning leaders. Contemporary measurements by the Atmosphere‐Space Interactions Monitor suggest that the production of TGFs is related to the leader step and associated streamer coronae when upward moving intracloud lightning illuminates. Based on these observations, we apply a particle‐in‐cell Monte Carlo code tracing electrons in the superposed electric field of two encountering streamer coronae and modeling the subsequent photon emission. We also perform a parameter study by solving the deterministic equations of motion for one electron. We find that this mechanism can explain the occurrence of TGFs with photons energies of several MeV lasting for tens to hundreds of μs, in agreement with observations.
Plain Language Summary
For more than two decades, it has been known that thunderstorms emit high‐energy X‐rays and γ rays, the so‐called terrestrial gamma ray flashes (TGFs) lasting for tens to hundreds of μs, which are the bremsstrahlung (“braking radiation”) of energetic electrons and are the most energetic natural phenomena on Earth. Within the last years, two theories have been crystallized out to explain the origin of energetic electrons: the acceleration and multiplication of energetic electrons as remnants of cosmic rays in the large‐scale electric fields of thunderclouds or the acceleration of thermal electrons in high electric fields in the vicinity of the tips of lightning leaders. Contemporary measurements of the Atmosphere‐Space Interactions Monitor (ASIM) show that TGFs are produced at the onset of the main optical lightning pulse, indicating that the electron acceleration is related to the upward pointing lighting leader tip. We have performed computational simulations of the electron acceleration in the superposed electric field of two encountering streamer coronae, a compilation of small plasma channels with high‐field tips, arising in the proximity of the lightning leader tip and the upper charge layer. We find that this scenario can explain the occurrence of TGFs with energies and durations compatible with previous and contemporary measurements.
Key Points
Relativistic electrons are produced during the breakdown of ICs during a current surge when two streamer coronae approach each other
The acceleration of electrons between two streamer coronae leads to TGFs lasting for tens to hundreds of μs with photon energies of
O(10 MeV)
The maximum photon energy in TGFs is determined by the electric field of the upper cloud charge layer
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