Christoph Köhn

Calculation of beams of positrons, neutrons, and protons associated with terrestrial gamma ray flashes

Positron beams have been observed by the Fermi satellite to be correlated with lightning leaders, and neutron emissions have been attributed to lightning and to laboratory sparks as well. Here we discuss the cross sections to be used for modeling these emissions, and we calculate the emissions of positrons, neutrons, and also protons from lightning leaders. Neutrons were first erroneously attributed to fusion reactions, but the photonuclear reaction responsible for neutrons should create protons as well. We predict them here; they have not been observed yet. In the paper, we first revisit the model for stepped lightning leaders of Xu, Celestin, and Pasko with updated cross sections, we analyze the spatial and energetic structure of the electron beam, and we calculate the spectrum of the generated gamma ray beam at 16 km altitude. Then we review the scattering processes of photons with emphasis on the processes above 5 MeV, in particular the photon energy losses in Compton scattering events and the generation of leptons and hadrons. We provide simple approximations for photon energy loss and lepton and hadron production for any photon with energy above 5 MeV passing through an arbitrary air layer. Finally, we launch a gamma ray beam with the earlier calculated spectrum of the negative stepped lightning leader from 16 km upward and calculate the production and energy of positrons, neutrons, and protons as well as the propagation of positrons.

Analyzing x-ray emissions from meter-scale negative discharges in ambient air

textabstractWhen voltage pulses of 1 MV drive meter long air discharges, short and intense bursts of x-rays are measured. Here we develop a model for electron acceleration and subsequent photon generation within this discharge to understand these bursts. We start from the observation that the encounter of two streamers of opposite polarity launches the electrons, that they are further accelerated in the discharge field and then lose their energy, e.g., by photon emission through Bremsstrahlung. We model electron and photon dynamics in space and energy with a Monte Carlo model. Also the detector response to incoming photons is modelled in detail. The model justifies the approximation that the x-ray bursts are isotropic in space; this assumption is used to conclude that x-ray bursts near the high-voltage electrode with 6.104 photons and characteristic energies of 160 keV closely reproduce the measured spectra and attenuation curves. The nanosecond duration of the bursts as well as their energy spectrum is consistent with model calculations.

The importance of electron–electron bremsstrahlung for terrestrial gamma-ray flashes, electron beams and electron–positron beams

Thunderstorms emit terrestrial gamma-ray flashes with photon energies of up to tens of MeV and electron-positron beams that are created by photons with energies above 1.022 MeV. These photons are produced through the bremsstrahlung process when energetic electrons collide with air molecules. However, presently used cross sections for bremsstrahlung treat only the interaction of the electrons with the nuclei of molecules while we here include their interaction with shell electrons. We simulate the production of energetic photons by a negative stepped lightning leader, and we find that electron–electron bremsstrahlung contributes significantly, although the direct photon emission is less than from electron–nucleus bremsstrahlung. However, electron–electron bremsstrahlung also ejects shell electrons and therefore feeds the electron population above 1 MeV significantly. We find that it hence dominates the photon spectrum of the stepped lightning leader at 10 MeV.

Influence of atmospheric electric fields on the radio emission from extensive air showers

The atmospheric electric fields in thunderclouds have been shown to significantly modify the intensity and polarization patterns of the radio footprint of cosmic-ray-induced extensive air showers. ...

Electron acceleration during streamer collisions in air

Abstract High‐voltage laboratory experiments show that discharges in air, generated over a gap of one meter with maximal voltage of 1 MV, may produce X‐rays with photon energies up to 1 MeV. It has been suggested that the photons are bremsstrahlung from electrons accelerated by the impulsive, enhanced field during collisions of negative and a positive streamers. To explore this process, we have conducted the first self‐consistent particle simulations of streamer encounters. Our simulation model is a 2‐D, cylindrically symmetric, particle‐in‐cell code tracing the electron dynamics and solving the space charge fields, with a Monte Carlo scheme accounting for collisions and ionization. We present the electron density, the electric field, and the velocity distribution as functions of space and time. Assuming a background electric field 1.5 times the breakdown field, we find that the electron density reaches 2·1021 m−3, the size of the encounter region is ∼3·10−12 m3 and that the field enhances to ∼9 times the breakdown field during ∼10−11 s. We further find that the radial component becomes comparable to the parallel component, which together with angular scattering leads to an almost isotropic distribution of electrons. This is consistent with laboratory observations that X‐rays are emitted isotropically. However, the maximum energy of electrons reached in the simulation is ∼600 eV, which is well below the energies required to explain observations. The reason is that the encounter region is small in size and duration. For the photon energies observed, the field must be enhanced in a larger region and/or for a longer time.

The influence of bremsstrahlung on electric discharge streamers in N2, O2 gas mixtures

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.

Production mechanisms of leptons, photons, and hadrons and their possible feedback close to lightning leaders

Abstract It has been discussed that lightning flashes emit high‐energy electrons, positrons, photons, and neutrons with single energies of several tens of MeV. In the first part of this paper we study the absorption of neutron beams in the atmosphere. We initiate neutron beams of initial energies of 350 keV, 10 MeV, and 20 MeV at source altitudes of 4 km and 16 km upward and downward and see that in all these cases neutrons reach ground altitudes and that the cross‐section areas extend to several km2. We estimate that for terrestrial gamma‐ray flashes approximately between 10 and 2000 neutrons per ms and m2 are possibly detectable at ground, at 6 km, or at 500 km altitude. In the second part of the paper we discuss a feedback model involving the generation and motion of electrons, positrons, neutrons, protons, and photons close to the vicinity of lightning leaders. In contrast to other feedback models, we do not consider large‐scale thundercloud fields but enhanced fields of lightning leaders. We launch different photon and electron beams upward at 4 km altitude. We present the spatial and energy distribution of leptons, hadrons, and photons after different times and see that leptons, hadrons, and photons with energies of at least 40 MeV are produced. Because of their high rest mass hadrons are measurable on a longer time scale than leptons and photons. The feedback mechanism together with the field enhancement by lightning leaders yields particle energies even above 40 MeV measurable at satellite altitudes.

The structure of ionization showers in air generated by electrons with 1 MeV energy or less

Ionization showers are created in the Earths atmosphere by cosmic particles or by run-away electrons from pulsed discharges or by the decay of radioactive elements like radon and krypton. These showers provide pre-ionization that can play a role for discharge inception or evolution; radioactive admixtures in plasma technology use the same effect. While the CORSIKA program provides cross sections and models for cosmic particle showers down to the MeV level, we here analyze the shower structure below 1 MeV by using a three-dimensional relativistic Monte Carlo discharge code for the electron dynamics. We provide a few analytical results to speed up the numerical implementation of the scattering processes. We derive and analyze the spatio-temporal structure of ionization and electron energies in the shower for incident electrons with energies of 1 keV to 1 MeV, at air pressures of 10, 100 and 1000 mbar at room temperature in great detail. We calculate the final density of and O− ions and the average input energy per ion. We show that the average input energy per ion increases from 20 eV for initial energies of 1 KeV to 33 eV for 250 MeV. We also derive the electric fields generated by the electrons and residual ions of the particle showers. Finally, we study how the shower evolution and the electron energy at 1 bar is influenced by ambient electric fields of 5 or 8 kV cm−1 and see that for 1 keV the electron number decreases, more slowly than without field, whereas the electron number continuously grows for 1 MeV.

The Planck Length and the Constancy of the Speed of Light in Five Dimensional Spacetime Parametrized with Two Time Coordinates

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant; the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe.

High‐Energy Emissions Induced by Air Density Fluctuations of Discharges

Abstract 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.