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, 122 (2), 1365-1383

Production Mechanisms of Leptons, Photons, and Hadrons and Their Possible Feedback Close to Lightning Leaders

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Production Mechanisms of Leptons, Photons, and Hadrons and Their Possible Feedback Close to Lightning Leaders

Christoph Köhn et al. J Geophys Res Atmos.

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.

Keywords: Monte Carlo simulation; cross‐section analysis; feedback model; neutron beam; positron beam; terrestrial gamma‐ray flash.

Figures

Figure 1
Figure 1
(a) The simulation results and NIST data of the average length ν until full energy loss of electrons for different initial energies E 0 at ground pressure. (b) The simulation results and NIST data of the mean‐free path Λ of photons in air as a function of the initial photon energy E 0. (c) The relative error (ν NISTν Simulation)/ν Simulation as a function of E 0. (d) The relative error (ΛNIST−ΛSimulation)/ΛSimulation as a function of E 0.
Figure 2
Figure 2
(a) The total cross section for elastic and inelastic scattering off nitrogen molecules as well as for the capture of neutrons on nitrogen molecules as a function of the energy E kin,n,i of the incident neutron. (b) The cumulative cross section of elastic and inelastic scattering in air as well as the inverse column density 1/N int, (black lines), at altitude ranges of 0–16 km, 13–16 km, 16–19 km, and 16–500 km.
Figure 3
Figure 3
The ratio E kin,n,f/E kin,n,i of the neutron energy in the final state E kin,n,f and in the initial state E kin,n,i after elastic scattering as a function of the scattering angle Θ. Different lines show different initial energies and nucleon numbers η (η = 32 for O2, η = 28 for N2, and η = 2 for H2).
Figure 4
Figure 4
The energy loss ΔE of neutrons after exciting air molecules (solid line) and the ratio of the energy loss to the incident neutron energy E kin,n,i (dotted line) as a function of the incident neutron energy.
Figure 5
Figure 5
The simulation results and the data by Nakamura and Kosako [1981] for the flux r·Φ(r) of neutron beams of different energies E 0 as a function of distance r.
Figure 6
Figure 6
The spatial distributions of neutrons after 1 ms for different initial energies E 0 and altitudes H 0. The color code on the right shows the kinetic energy. Note that the spatial scales are different for different panels. The current neutron number is given in brackets.
Figure 7
Figure 7
The energy distribution dn n/dE kin,n, i.e., the number of neutrons per energy bin, after different time steps for different initial energies E 0 and altitudes H 0. All simulations were initiated with 600 neutrons.
Figure 8
Figure 8
(a) The normalized neutron number N/N 0 for the same cases as in Figures 6 and 7 as a function of atmospheric layer ΔX. Here ΔX = 0 refers to the initial altitude and ΔX ≠ 0 denotes the air package in g/cm2 which a neutron passes where a negative sign of ΔX denotes the altitudes in the initial direction of the neutron beam. (b–f) N/N 0 for the different cases in Figure 8a distinguishing for different threshold energies E kin,n passing the air package ΔX (first xlabel) and equivalently the altitude H (second xlabel).
Figure 9
Figure 9
The time‐integrated normalized cross‐section area A=1/N·i=1Nxi2+yi2 as a function of atmospheric layer ΔX and equivalently of the altitude H. x i and y i are the positions of the ith neutron (out of N) parallel to the x y plane. The solid line at ΔX = 0 indicates the source altitude of the neutron beam. (a) All simulated cases; (b–f) 〈A〉 for different threshold energies E kin,n for different initial altitudes and different initial energies.
Figure 10
Figure 10
Electric field strength (color coded) in the vicinity of the tip for a leader of 1 km length in an ambient field of −0.5 kV/cm. Cylindrical coordinates (ϱ=x2+y2,z) are used, and the upper leader tip lies at the origin of the coordinate system. The black level lines indicate fixed values of the electric field strength from 5 to 1000 kV/cm as indicated.
Figure 11
Figure 11
The spatial distribution of (a) electrons, (b) photons, (c) positrons, (d) neutrons, and (e) protons after approximately 1 μs projected onto the x z plane (for all y) in the electric field of a leader of 1 km length and of 1 cm curvature radius in an ambient field of −0.5 kV/cm (as indicated by the black line). The color code shows the (kinetic) energy of all particles above 1 MeV on a logarithmic scale. The numbers in brackets give the particle numbers.
Figure 12
Figure 12
The energy distribution of electrons, photons, positrons, neutrons, and protons after (a, b) 1 μs and (c, d) 0.5 ms. Figures 12a and 12c are obtained in the absence of any field and Figures 12b and 12d in the field of a leader.
Figure 13
Figure 13
The energy distribution of electrons, photons, positrons, neutrons, and protons after (a) 28 ns and (b) 0.5 ms in the same field as in Figure 11.

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