In this work, it shows that nuclear reactions in lightning channel, which are produced by the deuterium-deuterium (D-D) and deuterium-tritium (D-T) nuclear reactions, represent a plausible mechanism for gamma-ray bursts observed at ground. Gamma-ray emissions from lightning can be explained by neutron inelastic scattering in the air. Neutrons (produced in lightning channel) will delay a definitive time (~33 ms) to cover the atmosphere before hitting a molecule and producing gamma rays, which is somewhat longer than the gamma-ray time delay (~20 ms) observed at ground.
Intense gamma-ray bursts on the ground, and produces in association with the initial-stage of rocket-triggered lightning, which have been recorded by Dwyer et al. [
On the other hand, experiments on board MIR orbital station (1991), ISS (2002), and Kolibri-2000 satellite (2002) at an altitude of 400 km detected neutron bursts (En ~ 0.1 eV - 1.0 MeV) in the equator regions connected with lightning discharges [
In this work, it shows that nuclear reactions in lightning channel, which are produced by D-D or D-T reactions, represent a plausible mechanism for gamma-ray bursts observed at ground. We have estimated that gamma-rays appear in about ~ 33 ms after the vaporization of the triggering copper wire, in a good agreement with the time delay of gamma-ray bursts observed at ground, which is 22 ms. Gamma-ray emissions from lightning can be explained by neutron inelastic scattering in the air.
Let us consider thunderclouds exhibiting a dipolar electrical charge structure (
When the positive charge center is discharged by the rocket-triggered lightning, deuterium ions are accelerated downward, producing downward bursts of neutrons below the thunderclouds. In lightning channel, deuterons of water (each hydrogen has a probability of 1 in 6400 of being deuterium; this corresponds to the natural isotopic abundance, 0.015%) are transformed in ions D+ and are accelerated, producing neutrons by thermonuclear reactions. Neutrons with 2.5 MeV energy arise from the D(d, n)He3 branch of D-D fusion reaction. Since the D(d, p)T branch occurs with about equal probability at low deuteron energy [
Intense burst of MeV gamma-rays was observed by Dwyer et al. [
In laboratory experiments, neutron pulses are observed in a brief portion of time (~70 ns) after the discharge current peak [
thermalization period in air occurring subsequent to the fast neutron burst and a thermal equilibrium. According to Samworth [
where is the macroscopic neutron capture cross section. It is the effective cross-sectional area per unit volume of material for capture of neutrons (in cm2/cm3 or cm−1), given by [
where σc is the microscopic neutron capture cross section and n is the particle density (i.e., number of atoms or molecules per volume unity of the absorber). Only hydrogen and nitrogen have significant cross sections for thermal neutron capture (0.33 and 1.75 barns, respectively [
where is the arithmetic mean of neutron capture cross section for hydrogen (from water) and nitrogen. Considering particle density in humid air as being [
where N is the Avogadro number, M is the mean molar mass of air particles, pd is the partial pressure of dry air (Pa), Rd is the specific gas constant for dry air, 287.05 J/(kg·K), T is air temperature on the Kelvin scale, Rv is the specific gas constant for water vapor, 461.495 J/(kg·K), is the relative humidity, and psat is the saturation vapor pressure. The saturation vapor pressure of water at any given temperature is the vapor pressure when relative humidity is 100%. A simplification of the regression used to find this, can be formulated as [
Inserting the numerical values in Equation (5), for T = 298 K and air humidity, we found n = 5 × 1025 m−3. Thus, we have ~ 33 ms. The attenuation length or mean free path is the medium length of a path covered by a particle between subsequent impacts. The mean free path of neutron in an absorber (air) is given by [
where sT is the total cross section of neutrons in the absorber. Thus, the time covered by a fast neutron between subsequent impacts is [
where ávñ is the mean speed of neutron. Thus [
where c is the speed of light, Ek is the kinetic energy of neutron, and m is its rest mass.
For 190 KeV neutrons (See
where pa is the partial pressure of air (Pa, N/m2), and T is the absolute dry bulb temperature (K). The density of water vapor can be expressed as [
where pw is the partial pressure water vapor (Pa, N/m2), and T is the absolute dry bulb temperature (K). The amount of water vapor in air at ground level can vary between θw = 0% to about θw = 5% (for example, in thunderstorm conditions). On the other hand, the 2.31 MeV gamma-ray mass attenuation coefficients of dry air and water are respectively μa = 0.03 (cm2/g) and μw = 0.02 (cm2/g) [
Electrical discharges through polymer fibers have been shown to produce up to 1012 neutrons by deuteron-deuteron fusion in dense plasma, consistent with ion densities of about 1019 cm−3 [
(0.015%) is identical in both water (for example, water droplets of cloud) and polymer molecules [
The “classical” lightning-triggering technique involves the use of a small rocket extending a thin grounded wire upward made of Kevlar-coated copper [
In this case, natural deuterium atoms from Kevlar are transformed in relativistic ions, producing neutrons by nuclear reactions after the wire disintegration.
According to our work, gamma-rays are produced by collisions of fast neutrons with air molecules. In triggered lightning, gamma-rays appear in about 33 ms after the lightning, in a good agreement with gamma-ray time delay observed at ground, which is 20 ms [
tering of the line emission should occur for the spectrum reported.
According to our model, one should expect an excess of He3—the other product of the D-D fusion reaction— near the lower levels of thunderclouds. If detection of this excess would be possible, it would provide further proof of the proposed mechanism. An effort in exploring such suggestion is in progress.
We acknowledge financial support from CNPq and Faperj (Brazil). The authors would like to express great appreciation to Dr. Sebastião Florentino da Silva (PROINFA from Eletrobrás, Rio de Janeiro, Brazil) for his encouragement and advice to this work.