Monte Carlo Simulations of Secondary Cosmic-Ray Variations in Atmospheric Electric Fields : Implications for Long Duration Electron and Gamma-ray Emissions from Thunderclouds

Abstract

Monte Carlo simulations were conducted using the Particle and Heavy Ion Transport code System (PHITS) to investigate the role of secondary cosmic rays in the generation of long-duration bursts from thunderclouds and to clarify the conditions of the electric field region responsible for particle acceleration. The simulations utilized realistic secondary cosmic-ray spectra, including gamma rays, electrons, positrons, and muons, as input. The simulation results indicate that gamma rays provide the dominant supply of seed electrons for long-duration bursts, regardless of the geometry or strength of the electric field region. They also reveal the structure and strength of the electric field region required to produce gamma rays exceeding several tens of MeV, which have so far been detected only by high-altitude observations. Furthermore, the fluxes of long-duration bursts estimated from the simulation results were compared with observational data to constrain the properties of the electric field region. In particular, the comparison with measurements at Yangbajing, located at an altitude of 4.3~km, helps narrow down the possible range of electric field strengths and configurations.

Figures (13)

• Figure 1: Secondary cosmic-ray spectra expected at Yangbajing (4.3 km a.s.l.), calculated by EXPACS EXPACS
• Figure 2: Assumed structure and orientation of the electric field. The assumed EF region is shown in light blue. Dashed arrows indicate the parameters $W$, $L$, and $H$ used in the simulations. The EF orientation is represented by a solid arrow. The origin of the simulation coordinate system is denoted as O. Particles are injected from the upper boundary of the electric field region.
• Figure 3: Spatial distributions of electron flux (cm$^{-2}$ src$^{-1}$) produced by various incident particles. The top, middle, and bottom panels correspond to electrons originating from $(W, \, L)=(250\, \mathrm{m}, 250\, \mathrm{m})$, $(W,\, L)=(250\, \mathrm{m}, 1000\, \mathrm{m})$, and $(W,\, L)=(1000\, \mathrm{m}, 250\, \mathrm{m})$, respectively. The rectangles in all panels indicate the EF regions assumed in the MC simulations. The EF strength is 260 $\mathrm{kV\,m^{-1}}$. The left panels show electrons with energies between 0.05 and 10 MeV, while the right panels show electrons with energies above 10 MeV. The horizontal and vertical axes represent the spacial extent in meters. Warmer colors (red) indicate higher fluxes.
• Figure 4: The sames as Fig. \ref{['fig:electron_L250_1000_E2.6']}, but for gamma rays in the 0.01-10 MeV (left) and $>$10 MeV (right).
• Figure 5: Electron (left) and gamma rays (right) fluences (cm$^{-2}$) in 0.05-10 MeV as a function of $L$ for panels (a) and (b), and as a function of $W$ for panels (c) and (d). Fluences in panels (a) and (b) were obtained with $W =$ 250 m, while those in (c) and (d) were obtained with $L=$ 250 m. Each colored circle corresponds to an EF strength ranging from 85 to 260 $\mathrm{kV\,m^{-1}}$. Black squares indicate electron fluences at 0 $\mathrm{kV\,m^{-1}}$, corresponding to the lowest values in each panel.