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

Ionization showers are created in the Earth's 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 O-2(-) 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.