Temporally self-similar electron distribution functions in atmospheric breakdown: The thermal runaway regime

Detailed Boltzmann kinetic calculations of the electron distribution functions resulting from thermal runaway in a constant electric field are presented. Thermal runaway is considered to occur when an initially thermal electron is accelerated above the 150 eV peak in the dynamical friction force in air and becomes a runaway electron. We investigate the role of runaway breakdown in situations where thermal runaway, as well as conventional breakdown, is occurring. The electric field strengths studied span the range from the threshold for runaway breakdown in air (similar to 0.3 MV/m at sea level) through conventional breakdown (2.4-3.2 MV/m at sea level) and exceeding the Dreicer field (25 MV/m at sea level), above which all electrons are runaways. We initiate our simulations with a population of pseudothermal electrons or with a combination of thermal and runaway (similar to 1 MeV) electrons. We find that when thermal runaway occurs the self-similar electron distribution function is identical in the presence or absence of a seed runaway population. We show that attempts to obtain the electric field from remote measurements of optical line ratios are ambiguous both in the context of the absolute field and in the underlying kinetics. By considering the runaway electrons as a separate population we conclude that the avalanche rate of low-energy electrons is equivalent to that of runaway electrons at a reduced field of 140 Td (3.8 MV/m at standard temperature and pressure). Above that field the conventional avalanche rate will control the avalanche rate of the entire population. Below that field the runaway avalanche rate will control the avalanche rate of the entire population.