Prediction of Lightning Inception by Large Ice Particles and Extensive Air Showers

Abstract

We derive that lightning can start if the electric field is 15% of the breakdown field, and if elongated ice particles of 6 cm length and 100 free electrons per ${\mathrm{cm}}^{3}$ are present. This is one particular example set from a parameter range that we discuss as well. Our simulations include the permittivity $\ensuremath{\epsilon}(\ensuremath{\omega})$ of ice. 100 free electrons per ${\mathrm{cm}}^{3}$ exist at 5.5 km altitude in air showers created by cosmic particles of at least $5\ifmmode\times\else\texttimes\fi{}{10}^{15}\text{ }\text{ }\mathrm{eV}$. If the electric field zone is 3 m high and $0.2\text{ }\text{ }{\mathrm{km}}^{2}$ in the horizontal direction, at least one discharge per minute can be triggered. The size distribution of the ice particles is crucial for our argument; more detailed measurements would be desirable.