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 cm3 are present. This is one particular example set from a parameter range that we discuss as well. Our simulations include the permittivity ε(ω) of ice. 100 free electrons per cm3 exist at 5.5 km altitude in air showers created by cosmic particles of at least 5×1015  eV. If the electric field zone is 3 m high and 0.2  km2 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.
American Physical Society
Physical Review Letters
Cosmic Lightning
Multiscale Dynamics

A. Dubinova, A., Rutjes, C., Ebert, U., Buitink, S., Scholten, O., & Trinh, G. (2015). Prediction of lightning inception by large ice particles and extensive air showers. Physical Review Letters, 115(1), 015002:1–015002:5. doi:10.1103/PhysRevLett.115.015002