Analytical and numerical models of the radio frequency emissions produced by relativistic runaway electron avalanches initiated by cosmic ray extensive air showers are presented. It is found that single‐point measurements of the distant electromagnetic fields allow the remote determination of the electrostatic field in the runaway electron avalanche region. For instance, it is possible to use ground‐based and/or remote airborne measurements of the radio frequency pulses from the runaway electron avalanches to map the magnitudes and directions of the electrostatic field within a thundercloud for regions with electric fields above the runaway avalanche threshold. Such measurements, which are difficult to perform in situ, may help answer several key questions regarding lightning initiation, such as what electric fields are usually present when lightning initiates and whether electric fields in small regions ever reach the conventional breakdown field.
