By modifying the avalanche mode of runaway breakdown to include positive feedback from gamma-rays and positrons, it is found that enormous bursts of energetic radiation can be produced in strong electric fields in air, with peak fluxes up to one billion times greater than from conventional models. These bursts generate so many runaway electrons that the electric field is very rapidly discharged, resulting in a fundamental upper limit on the electric field strength achievable in air. This limit has important implications for the electrification of thunderstorms and the production of lightning.