Theory of ball lightning

We present a comprehensive theory on the formation of ball lightning, a luminous sphere sometimes observed after normal lightning. In a ball lightning event, a relativistic electron bunch can be produced by the stepped leader of lightning and coherently emit high-power microwave when striking the ground. The intense microwave ionizes the local air and evacuates the resulting plasma by its radiation pressure, thereby forming a spherical plasma cavity that traps the microwave. The theory can explain observed properties of ball lightning and should be useful to lightning protection and aviation safety.