Coherent radio emission from cosmic ray air-showers in the turbulent atmosphere

Coherent electromagnetic erenkov radiation is produced by cosmic ray air showers passing through the atmosphere. This radiation is detected by radio telescopes. We demonstrate here that the effect of random spatial fluctuations in the refractive index of air, about a mean exceeding unity, causes the airshower to emit not only the spontaneous coherent radio emission described elsewhere by Kahn and Lerche, but also an induced radiation field which can exceed the spontaneous field in certain frequency bands. Further the conditions for emission of the coherent radio erenkov radiation are altered by the presence of the refractive index fluctuations. And the Earth's magnetic field gives rise to the dominant term in the far-field radiation, be it spontaneous or induced, since it causes a systematic separation of electrons and positrons in the shower which, for parameters currently acceptable for air showers, is the major factor in determining the far-field radiation pattern. Also we suggest that the coherent 500 Mc/sec radiation seen from occasional showers is probably a reflection of an atmospheric correlation length of order 15 cm at the time the shower passes through the atmosphere.