Radio Detection of High Energy Particles: Coherence Versus Multiple Scales

Radio Cherenkov emission underlines detection of high energy particles via a signal growing like the particle-energy-squared. Cosmic ray-induced electromagnetic showers are a primary application. While many studies have treated the phenomenon approximately, none have attempted to incorporate all the physical scales involved in problems with time- or spatially- evolving charges. We find it is possible to decompose the calculated fields into the product of a form factor, characterizing a moving charge distribution, multiplying a general integral which depends on the charge evolution. In circumstances of interest for cosmic ray physics, the resulting expressions can be evaluated explicitely in terms of a few parameters obtainable from shower codes. The classic issues of Frauhofer and Fresnel zones play a crucial role in the coherence.