  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.
