  Extensive air showers (EAS) have been known for over 30 years to emit pulses
of radio emission at frequencies from a few to a few hundred MHz, an effect
that offers great opportunities for the study of EAS with the next generation
of "software radio interferometers" such as LOFAR and LOPES. The details of the
emission mechanism, however, remain rather uncertain to date. Following past
suggestions that the bulk of the emission is of geomagnetic origin, we model
the radio pulses as "coherent geosynchrotron radiation" arising from the
deflection of electrons and positrons in the earth's magnetic field. We
analytically develop our model in a step-by-step procedure to disentangle the
coherence effects arising from different scales present in the shower structure
and infer which shower characteristics govern the frequency spectrum and radial
dependence of the emission. The effect is unavoidable and our predictions are
in good agreement with the available experimental data within their large
margins of error.
