  We present a macroscopic calculation of coherent electro-magnetic radiation
from air showers initiated by ultra-high energy cosmic rays, based on currents
obtained from three-dimensional Monte Carlo simulations of air showers in a
realistic geo-magnetic field. We discuss the importance of a correct treatment
of the index of refraction in air, given by the law of Gladstone and Dale,
which affects the pulses enormously for certain configurations, compared to a
simplified treatment using a constant index. We predict in particular a
geomagnetic Cherenkov radiation, which provides strong signals at high
frequencies (GHz), for certain geometries together with "normal radiation" from
the shower maximum, leading to a double peak structure in the frequency
spectrum. We also provide some information about the numerical procedures
referred to as EVA 1.0.
