We present a novel semi-analytical treatment of the radio emission of air showers that is able to
reproduce the results of full ZHAireS simulations, in theory at a fraction of the computational
cost. Traditionally, the contribution to the vector potential of every single particle track in the
shower is calculated separately. Instead, in our approach we divide the air shower into 4-D
spacetime volumes, so that the contribution of the volume needs to be calculated only once, based
on the average particle track inside it. This almost amounts to a macroscopic treatment of the
shower, but retaining the precision of the successful microscopic approach.
The size of the 4-D spacetime volumes is chosen so that the traditional vector potential expression
can be further simplified, as many of its terms can be taken to be the same for the whole volume.
Computationally expensive terms, such as the the effective refractive index from the track to the
observer, can then be calculated only once, making it possible to obtain the precise radio emission
at a fraction of the cost.
This approach also allows us to perform more precise calculations that would otherwise be too
expensive to apply on a track-by-track basis. These could include a more detailed treatment of
atmospheric effects for near horizontal showers and high altitude detectors, such as balloons and
satellites.