Radio emission in a toy model with point-charge-like air showers

In the present paper we stress some characteristics of the electric field produced by a point-charge-like air shower developing in an atmosphere of refractive index fixed to unity and restricting ourselves to the charge excess and geosynchrotron terms. The aim of this toy model is obviously not to compete with refined theories nor full Monte Carlo simulations but to understand the main features of radio emission process as observed in recent experiments, in particular the field polarization effects. In this simplified frame, the antenna radio time pulse for vertical or inclined showers is merely given by the product of two analytical functions. The calculation time is reduced to a fraction of a second. The analytical pulse amplitudes are relatively close to those obtained with the ReAIRES code. Further works must be carried out to evaluate the limitations and the possible extensions of this toy model.