Computing the electric field from Extensive Air Showers using a realistic description of the atmosphere

The composition of ultra-high energy cosmic rays is still poorly known and constitutes a very important topic in the field of high-energy astrophysics. Detection of ultra-high energy cosmic rays is carried out via the extensive air showers they create after interacting with the atmosphere constituents. The secondary electrons and positrons within the showers emit a detectable electric field in the kHz-GHz range. It is possible to use this radio signal for the estimation of the atmospheric depth of maximal development of the showers \xmax, with a good accuracy and a duty cycle close to $100\%$. This value of \xmax\ is strongly correlated to the nature of the primary cosmic ray that initiated the shower. We show in this paper the importance of using a realistic atmospheric model in order to correct for systematic errors that can prevent a correct and unbiased estimation of~\xmax.