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The spatial signal distribution of the radio frequency radiation from extensive air showers on the ground contains information on crucial cosmic-ray properties, such as energy and mass. A long-standing challenge to access this information experimentally with a sparse grid of antennas is an analytic modeling of the radio signal distribution, which will be addressed in this contribution. We present an analytic model based on the two physical processes generating radio emission in air showers: the geomagnetic and the charge-excess emission. Our study is based on full Monte-Carlo simulations with the CoREAS code. Besides an improved theoretical understanding of radio emission, our model describes the radio signal distribution with unprecedented precision. Our model explicitly includes polarization information, which basically doubles the information that is used from a single radio station. The model depends only on the definition of the shower axis and on the parameters energy and distance to the emission region, where the distance to the emission region has a direct relation to the cosmic-ray mass. The model describes the true signal distribution precisely such that the model uncertainties are negligible compared to typical experimental uncertainties.

An analytic description of the radio emission of air showers based on its emission mechanisms