Radio wavefront of very inclined extensive air-showers observed with extended and sparse radio arrays Valentin Decoene a,b,c , Olivier Martineau-Huynh d,c , Matias Tueros e,c a Department of Physics, Pennsylvania State University, University Park, USA b Center for Multimessenger Astrophysics, Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, USA c Sorbonne Universit´ e, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France d Sorbonne Universit´ e, Universit´ e Paris Diderot, Sorbonne Paris Cit´ e, CNRS/IN2P3, LPNHE, Paris, France e Instituto de F´ ısica La Plata - CONICET, Argentina Abstract In this article we perform a simulation-based study of the shape of the elec- tromagnetic wavefront of air showers induced by cosmic rays. We show that for showers with zenith angles larger than 60°, a point-source like descrip- tion of the wave-front is sufficient and that the reconstructed position of this point-source is a potential proxy for the determination of the nature of the cosmic rays initiating the showers, with performances similar to those obtained using the depth of shower maximum. Keywords: ultra-high-energy cosmic rays, ultra-high-energy neutrinos, extensive-air-showers physics, radio-emission, radio-detection, radio . 1. Introduction A proper description of the shape of the electromagnetic wavefront emit- ted by an extensive air shower can be a key tool to reconstruct the properties of the cosmic particle at the origin of the air shower. Substantial modeling efforts and experimental work have already been carried out on this issue. The LOPES and LOFAR collaborations have in Email address: decoene@iap.fr (Valentin Decoene) Preprint submitted to Elsevier December 15, 2021 arXiv:2112.07542v1 [astro-ph.IM] 14 Dec 2021