Title: Loss of coherence and change in emission physics for radio emission from very inclined cosmic-ray air showers

Abstract: Next-generation radio experiments such as the Radio Detector of the upgraded Pierre Auger Observatory and the planned GRAND and BEACON arrays target the detection of ultra-high-energy particle air showers arriving at low elevation angles. These inclined cosmic-ray air showers develop higher in the atmosphere than vertical ones, enhancing magnetic deflections of electrons and positrons inside the cascade. We evidence two novel features in their radio emission: a new polarization pattern, consistent with a geo-synchrotron emission model and a coherence loss of the radio emission, both for showers with zenith angle $\theta \gtrsim 65^{\circ}$ and strong enough magnetic field amplitude (typical strength of $B\sim 50\, \rm \mu T$). Our model is compared with both ZHAireS and CoREAS Monte-Carlo simulations. Our results break the cannonical description of a radio signal made of Askaryan and transverse current emission only, and provide guidelines for the detection and reconstruction strategies of next-generation experiments, including cosmic-ray/neutrino discrimination.