Radio pulses from cosmic ray air showers

Boosted Coulomb and Čerenkov fields

¹ LESIA, Observatoire de Paris, CNRS, UPMC, Université Paris Diderot, 5 place Jules Janssen, 92190 Meudon, France e-mail: nicole.meyer@obspm.fr
² SUBATECH, IN2P3/CNRS, Université de Nantes, École des Mines de Nantes, 4 rue Alfred Kastler, 44307 Nantes, France

Received: 28 September 2007
Accepted: 4 December 2007

Abstract

High-energy cosmic rays passing through the Earth's atmosphere produce extensive showers whose charges emit radio frequency pulses. Despite the low density of the Earth's atmosphere, this emission should be affected by the air refractive index because the bulk of the shower particles move roughly at the speed of radio waves, so that the retarded altitude of emission, the relativistic boost, and the emission pattern are modified. In this paper we consider the contribution of the boosted Coulomb and the Čerenkov fields and calculate analytically the spectrum using a very simplified model in order to highlight the main properties. We find that typically the lower half of the shower charge energy distribution produces a boosted Coulomb field, of amplitude comparable to the levels measured and to those calculated previously for synchrotron emission. Higher energy particles instead produce a Čerenkov-like field, whose amplitude may be smaller because both the negative charge excess and the separation between charges of opposite signs are small at these energies.