The radio detection of cosmic rays consists in the estimation of the properties of a primary cosmic ray by observing the electric field emitted by the extensive air shower (EAS) created when the primary cosmic ray enters the atmosphere. This technique is fully operative nowadays and presents a good degree of maturity. In addition, several projects intend to employ this technique for the detection of neutrinos. In order for the technique to be useful, accurate methods for computing the electric field created by a particle shower in the context of a particular experiment must exist. Although current ground-based radio experiments lie on the air-soil interface and some planned experiments on the South Pole envision antennas near the air-ice interface, most of the analytical approaches and Monte Carlo codes used for calculating the electric field either do not take into account the effect of the boundary or calculate the radiation fields only (direct, reflected and transmitted radiation fields). When the particle shower and the antenna are close to the boundary, compared to the observation wavelength, the far-field approximation breaks down, which is the case for the low-frequency EXTASIS experiment, for instance. We present in this work a new formula for calculating the exact field emitted by a particle track in two semi-infinite media separated by a planar boundary. We also explore the validity of the far-field approximation and make some predictions for EAS using a simple shower model.

• Received 28 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.063009