Influence of a planar boundary on the electric field emitted by a particle shower

Abstract

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.

On the transition radiation interpretation of anomalous ANITA events

“…As shown in figure 3, the geomagnetic effect dominates in air when compared to ice because the density is ∼ 1000 times lower and the transverse currents are much larger, in fact, E y is close to two orders of magnitude larger than E x. The relative contribution to E y from the tracks in ice displayed in figure 3 (a) is shown to be negligible, and the bulk of coherent TR can be obtained keeping only the contributions of the tracks in air [37][38][39]. However, the tracks in ice contribute mostly to the E x polarization (after refraction) as shown in figure 3 (b), because the Askaryan effect dominates in ice.…”

NuRadioMC: simulating the radio emission of neutrinos from interaction to detector

“…While this is appropriate in most practical cases, i.e., when the ice is uniform or has a slowly-varying index of refraction, ray tracing does not offer a full description of light propagation near dielectric interfaces, where additional solutions to Maxwell's equations exist, (see e.g. [74] for a pedagogical tutorial on some of the solutions, or [75] for a complete solution for the field of a particle track). In addition to the iceair interface at the surface, variations in ice density are present below the surface, producing a set of dielectric interfaces.…”

Coherent transition radiation from the geomagnetic air shower current

“…As such the potentials are typically not defined at the boundary, where boundary conditions have to be applied. Other, more direct approaches are found by calculating the boundary emission directly from Maxwell's equations [13].…”

“…In this work we discuss that for observers located far from the air-Earth boundary a different emission has to be considered, coherent transition radiation from the air shower traversing from air into Earth or more interestingly ice. This emission was already discussed in [8,9,10] where the focus was put on transition radiation from the net excess charge in the cascade front, where in [11,12,13], the sudden death signal due to the absorption of the air shower by Earth was considered. In this work, we show that transition radiation is a geometrical effect and as such is not limited to a net charge traversing a boundary layer, but applies equally well to the geomagnetically induced current in the air shower front, to which we will refer to as CTR-GM.…”