Air shower development through the time dependence of its induced electric field

Abstract

Ultra-high energy cosmic rays impinge on the atmosphere and induce air shower cascades, in which huge numbers of particles are produced. By traveling through the Earth's atmosphere and magnetic field, these particles create a noticeable effect on the electric field at the surface. In this article, we demonstrate that parameters of the shower longitudinal development can be inferred from mapping the time dependence of the observed electric field to the emitted electric field as a function of slant depth along the shower axis.

Figures (9)

• Figure 1: Simplified geometry of an air shower with its complete development contained along the shower axis. The top of the atmosphere is set at 50 km. The shower axis is at an angle $\theta$ w.r.t. the zenith at the core position. The detection plane is at an altitude h above sea-level. Radiation emitted from point P, located on the shower axis at distance L from the core, is observed at point R, at a distance D to the emission point. The radiation path is parametrised by $\vec{l}$.
• Figure 2: Left: Detector array on the ground plane used for the simulations. The layout consists of a star-shape with 16 spokes and 21 concentric rings. The colour scale shows the maximum electric field intensity for each observer, representative of the radio-wave footprint of a 1 EeV proton-induced shower, with a zenith angle of $\theta = 80\degree$, and an azimuth angle of $\phi=345\degree$. The observers on the spoke at $120\degree$ from north, highlighted in grey, are used to exemplify the method in the following sections. Right: A detailed view of the denser setup region near the shower core.
• Figure 3: Top:$T_{R_{abs}}$ as a function of the slant depth, calculated for five observers located along the highlighted spoke in Figure \ref{['fig:simusetup']}, and an air shower geometry of $\theta = 80\degree$ and $\phi=345\degree$. The observers were chosen for their positions w.r.t. the Čerenkov ring: two outside and close to the core (at 100 and 700 m), one within the Čerenkov region (at 1400 m), and two outside and far away from the core (at 2200 and 3000 m). Bottom: The simulated electric field time series for the five selected observers. The marked labels in the horizontal axis correspond to the time the electric field becomes non-zero at each observer, representative of when the first signal arrives at each location.
• Figure 4: Left: Mapping profiles for detectors positioned outside the Čerenkov region and close to the core (100 and 700 m), within the Čerenkov region (1400 m), and outside the Čerenkov and far away from the core (2200 and 3000 m). All profiles are normalized from their maximum amplitude, so to better illustrate their similarities in shape. Right: The normalized mapping profile shapes correlate with the normalized longitudinal particle profile of the air shower. The sharp particles profile is due to conversion from vertical to slant depth.
• Figure 5: Original harsher field mapping profile, in black, and its smoothed output, in red. The profile shape parameters, $\mathrm{FM_{max}}$ and $\mathrm{FM_{FWHM}}$, are extracted from the smoothed profile.