On the Minimisation of Beam Chromaticity in a TEM Horn Antenna for Global 21-cm Cosmology

Abstract

The detection of the sky-averaged 21 cm signal from the Cosmic Dawn requires antennas whose beam pattern varies minimally with frequency, since beam chromaticity couples the bright, spatially structured Galactic foreground into spurious spectral structure that can obscure the faint cosmological signal. We present a Particle Swarm Optimisation (PSO) framework that optimises a double-ridged TEM horn antenna operating from 60 to 85MHz against a cost function targeting beam chromaticity directly, and benchmark it against both an unoptimised baseline and an established directivity-based cost function (Restrepo et al. 2023). The designs are evaluated by convolving CST-simulated beam patterns with the Global Sky Model to produce antenna-temperature spectra over Local Sidereal Time, and assessed through a mock signal-injection test and a spectral-index analysis. The proposed cost function reduces the directivity smoothness metric by 97% and the beam-solid-angle variation by 52%, and yields the lowest beam-induced foreground residual of the three designs at every foreground order, falling below the depth of an injected 500mK signal already at fourth order. In the cold-sky window used for a global-signal integration it is also the least chromatic (σ β = 0.018). We show that the single-power-law spectral index is an incomplete chromaticity metric—its full-day scatter is dominated by Galactic-transit hours excluded from the science integration—and that the foreground-fit residual is the more direct measure of recoverability. These results demonstrate that targeting beam chromaticity directly produces a TEM horn better suited to foreground subtraction than either the baseline or a directivity-based optimisation, and provide an observation-driven framework for antenna design in global 21 cm experiments.