Context. Repeating fast radio bursts (FRBs) present excellent opportunities to identify FRB progenitors and host environments, as well as decipher the underlying emission mechanism. Detailed studies of repeating FRBs might also hold clues to the origin of FRBs as a population. Aims. We aim to detect bursts from the first two repeating FRBs: FRB 121102 (R1) and FRB 180814.J0422+73 (R2), and characterise their repeat statistics. We also want to significantly improve the sky localisation of R2 and identify its host galaxy. Methods. We use the Westerbork Synthesis Radio Telescope to conduct extensive follow-up of these two repeating FRBs. The new phased-array feed system, Apertif, allows covering the entire sky position uncertainty of R2 with fine spatial resolution in a single pointing. The data were searched for bursts around the known dispersion measures of the two sources. We characterise the energy distribution and the clustering of detected R1 bursts. Results. We detected 30 bursts from R1. The non-Poissonian nature is clearly evident from the burst arrival times, consistent with earlier claims. Our measurements indicate a dispersion measure of 563.5(2) pc cm −3 , suggesting a significant increase in DM over the past few years. Assuming a constant position angle across the burst, we place an upper limit of 8% on the linear polarisation fraction for the brightest burst in our sample. We did not detect any bursts from R2. Conclusions. A single power-law might not fit the R1 burst energy distribution across the full energy range or widely separated detections. Our observations provide improved constraints on the clustering of R1 bursts. Our stringent upper limits on the linear polarisation fraction imply a significant depolarisation, either intrinsic to the emission mechanism or caused by the intervening medium, at 1400 MHz that is not observed at higher frequencies. The non-detection of any bursts from R2, despite nearly 300 hrs of observations, implies either a highly clustered nature of the bursts, a steep spectral index, or a combination of both assuming the source is still active. Another possibility is that R2 has turned off completely, either permanently or for an extended period of time.

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An optimal beamforming strategy is proposed for performing large-field surveys with dual-polarized phased-array-fed reflector antennas. This strategy uses signal-processing algorithms that maximize the beam sensitivity and the continuity of a field of view (FOV) that is formed by multiple closely overlapping beams. A mathematical framework and a newly developed numerical approach are described to analyze and optimize a phased array feed (PAF) system. The modeling approach has been applied to an experimental PAF system (APERTIF prototype) that is installed on the Westerbork Synthesis Radio Telescope. The resulting beam shapes, sensitivity, and polarization diversity characteristics (such as the beam orthogonality and the intrinsic cross-polarization ratio) are examined over a large FOV and frequency bandwidth. We consider weighting schemes to achieve a conjugate-field matched situation (max. received power), maximum signal-to-noise ratio (SNR), and a reduced SNR scenario but with constraints on the beam shape. The latter improves the rotational symmetry of the beam and reduces the sensitivity ripple, at a modest maximum sensitivity penalty. The obtained numerical results demonstrate a very good agreement with the measurements performed at the telescope.Index Terms-Antenna arrays, array signal processing, focal plane arrays, phased array feeds (PAFs), polarimetry, radio astronomy, reflector antenna feeds, system modeling techniques.

Abstract. In this paper we describe a focal plane array (FPA) prototype, based on Vivaldi elements, developed for the Westerbork Synthesis Radio Telescope (WSRT) to increase its instantaneous field of view by a factor 25 and double its current bandwidth. This prototype is the first step in a project that has the ambition to equip most of the WSRT antennas with FPAs to improve the survey speed of the telescope. Examples of scientific applications are surveys of the northern sky in polarised continuum and HI emission, and efficient searches for pulsars and transients.