The Hydrogen Epoch of Reionization Array (HERA) is a radio interferometer aiming to detect the power spectrum of 21 cm fluctuations from neutral hydrogen from the Epoch of Reionization (EOR). Drawing on lessons from the Murchison Widefield Array (MWA) and the Precision Array for Probing the Epoch of Reionization (PAPER), HERA is a hexagonal array of large (14 m diameter) dishes with suspended dipole feeds. Not only does the dish determine overall sensitivity, it affects the observed frequency structure of foregrounds in the interferometer. This is the first of a series of four papers characterizing the frequency and angular response of the dish with simulations and measurements. We focus in this paper on the angular response (i.e., power pattern), which sets the relative weighting between sky regions of high and low delay, and thus, apparent source frequency structure. We measure the angular response at 137 MHz using the ORBCOMM beam mapping system of Neben et al. (2015). We measure a collecting area of 93 m 2 in the optimal dish/feed configuration, implying HERA-320 should detect the EOR power spectrum at z ∼ 9 with a signal-to-noise ratio of 12.7 using a foreground avoidance approach with a single season of observations, and 74.3 using a foreground subtraction approach. Lastly we study the impact of these beam measurements on the distribution of foregrounds in Fourier space.

A second-order method is presented which uses the results of static mechanics analysis for the systematic derivation of ordinary differential equations describing the lateral dynamic behavior of massless, moving webs. The theory relates the lateral dynamics of a web at a downstream roller to the longitudinal web velocity, the angle between the web and the roller, the induced web curvature, and the roller dynamics. Transfer functions are derived for several fundamental elements which are found in practical web guide control systems. A comparison of these results with those of a first-order analysis presented in a companion paper, is presented to illustrate the inadequacy of the latter for certain frequency ranges and operating conditions. Experimental verification of two transfer functions is presented.

We use time-domain electromagnetic simulations to determine the spectral characteristics of the Hydrogen Epoch of Reionization Arrays (HERA) antenna. These simulations are part of a multi-faceted campaign to determine the effectiveness of the dish's design for obtaining a detection of redshifted 21 cm emission from the epoch of reionization. Our simulations show the existence of reflections between HERA's suspended feed and its parabolic dish reflector that fall below −40 dB at 150 ns and, for reasonable impedance matches, have a negligible impact on HERA's ability to constrain EoR parameters. It follows that despite the reflections they introduce, dishes are effective for increasing the sensitivity of EoR experiments at arelatively low cost. We find that electromagnetic resonances in the HERA feed's cylindrical skirt, which is intended to reduce cross coupling and beam ellipticity, introduces significant power at large delays (−40 dB at 200 ns), which can lead to some loss of measurable Fourier modes and a modest reduction in sensitivity. Even in the presence of this structure, we find that the spectral response of the antenna is sufficiently smooth for delay filtering to contain foreground emission at line-of-sight wave numbers below k P 0.2 h Mpc −1 , in the region where the current PAPER experiment operates. Incorporating these results into a Fisher Matrix analysis, we find that the spectral structure observed in our simulations has only a small effect on the tight constraints HERA can achieve on parameters associated with the astrophysics of reionization.

A simplified dynamic analysis of a moving web which neglects materials properties is presented, and the transfer functions of several fundamental elements of lateral web behavior are derived. The transfer functions facilitate analysis of a wide variety of web guide control systems, and examples of two practical systems are given. The idealized analysis is useful for a qualitative understanding, and in most situations is sufficiently accurate for current needs of engineering analysis.

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