Expected rates with mini-arrays for air showers

As a guide in the design of mini-arrays used to exploit the Linsley effect in the study of air showers, it is useful to calculate the expected rates. The results can aid in the choice of detectors and their placement or in predicting the utility of existing detector systems. Furthermore, the potential of the method can be appraised for the study of large showers. Specifically, we treat the case of a mini-array of dimensions small enough compared to the distance of axes of showers of interest so that it can be considered a point detector. The input information is taken from the many previous studies of air showers by other groups. The calculations will give: (1) the expected integral rate, F(sigma, rho), for disk thickness, sigma, or rise time, t sub 1/2, with local particle density, rho, as a parameter; (2) the effective detection area A(N) with sigma (min) and rho (min) and rho (min) as parameters; (3) the expected rate of collection of data F sub L (N) versus shower size, N.