2-beam & 3-beam\
\
Central, $\alpha=0.5$ & 0.7839 & 0.0452 & 0.0476\
Central, $\alpha=1.0$ & 0.9608 & 0.0146 & 0.0116\
Central, $\alpha=1.5$ & 0.9935 & 0.0033 & 0.0019\
Inner, $\alpha=0.5$ & 0.7506 & 0.1074 & 0.0530\
Inner, $\alpha=1.0$ & 0.9542 & 0.0311 & 0.0099\
Inner, $\alpha=1.5$ & 0.9918 & 0.0065 & 0.0014\
Outer, $\alpha=0.5$ & 0.8409 & 0.0155 & 0.0155\
Outer, $\alpha=1.0$ & 0.9775 & 0.0194 & 0.0014\
Outer, $\alpha=1.5$ & 0.9954 & 0.0044 & 0.0001\
\

As seen from Table 1, the expected number of multiple-beam detections from a non-evolving population in Euclidean space ($\alpha=1.5$) is very low: $\lesssim$ 1 in 300, 150 and 230 events for central inner-ring and outer-ring feeds as their principal beams respectively (95% confidence). The Parkes beams are spaced further apart than their half-power widths which leads to such low probabilities for multiple-beam detections. These numbers are in stark contrast with 2 in 16 events seen at Parkes in two or more beams.

Parkes multi-beam constraints on $\bm{\alpha}$ {#sec:alpha_mbs}
==============================================

We will now compute the value of $\alpha$ that best satisfies the rate of multiple-beam detections among FRBs discovered at the Parkes telescope. If the probability of detecting a burst in $i$ beams is 