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We demonstrate a compact, non-toxic, low-cost neutron-yield diagnostic for pulsed D--T fusion systems using an undoped fused-silica (SiO$2$) rod as both activation target and Cherenkov radiator. D--T neutrons (14.1 MeV) activate $^{28}$Si and $^{16}$O to produce short-lived $^{28}$Al ($T{1/2}=134,\mathrm{s}$) and $^{16}$N ($T_{1/2}=7.13,\mathrm{s}$). The resulting $β^-$ particles exceed the Cherenkov threshold and generate UV--visible light detected by a fast photomultiplier tube. A SiO$_2$ rod of dimensions $6,\mathrm{in}\times1,\mathrm{in}$ (length $\times$ diameter) is optically coupled and read out with a CAEN DT5730 digitizer operating in list mode with digital pulse processing. The post-pulse count rate is fit using fixed $^{16}$N and $^{28}$Al half-lives together with background terms to infer neutron fluence. Testing at the ZEUS D--T Dense Plasma Focus established a reference calibration and agreement with a praseodymium-calibrated silver activation detector. Measurements near a D--D Dense Plasma Focus show no activation signal, confirming D--T selectivity. The diagnostic enables pulse-to-pulse yield measurements within minutes following a pulse and is being deployed on Helion Energy's seventh fusion prototype, Polaris.