 Solution

Use a calibrated, nonintercepting DC beam current transformer to measure the circulating current repeatedly during a fill, with top-up injection absent or separately recorded. At fixed revolution frequency, $I=eN{f}_{\mathrm{rev}}$, so a fit to $\log I$ versus time gives slope $-1/\tau$ for exponential decay. The transformer's zero offset and long-term drift must be controlled, especially at low current. An AC current transformer or a calibrated bunch pickup can additionally resolve bunch charge, whereas a DC transformer provides the total circulating intensity needed here.