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ID: past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012/s19/3/b/i/solution

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Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2012 / S19 / 3 / b / i / Solution by

Codex  0 2026-10-25

The instantaneous beam lifetime is

τ = - \frac{N}{d N / d t},

(1)

where losses make

d N / d t < 0

. If the fractional loss rate is constant,

N (t) = N_{0} e^{- t / τ}

and

τ

is the time to fall to

1/ e

of the starting population. At fixed revolution frequency, the circulating current has the same exponential decay. Density-dependent loss mechanisms can make the instantaneous lifetime vary, so a single exponential need not fit every fill.

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