My polarimeter

Time resolution requirement#

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Harmonic number \(h = 6\), SRC extraction radius \(R_{ext} = 5.36\ \mathrm{m}\), beam kinetic energy \(T_u = 190\ \mathrm{MeV}/u\).

The time interval between bunches \(\Delta t\) is actually the period of the RF field \(T_{RF}\), i.e.:

\[ \Delta t = T_{RF} = \frac{1}{f_{RF}} = \frac{1}{h \times f_{rev}} \]

First, from \(T_u = 190\ \mathrm{MeV}/u\) compute the relativistic factors (taking \(m_u c^2 = 931.494\ \mathrm{MeV}\)):

\[ \gamma = 1 + \frac{T_u}{m_u c^2} = 1 + \frac{190}{931.494} = 1.20397 \]

\[ \beta = \sqrt{1 - \gamma^{-2}} = 0.55689 \]

\[ v = \beta c = 1.6695 \times 10^{8}\ \mathrm{m/s} \]

Then from the extraction radius \(R_{ext} = 5.36\ \mathrm{m}\) obtain the orbit circumference and revolution frequency:

\[ C = 2\pi R_{ext} = 33.678\ \mathrm{m} \]

\[ f_{rev} = \frac{v}{C} = 4.9573\ \mathrm{MHz} \]

Hence the bucket frequency and bunch spacing:

\[ f_{bucket} = h \times f_{rev} = 6 \times 4.9573\ \mathrm{MHz} = 29.7441\ \mathrm{MHz} \]

\[ \Delta t = \frac{1}{f_{bucket}} \approx 33.62\ \mathrm{ns} \]

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Last update: 2026-05-09
Created: 2025-08-31