Vacuum Lifetime

Some vacuum lifetime formulae are give in A. Streun's SLS-TIME-TA-2001-0191

For elastic scattering, the formula is

(1)\begin{align} \frac{1}{\tau} = \frac{2\pi r_e^2 c N_A}{R\gamma^2} \frac{<\beta_y>}{A_y[m-rad]}\frac{r_p Z^2 N}{T}P[Pa] \end{align}

A typical ESRF pressure is 1e-9 mBar (is this right? conversion to Pa?)

For the vertical acceptance, consider the minimum acceptance (say from a scraper, or an ID vacuum chamber), we have

\begin{align} A_y = \frac{\Delta y}{\beta_y} \end{align}

For the case of Bremsstrahlung, Streun quotes ZAP as

(3)\begin{align} \frac{1}{\tau} = \frac{4r_e^2 c N_A}{137 R} L(\delta_{acc})ln\frac{183}{Z^{1/3}}\frac{r_p Z^2 N}{T} P[Pa] \end{align}

and the function L is given by

(4)\begin{align} L = \frac{4}{3}(ln\frac{1}{\delta_{acc}}-\frac{5}{8}) \end{align}