$2.$ Vacuum System $(12$ points$)$

You have been asked to design a vacuum chamber which can reach an ultimate pressure of $\backslash (10^\{-10\}\backslash )$ torr, after bakeout. We expect the chamber surfaces, even after cleaning and baking them, will have an outgassing rate of $\backslash (10^\{-7\}\backslash )$ torr$-$liters $\backslash (/\backslash$mathrm$\{$sec$\}\backslash ).$ The chamber will be used as a sputtering chamber, where it is necessary to pump large quantities of argon at pressures of about $\backslash (10^\{-5\}\backslash )$ torr.

$1)$ What pumping speed is needed to maintain the base pressure? $(3$ pts$)$

$2)$ What kind of pump$($s$)$ would you recommend we use and why? $(3$ pts$)$

$3)$ We must connect the pump to the chamber through a pipe $50$ cm long. What should the diameter of the pipe be$?$ Assume a pressure drop of $\backslash (5\backslash$times $10^\{-11\}\backslash )$ torr and the conductance is expressed in the molecular flow regime as $\backslash (\backslash$mathrm$\{$C$\}=12\mathrm{.}2\backslash$mathrm$\{$~d$\}^\{3\}/\backslash$mathrm$\{$L$\}\backslash )$ where d is a diameter and L is a length. $(3$ pts$)$

$4)$ Sketch the configuration of this chamber, showing the interconnections between the pump$($s$)$ and the chamber. $(3$ pts$)$