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Background

A given gas behind a nozzle has a relatively small velocity, called the stagnation state with a pressure and temperature, P0 and T0 respectively. The region into which the gas will expand has a pressure of P$_{\rm b}$. The difference between the nozzle and background pressure causes gas to expand from the nozzle region. The molecules may reach speeds greater than the speed of sound in the region directly in front of the nozzle. At a given distance from the nozzle (the Mach disk), the gas will reach sub-sonic speeds and shock waves result between the supersonic and subsonic flowing gas. The distance (x$_{\rm M}$) of the Mach disk from the nozzle aperture (of diameter D) can be approximated by Equation 5.1.
\begin{displaymath}
{\rm\left(\frac{x_{M}}{D}\right) = 0.67 \left(\frac{P_0}{P_b}\right)^\frac{1}{2}}
\end{displaymath} (4.1)

To minimise collisions in the beam and avoid re-heating, the skimmer has to lie inside this disk. The temperature of the gas upon expansion is given in Equation  5.2


\begin{displaymath}
{\rm\frac{T}{T_0}=\left(1+\left(\frac{\gamma-1}{2}\right)M^{2}\right)^{-1}}
\end{displaymath} (4.2)

where M is the Mach number (Equation 5.3) and $\gamma$ is the ratio of the heat capacities.


\begin{displaymath}
{\rm M= \frac{speed~of~molecules}{local~speed~of~sound}}
\end{displaymath} (4.3)

For clustering to occur and for cooling to be observed, it is desirable to maximise the stagnation (nozzle) pressure and minimise the nozzle diameter. However, decreasing the nozzle diameter reduces the gas throughput and hence beam strength. The pumping speed of the vacuum apparatus, the nozzle diameter, the position of the Mach disk from the source, the stagnation pressure and the desired temperature are all considered before such an experiment is designed.


next up previous contents
Next: Related Literature Up: Jet cooling of ion Previous: Overview   Contents
Tim Gibbon
1999-09-06