(13)
where:
(14) 
The peaking factor kappa was determined by numerical solution of the hyperbolic differential equations (Ref. 60) describing the flow downstream of the sonic plane and is partially responsible for the "jetting action" discussed in more detail in the concluding section as well as the appendix.
The effect of the skimmer, and the supporting wall that separates the source chamber from the beam utilization chamber, can be drastic. Note that for all jets designed by our group r>>x_q, and therefore Beer law scattering is the most dominant effect. Consider the red molecule shown in Figure 3 leaving the quitting surface with sufficient T_(perpendicular),_(infinity), and hence V_(perpendicular),_(infinity), to reach the detector if no wall were present. Instead, the skimmer wall reflects the molecule, decreasing the detector signal below the ideal value I_o, and scatters the molecule into the path of a centerline molecule, further decreasing the beam intensity. In addition, background gases measured as the background pressure P_b may also scatter free jet molecules, which would have otherwise reached the detector.
The transmission coefficient lamda_s resulting from attenuation due to jet effects are calculated by setting S approximately to S_(infinity) and using:
(15) 
This coefficient was found to be 1 for all our jets since x_q<<r. The transmission coefficient lb resulting from Beer's law can be obtained from:
(16) 
where l is the path length traveled by the molecules between the quitting surface and the skimmer (x_s-x_q) and l_m is the mean free path depending on the background pressure P_b between the quitting surface and the skimmer. Figure 4 shows a typical intensity versus nozzle pressure P_o graph. While the ideal intensity is a linear function of the nozzle pressure P_o, it is attenuated severely be the background pressure P_b which also increases with increasing P_o.
The intensity I_b due to the background pressure P_b escaping through the skimmer aperture can be calculated assuming a Knudsen cell (see appendix:)
(17) 
Figure 4: Typical I versus P_o Curve
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