Shot Noise in the Ion Beam

As noted above, in practical applications shot noise ( statistical noise ) in the ion beam arriving at the ion 

The statistical distribution of rare events, such as the probabihty that an ion in a low intensity ion beam will strike a detector within a short sampling time inta-val, follows a distribution law first derived by the famous French math atician Simdon-Denis Poisson (1781-1840). Despite his many official duties, he found time to publish more than 300 works, sevraal of them extensive treatises most of which were intended to form part of a great work on mathematical physics, which sadly he did not live to complete. 

An important property of the Poisson distribution is the standard deviation of k  

For a measurement of continuous beam current (i.e. for rates of ion arrival that are too large for ion counting detection as a result of detector dead time, see below), it is appropriate to replace the ion counting time window with a more suitable parameter the appropriate parameter is the time constant (t ) of the detection chain (usually dominated by the RC time constant of the current-to-voltage converter, see Section 7.4). If the 4 value is instantaneously increased to a new value, the time 

In the remainder of this chapter it is mostly S/B values that are referred to, with S/N used only on the few occasions when required. Unfoitunately, the analytical htera-ture does not uniformly make this distinction and noise is frequently used when background is appropriate. 

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These expressions for the S/N, corresponding to only the shot noise in the ion beam itself (i.e. ignoring contributions from the components of the detection chain. Figure 7.1), reflect the intuitive appreciation that these statistical variations should become relatively less important as the total number of ions actually recorded increases, i.e. as either or both of the average ion current and time window of detection are increased. Of course the value of 4 is primarily determined by the size of the original analytical sample and the concentration of analyte within it, and is thus not within the control of the analyst other than via efficient extraction and clean-up procedures (Chapter 4). Increasing (S/N)j by increasing... 

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