Airborne Particulate Radioactivity Monitoring - The Inverse Problem: Estimating A Concentration From The Observed Response - Quantitative Methods For CPAM Applications

Quantitative Methods For CPAM Applications

As discussed in the referenced paper, there are at least 11 possible quantitative methods for estimating the concentration or quantities derived from it. The "concentration" may only be at a specific time, or it might be an average over some time interval; this averaging is perfectly acceptable in some applications. In a few cases, the time-dependent concentration itself can be estimated. These various methods involve the countrate, the time derivative of the countrate, the time integral of the countrate, and various combinations of these.

The countrate is, as mentioned above, developed from the raw detector pulses by either an analog or digital ratemeter. The integrated counts are easily obtained simply by accumulating the pulses in a "scaler" or, in more modern implementations, in software. Estimating the rate of change (time derivative) of the countrate is difficult to do with any reasonable precision, but modern digital signal processing methods can be used to good effect.

It turns out that it is very useful to find the time integral of the concentration, as opposed to estimating the time-dependent concentration itself. It is essential to consider this choice for any CPAM application; in many cases the integrated concentration is not only more useful in a radiological protection sense, but is also more readily accomplished, since estimating a concentration in (more or less) real-time is difficult.

For example, the total activity released from a plant stack over a time interval is

Then, for a fixed-filter monitor, assuming a constant stack and monitor flowrate, it can be shown that


R_{stack} \left( \eta \right)\,\,\, = \,\,\,{{F_{stack} \left} \over {\varepsilon \,k\,F_m \,\phi }}

so that the release is a function of both the countrate and integrated counts. This approach was implemented at the SM-1 Nuclear Power Plant in the late 1960s, for estimating the releases of episodic containment purges, with a predominant, and strongly time-varying, nuclide of 88Rb. For a LL nuclide, the integral term vanishes, and the release depends only on the attained countrate. A similar equation applies for the occupational exposure situation, replacing the stack flowrate with a worker's breathing rate.

An interesting subtlety to these calculations is that the time in the CPAM response equations is measured from the start of a concentration transient, so that some method of detecting the resulting change in a noisy countrate must be developed. Again, this is a good application for statistical signal processing that is made possible by the use of computing power in modern CPAMs.

Which of these 11 methods to use for the applications discussed previously is not especially obvious, although there are some candidate methods that logically would be used in some applications and not in others. For example, the response time of a given CPAM quantitative method may be far too slow for some applications, and perfectly reasonable for others. The methods have varying sensitivities (detection capabilities; how small a concentration or quantity of radioactivity can reliably be detected) as well, and this must enter into the decision.

Read more about this topic:  Airborne Particulate Radioactivity Monitoring, The Inverse Problem: Estimating A Concentration From The Observed Response

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