CAM Equations De-Mystified LA-UR

Transcription

1 CAM Equations De-Mystified LA-UR Alan Justus Health Physics Measurement Group (RP-2) Radiation Instrumentation and Calibration eam (RIC) Presented at HPIC 2009 Annual Meeting U N C L A S S I F I ED Slide

2 erminology = fast or slow window time (as appropriate) in seconds = net Pu counts in most recent interval from to 0 = net Pu counts in previous interval from 2 to - Eff = detector alpha efficiency (4) Flow = sample flow rate (lpm) Vol = sampled volume (l) during (i.e., equals Flow * /60) K = value (i.e., now pci/l for Pu-239) Yield = isotope alpha yield (i.e.,.0 for Pu-239) λ = decay constant (i.e., ln(2)/half-life), note: equal to zero for long-lived 239Pu Cal = calibration constant of 6.66x0-4 determined by the chosen units Variance = measured fit variance of K = the sigma factor MeV = counts within Pu region due to tailing from Rn- and n-progeny. Slide 2

3 Equations for activity and exposure Equations for activity and exposure using the counts from the most recent interval (or window): Activity( dps) ( counts) (sec) Eff Yield where efficiency, eff, = counts/ dis, and yield = dis/ isotopic dis. Exposure( h) K Activity( dps) ( pci / l) Flow ( lpm) 2.22 where K = value (i.e., now pci/l for Pu-239) Slide 3

4 Equations for Concentration he concentration equation is based on the ISO Standard approach, utilizing the difference in counts between two adjacent counting intervals divided by the (t) 2. In our terminology, this would equate to ( 0 )/ 2. Concentration ) ( 2 Flow ( lpm) K 0 ( pci / l) Eff Yield Cal If the isotope is relatively short-lived, the activity (and hence count rate) sampled during the 0 count will on average due to decay yield only 0 * exp(-λ* ) during the count interval. Concentration ) ( 2 Flow ( ) 0 ( lpm) K ( pci / l) Eff Yield Cal Slide 4

5 Determinations for Peak Variance Often, a minimum detectable activity, MDA, is (mis)used as the minimum alarm level for the socalled dose alarm and is given by: MDA( dps) K Variance Eff Yield where the variance is taken from the least-squares fitting routine. his is not reliable, since is related to method of fit (i.e., grid search, gradient search, Marquardt), weighting factors chosen, degrees of freedom (i.e., exact number of free fitting parameters)! An alternate and more reliable determination of the variance is a hybrid approach utilizing both the fitted peaks and classic Poisson statistics. Contributing counts to the Pu region (i.e., 5.2 MeV) from the tails of the fitted Rn- and n-progeny peaks are determined. hese counts are and 7.69 from the Rn-progeny and 6.05 and 8.78 from the n-progeny. he variance in, the fitted Pu counts, is then given by: 2 2 ( ) Slide 5

6 Equations for Dose Alarm Level he alarm (or critical or decision) level, L C, in units of dps, used as the minimum alarm level for the so-called dose alarm is then given by: L C ( dps) K Eff Yield where the variance is taken from the hybrid approach above and the equivalency between the sigma factor, K, times σ netpu and k times σ 0 is utilized. he alternate decision level, L C, in units of -h, is, ignoring any uncertainty in flow rate, given by: L C ( h) K L C ( dps) ( pci / l) Flow ( lpm) 2.22 Slide 6

7 Equations for Concentration Alarm Level Although the equation for a most sensitive concentration alarm could be offered here, the reality is that concentration alarms are utilized not for routine monitoring but rather for hot job monitoring. he user-entered high-level alarm suffices here, just as a 5 mr/h alarm level would suffice in an alarming area monitor used for external dose protection. One never sets the alarm to 4.8 mr/h in order to achieve a 95% detection probability of 5.0 mr/h! Slide 7