# Presentation: 787411

## BLM Trip Limits RevisitedMay 28, 2004Peter Kasper

## Relating Measured Losses to Measured Activation

- Measured activations A(t) and losses L(t) are related as follows..
- 	A(T) = i [ A(0) . Xi . e-KiT + Fi . T L(t) . e-Ki(T-t) . dt ]
- 	where the sum is over produced isotopes i ..
- 		Xi is the initial fraction of isotope i
- 		Ki is the decay constant for isotope i
- 	and	Fi is a geometry dependent conversion factor for isotope i
- The maximum activation  Amax from running at a constant loss rate Lmax for an infinite time is given by ..
- 	 Amax = i ( Lmax . Fi / Ki )
- If we can determine Xi, Fi, and Ki, we can use Lmax to limit Amax.

## Determining Ki

- Cool down data from 13-Jan-03 to 27-Jan-03 plus measurements during the long shutdown (10-Sep-03 and 03-Nov-03)
- Data from each location normalized to have the same average
- Fit to both a single and a double exponential

## Lifetime Measurements

- Fit a double exponential to averaged, normalized data assuming long-lived isotope is 54Mn ( half life = 303 days)
- Fitted lifetime of 2nd exponential is 5.6 days. This is very close to that of 18Fe  (5.7 days)
- Choice of long-lived isotope is not important; good fits can also be obtained with 57Co (282 days) or 22Na (2.6 years)
- Short-lived isotopes affect measurements taken within an hour or so of beam
- Assume a short-lived component due to (I forget) with half life 1.8 hours
- Thus model for a given location has three isotopes and 6 free parameters Xi and Fi.

## Determining Maximum Activations

- Assume only two isotopes K1 = 1.24E-1 and K2 = 2.46E-3.
- 	also X1 = 1 – X2
- Assume that the asymptotic isotope mixture is 50:50 for all locations
- 	i.e. F1 / K1 = F2 / K2 => F2 = F1 . ( K2 / K1 )
- Use two activation measurements to constrain F1 ...
- 	F1 = [ AT – AO.(1 - X2).e-K1T - AO.X2.e-K1T ] / [ S1T + S2T.K2/K1 ]
- 	SiT = T L(t) . e-Ki(T-t) . dt
-  SiT is determined by using D44 to obtain BLM readings (B:BLxxx0) at ~1 minute intervals and then calculating weighted sums
- Either set X2 = 0.5 (asymptotic assumption) or fit to the recent series of weekly activation measurements
- Calculate Amax for each location using current trip points

## Fit Residuals

## Fit Quality vs Location

## Fit Summary - I

- Predicted maximum activation is inversely correlated with X2. (X0)
- 1st column: X2 fixed at 0.5 or value where Amax is less than the maximum measured activation.
- 2nd column: X2 is fitted.
- <error> is r.m.s. of fractional fit residuals not constrained to be zero
- Red numbers correspond to Amax > 200 mr/hr and good fit ( <error> < 0.2 )

## Fit Summary - II

- Predicted maximum activation is inversely correlated with X2. (X0)
- 1st column: X2 fixed at 0.5 or value where Amax is less than the maximum measured activation.
- 2nd column: X2 is fitted.
- <error> is r.m.s. of fractional fit residuals not constrained to be zero
- Red numbers correspond to Amax > 200 mr/hr and good fit ( <error> < 0.2 )

## Suggested Changes I

- RF sections – limit to 200 mr/hr assuming fitted value of X2
- 	B:BLL140	150 →  50	< 15 last week
- 	B:BLL160	No action 	Low Amax
- 	B:BLL170	  75 →  25	< 10 last week
- 	B:BLL190	No action 	Low Amax
- 	B:BLL210	  80 →  65	< 25 last week
- 	B:BLL220	225 → 170	< 65 last week
- 	B:BLL230	115 →  90	< 15 last week
- 		Fit quality dominated by one dubious measurement
- 	B:BLL240	225 →  70	< 50 last week
- RF sections – limit to 200 mr/hr assuming X2 = 0.5 (fitted Amax is OK)
- 	B:BLL150	150 →  55	< 49 last week

## Suggested Changes II

- Other areas with good fits – limit to 200 mr/hr assuming fitted value of X2
- 	B:BL0110	375 → 105	< 86 last week
- 	B:BL0210	 30 → 21	< 26 & averaged 15 last week
- 	B:BLL040	150 → 140	< 30 last week
- 	B:BLL110	 75 → 55	< 12 last week
- 	B:BLL180	150 →  85	< 23 last week
- 	B:BLS010	675 → 590	< 300 last week
- 	B:BLS030	900 → 345	< 245 last week
- 	B:BLS060	900 → 570	< 700 & averaged 464 last week
- 	B:BLS110	900 → 255	< 27 last week
- 	B:BLS130	1500 → 940	< 600 last week
- 	B:BLS140	900 → 355	< 35 last week
- 	B:BLS160	900 → 365	< 20 last week
- 	B:BLS170	900 → 370	< 30 last week
- 	B:BLS180	900 → 865	< 35 last week

## Suggested Changes III

- Other areas – limit to 200 mr/hr assuming fitted value of X2
- 	B:BLS050	900 → 130	< 75 last week
- 		Fit quality dominated by one dubious measurement
- 	B:BLS200	900 → 205	< 15 last week
- 		Fit better than indicated due to low activation levels
- 	B:BL1210	1500 → 50	< 100 & averaged 36 last week
- 		Fit borderline OK
- Other areas – limit to 200 mr/hr assuming X2 = 0.5 (fitted Amax is OK)
- 	 B:BLS100	450 → 170	< 100 last week
- 	 B:BLS150	900 → 570	< 75 last week
- Extraction regions - limit to 300 mr/hr assuming X2 = 0.5
- 	B:BL0260	 525 → 195	< 300 & averaged 190 last week
- 	B:BLL130	1500 → 605	< 500 last week
- 	B:BL1250	 205 →  95	< 70 last week
- 	B:BL1260	 845 → 135	averaged 36 last week
- L10 - limit to 300 mr/hr assuming X2 = 0.5
- 	B:BLL100	350 → 200	 < 300 & averaged 211 last week !!

## The Rest I

- 	B:BLL010	No action	Poor fit
- 	B:BLL020	No action	Poor fit & Low Amax
- 	B:BLL030	No action	Poor fit & Low Amax for X2=0.5
- 	B:BLL050	No action 	Poor fit & Low Amax
- 	B:BLL060	No action	Poor fit
- 	B:BLL070	No action 	Low Amax
- 	B:BLL080	No action	Poor fit & Low Amax
- 	B:BLL090	No action 	Low Amax
- 	B:BLL120	No action	Poor fit & Low Amax
- 	B:BLL200	No action 	Low Amax
- 	B:BL0250	No action 	Amax < 300 mr/hr
- 	B:BL0510	No action	Poor fit & Low Amax
- 	B:BL0520	No action	Poor fit
- 	B:BL0610	No action	Poor fit
- 	B:BL0710	No action	Poor fit

## The Rest II

- 	B:BLS020	No action	Marginal fit & Low Amax
- 	B:BLS040	No action 	Low Amax
- 	B:BLS070	No action 	Poor fit
- 	B:BLS080	No action	Low Amax
- 	B:BLS090	No action	Poor fit & Low Amax
- 	B:BLS120	No action	Amax OK
- 	B:BLS190	No action 	Poor fit & Low Amax
- 	B:BLS210	No action 	Low Amax
- 	B:BLS220	No action 	Low Amax
- 	B:BLS230	No action 	Poor fit & Low Amax
- 	B:BLS240	No action 	Low Amax