BLM Trip Limits Revisited May 28, 2004 Peter Kasper

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

3 Determining K i 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

4 Lifetime Measurements Fit a double exponential to averaged, normalized data assuming long-lived isotope is 54 Mn ( half life = 303 days) Fitted lifetime of 2 nd exponential is 5.6 days. This is very close to that of 18 Fe (5.7 days) Choice of long-lived isotope is not important; good fits can also be obtained with 57 Co (282 days) or 22 Na (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 X i and F i.

5 Determining Maximum Activations Assume only two isotopes K 1 = 1.24E-1 and K 2 = 2.46E-3. also X 1 = 1 – X 2 Assume that the asymptotic isotope mixture is 50:50 for all locations i.e. F 1 / K 1 = F 2 / K 2 => F 2 = F 1. ( K 2 / K 1 ) Use two activation measurements to constrain F 1 … F 1 = [ A T – A O.(1 - X 2 ). e -K 1 T - A O. X 2. e -K 1 T ] / [ S 1 T + S 2 T. K 2 /K 1 ] S i T =  T L(t). e -K i( T-t). dt S i T is determined by using D44 to obtain BLM readings (B:BLxxx0) at ~1 minute intervals and then calculating weighted sums Either set X 2 = 0.5 (asymptotic assumption) or fit to the recent series of weekly activation measurements Calculate A max for each location using current trip points

6 Fit Residuals

7 Fit Quality vs Location

8 Fit Summary - I Predicted maximum activation is inversely correlated with X 2. (X 0 ) 1 st column: X 2 fixed at 0.5 or value where A max is less than the maximum measured activation. 2 nd column: X 2 is fitted. is r.m.s. of fractional fit residuals not constrained to be zero Red numbers correspond to A max > 200 mr/hr and good fit ( < 0.2 )

9 Fit Summary - II Predicted maximum activation is inversely correlated with X 2. (X 0 ) 1 st column: X 2 fixed at 0.5 or value where A max is less than the maximum measured activation. 2 nd column: X 2 is fitted. is r.m.s. of fractional fit residuals not constrained to be zero Red numbers correspond to A max > 200 mr/hr and good fit ( < 0.2 )

10 Suggested Changes I RF sections – limit to 200 mr/hr assuming fitted value of X 2 B:BLL → 50< 15 last week B:BLL160No action Low A max B:BLL → 25< 10 last week B:BLL190No action Low A max B:BLL → 65< 25 last week B:BLL → 170< 65 last week B:BLL → 90< 15 last week Fit quality dominated by one dubious measurement B:BLL → 70< 50 last week RF sections – limit to 200 mr/hr assuming X 2 = 0.5 (fitted A max is OK) B:BLL → 55< 49 last week

11 Suggested Changes II Other areas with good fits – limit to 200 mr/hr assuming fitted value of X 2 B:BL → 105< 86 last week B:BL → 21< 26 & averaged 15 last week B:BLL → 140< 30 last week B:BLL → 55< 12 last week B:BLL → 85< 23 last week B:BLS → 590< 300 last week B:BLS → 345< 245 last week B:BLS → 570< 700 & averaged 464 last week B:BLS → 255< 27 last week B:BLS → 940< 600 last week B:BLS → 355< 35 last week B:BLS → 365< 20 last week B:BLS → 370< 30 last week B:BLS → 865< 35 last week

12 Suggested Changes III Other areas – limit to 200 mr/hr assuming fitted value of X 2 B:BLS → 130< 75 last week Fit quality dominated by one dubious measurement B:BLS → 205< 15 last week Fit better than indicated due to low activation levels B:BL → 50< 100 & averaged 36 last week Fit borderline OK Other areas – limit to 200 mr/hr assuming X 2 = 0.5 (fitted A max is OK) B:BLS → 170< 100 last week B:BLS → 570< 75 last week Extraction regions - limit to 300 mr/hr assuming X 2 = 0.5 B:BL → 195< 300 & averaged 190 last week B:BLL → 605< 500 last week B:BL → 95< 70 last week B:BL → 135averaged 36 last week L10 - limit to 300 mr/hr assuming X 2 = 0.5 B:BLL → 200 < 300 & averaged 211 last week !!

13 The Rest I B:BLL010No actionPoor fit B:BLL020No actionPoor fit & Low A max B:BLL030No actionPoor fit & Low A max for X 2 =0.5 B:BLL050No action Poor fit & Low A max B:BLL060No actionPoor fit B:BLL070No action Low A max B:BLL080No actionPoor fit & Low A max B:BLL090No action Low A max B:BLL120No actionPoor fit & Low A max B:BLL200No action Low A max B:BL0250No action A max < 300 mr/hr B:BL0510No actionPoor fit & Low A max B:BL0520No actionPoor fit B:BL0610No actionPoor fit B:BL0710No actionPoor fit

14 The Rest II B:BLS020No actionMarginal fit & Low A max B:BLS040No action Low A max B:BLS070No action Poor fit B:BLS080No actionLow A max B:BLS090No actionPoor fit & Low A max B:BLS120No actionA max OK B:BLS190No action Poor fit & Low A max B:BLS210No action Low A max B:BLS220No action Low A max B:BLS230No action Poor fit & Low A max B:BLS240No action Low A max