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BLM Trip Limits Revisited May 28, 2004 Peter Kasper

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

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**Relating Measured Losses to Measured Activation**• Measured activations A(t)and losses L(t)are related as follows.. • A(T) = Si[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 = Si(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 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