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BLM Trip Limits Revisited May 28, 2004 Peter Kasper

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) = S i [ A(0) . X i . e - K i T + F i .  T L(t) . e - K i ( T-t) . dt ]

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BLM Trip Limits Revisited May 28, 2004 Peter Kasper

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  1. BLM Trip Limits RevisitedMay 28, 2004Peter Kasper

  2. 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.

  3. 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

  4. 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.

  5. 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

  6. Fit Residuals

  7. Fit Quality vs Location

  8. 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 )

  9. 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 )

  10. 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

  11. 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

  12. 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 !!

  13. 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

  14. 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

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