BLM Trip Limits RevisitedMay 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) . 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 iKi is the decay constant for isotope iand 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.

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

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

21-Apr-04 29-Apr-04 06-May-04 13-May-04 20-May-04 27-May-04

Measurement Date

( Mea

sure

d - P

redi

cted

) / M

easu

red

7

Fit Quality vs Location

0

0.1

0.2

0.3

0.4

0.5

011

021

025

026

051

052

061

071

121

125

126

L01

L02

L03

L04

L05

L06

L07

L08

L09

L10

L11

L12

L13

L14

L15

L16

L17

L18

L19

L20

L21

L22

L23

L24

S01

S02

S03

S04

S05

S06

S07

S08

S09

S10

S11

S12

S13

S14

S15

S16

S17

S18

S19

S20

S21

S22

S23

S24

RM

S o

f Fra

ctio

nal E

rrors

Fitted Initial Fraction Asymptotic Assumption

8

Fit Summary - I

BLML01 0.50 0.95 0.34 0.32 284 258L02 0.50 0.05 0.39 0.26 75 206L03 0.50 0.21 0.25 0.22 189 658L04 0.49 0.36 0.14 0.12 60 219L05 0.34 0.03 0.27 0.21 40 137L06 0.50 0.97 0.39 0.38 2279 2207L07 0.50 0.74 0.11 0.06 180 136L08 0.50 0.95 0.39 0.38 978 131L09 0.30 0.13 0.24 0.13 45 197L10 0.50 0.05 0.11 0.10 522 792L11 0.40 0.28 0.16 0.13 90 279L12 0.50 0.73 0.28 0.27 218 109L13 0.50 0.34 0.14 0.12 743 1464L14 0.50 0.56 0.08 0.06 855 639 *L15 0.50 0.90 0.14 0.11 578 193 *L16 0.50 0.50 0.18 0.18 113 112 *L17 0.50 0.24 0.17 0.07 156 634 *L18 0.50 0.10 0.11 0.06 257 357L19 0.50 0.10 0.21 0.18 63 187 *L20 0.50 0.05 0.15 0.14 10 119L21 0.50 0.54 0.12 0.12 305 252 *L22 0.50 0.50 0.16 0.16 269 267 *L23 0.50 0.22 0.27 0.25 138 254 *L24 0.42 0.38 0.05 0.04 400 646 *021 0.50 0.71 0.21 0.20 371 292025 0.40 0.04 0.18 0.14 120 302026 0.50 0.05 0.15 0.08 809 2123121 0.50 0.35 0.22 0.21 3654 6269125 0.50 0.39 0.12 0.11 644 1056126 0.50 0.16 0.19 0.11 1874 7930

Xo <error> Max. Activation 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 )

BLMS01 0.50 0.31 0.09 0.08 166 230S02 0.39 0.41 0.22 0.21 80 40S03 0.50 0.16 0.20 0.19 251 523S04 0.50 0.27 0.20 0.20 54 109S05 0.50 0.05 0.23 0.21 961 1411S06 0.50 0.89 0.22 0.16 609 317S07 0.50 0.95 0.37 0.33 464 112S08 0.50 0.93 0.10 0.09 142 59S09 0.50 0.63 0.38 0.24 770 124S10 0.50 0.68 0.11 0.09 532 117S11 0.50 0.44 0.11 0.10 502 713S12 0.41 0.26 0.25 0.19 72 202S13 0.37 0.27 0.20 0.19 200 319S14 0.49 0.22 0.25 0.10 30 506S15 0.50 0.95 0.16 0.09 317 77S16 0.42 0.30 0.16 0.06 30 492S17 0.50 0.29 0.15 0.06 78 485S18 0.50 0.48 0.15 0.15 185 208S19 0.50 0.70 0.31 0.30 146 93S20 0.31 0.03 0.28 0.27 17 887S21 0.50 0.23 0.26 0.16 22 171S22 0.50 0.63 0.12 0.11 140 22S23 0.50 0.47 0.23 0.22 72 84S24 0.50 0.63 0.22 0.18 107 23011 0.50 1.00 0.19 0.09 5278 718051 0.50 0.66 0.40 0.38 39 10052 0.50 0.95 0.42 0.36 1311 896061 0.50 0.95 0.30 0.25 5425 4460071 0.50 0.95 0.24 0.22 356 229

<error> Max. ActivationXo

10

Suggested Changes I

RF sections – limit to 200 mr/hr assuming fitted value of X2

B:BLL140 150 → 50 < 15 last weekB:BLL160 No action Low Amax B:BLL170 75 → 25 < 10 last weekB:BLL190 No action Low Amax B:BLL210 80 → 65 < 25 last weekB:BLL220 225 → 170 < 65 last weekB:BLL230 115 → 90 < 15 last week

Fit quality dominated by one dubious measurementB: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 weekB:BL0210 30 → 21 < 26 & averaged 15 last weekB:BLL040 150 → 140 < 30 last weekB:BLL110 75 → 55 < 12 last weekB:BLL180 150 → 85 < 23 last weekB:BLS010 675 → 590 < 300 last weekB:BLS030 900 → 345 < 245 last weekB:BLS060 900 → 570 < 700 & averaged 464 last weekB:BLS110 900 → 255 < 27 last weekB:BLS130 1500 → 940 < 600 last weekB:BLS140 900 → 355 < 35 last weekB:BLS160 900 → 365 < 20 last weekB:BLS170 900 → 370 < 30 last weekB:BLS180 900 → 865 < 35 last week

12

Suggested Changes III

Other areas – limit to 200 mr/hr assuming fitted value of X2B:BLS050 900 → 130 < 75 last weekFit quality dominated by one dubious measurementB:BLS200 900 → 205 < 15 last weekFit better than indicated due to low activation levelsB:BL1210 1500 → 50 < 100 & averaged 36 last weekFit 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 = 0.5B:BL0260 525 → 195 < 300 & averaged 190 last weekB:BLL130 1500 → 605 < 500 last weekB:BL1250 205 → 95 < 70 last weekB:BL1260 845 → 135 averaged 36 last week

L10 - limit to 300 mr/hr assuming X2 = 0.5B:BLL100 350 → 200 < 300 & averaged 211 last week !!

13

The Rest I

B:BLL010 No action Poor fitB:BLL020 No action Poor fit & Low Amax

B:BLL030 No action Poor fit & Low Amax for X2=0.5B:BLL050 No action Poor fit & Low AmaxB:BLL060 No action Poor fitB:BLL070 No action Low Amax B:BLL080 No action Poor fit & Low AmaxB:BLL090 No action Low Amax B:BLL120 No action Poor fit & Low AmaxB:BLL200 No action Low Amax

B:BL0250 No action Amax < 300 mr/hrB:BL0510 No action Poor fit & Low AmaxB:BL0520 No action Poor fitB:BL0610 No action Poor fitB: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 fitB:BLS080 No action Low Amax B:BLS090 No action Poor fit & Low Amax

B:BLS120 No action Amax OKB: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