BLM Trip Limits Revisited May 28, 2004 Peter Kasper

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BLM Trip Limits RevisitedMay 28, 2004Peter
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.

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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

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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.

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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
  5050 for all locations
• i.e. F1 / K1 F2 / K2 gt 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 (BBLxxx0) 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

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Fit Residuals
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Fit Quality vs Location
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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. lterrorgt is r.m.s. of fractional fit
residuals not constrained to be zero Red numbers
correspond to Amax gt 200 mr/hr and good fit (
lterrorgt lt 0.2 )
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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. lterrorgt is r.m.s. of fractional fit
residuals not constrained to be zero Red numbers
correspond to Amax gt 200 mr/hr and good fit (
lterrorgt lt 0.2 )
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Suggested Changes I

• RF sections limit to 200 mr/hr assuming fitted
  value of X2
• BBLL140 150 ? 50 lt 15 last week
• BBLL160 No action Low Amax
• BBLL170 75 ? 25 lt 10 last week
• BBLL190 No action Low Amax
• BBLL210 80 ? 65 lt 25 last week
• BBLL220 225 ? 170 lt 65 last week
• BBLL230 115 ? 90 lt 15 last week
• Fit quality dominated by one dubious
  measurement
• BBLL240 225 ? 70 lt 50 last week
• RF sections limit to 200 mr/hr assuming X2
  0.5 (fitted Amax is OK)
• BBLL150 150 ? 55 lt 49 last week

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Suggested Changes II

• Other areas with good fits limit to 200 mr/hr
  assuming fitted value of X2
• BBL0110 375 ? 105 lt 86 last week
• BBL0210 30 ? 21 lt 26 averaged 15 last week
• BBLL040 150 ? 140 lt 30 last week
• BBLL110 75 ? 55 lt 12 last week
• BBLL180 150 ? 85 lt 23 last week
• BBLS010 675 ? 590 lt 300 last week
• BBLS030 900 ? 345 lt 245 last week
• BBLS060 900 ? 570 lt 700 averaged 464 last
  week
• BBLS110 900 ? 255 lt 27 last week
• BBLS130 1500 ? 940 lt 600 last week
• BBLS140 900 ? 355 lt 35 last week
• BBLS160 900 ? 365 lt 20 last week
• BBLS170 900 ? 370 lt 30 last week
• BBLS180 900 ? 865 lt 35 last week

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Suggested Changes III

• Other areas limit to 200 mr/hr assuming fitted
  value of X2
• BBLS050 900 ? 130 lt 75 last week
• Fit quality dominated by one dubious
  measurement
• BBLS200 900 ? 205 lt 15 last week
• Fit better than indicated due to low activation
  levels
• BBL1210 1500 ? 50 lt 100 averaged 36 last week
• Fit borderline OK
• Other areas limit to 200 mr/hr assuming X2
  0.5 (fitted Amax is OK)
• BBLS100 450 ? 170 lt 100 last week
• BBLS150 900 ? 570 lt 75 last week
• Extraction regions - limit to 300 mr/hr assuming
  X2 0.5
• BBL0260 525 ? 195 lt 300 averaged 190 last
  week
• BBLL130 1500 ? 605 lt 500 last week
• BBL1250 205 ? 95 lt 70 last week
• BBL1260 845 ? 135 averaged 36 last week
• L10 - limit to 300 mr/hr assuming X2 0.5
• BBLL100 350 ? 200 lt 300 averaged 211 last
  week !!

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The Rest I

• BBLL010 No action Poor fit
• BBLL020 No action Poor fit Low Amax
• BBLL030 No action Poor fit Low Amax for
  X20.5
• BBLL050 No action Poor fit Low Amax
• BBLL060 No action Poor fit
• BBLL070 No action Low Amax
• BBLL080 No action Poor fit Low Amax
• BBLL090 No action Low Amax
• BBLL120 No action Poor fit Low Amax
• BBLL200 No action Low Amax
• BBL0250 No action Amax lt 300 mr/hr
• BBL0510 No action Poor fit Low Amax
• BBL0520 No action Poor fit
• BBL0610 No action Poor fit
• BBL0710 No action Poor fit

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The Rest II

• BBLS020 No action Marginal fit Low Amax
• BBLS040 No action Low Amax
• BBLS070 No action Poor fit
• BBLS080 No action Low Amax
• BBLS090 No action Poor fit Low Amax
• BBLS120 No action Amax OK
• BBLS190 No action Poor fit Low Amax
• BBLS210 No action Low Amax
• BBLS220 No action Low Amax
• BBLS230 No action Poor fit Low Amax
• BBLS240 No action Low Amax