Pile-up, dead time and counting statistics

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1 BIPM, 17 St 2007 Uncrtainty Worksho 1 Pil-u, dad tim and counting statistics Stfaan Pommé

2 BIPM, 17 St 2007 Uncrtainty Worksho 2 Nuclar counting in uls mod nuclar sourc masuring dvic lctronic ulss / discriminator

3 BIPM, 17 St 2007 Uncrtainty Worksho 3 Schmatic rrsntation of dtctor uls uls dtct thrshold uls width τ P

4 Count loss du to il-u BIPM, 17 St 2007 Uncrtainty Worksho 4 dtctd uls unrsolvd uls thrshold uls width τ P xtnsion

5 On xaml BIPM, 17 St 2007 Uncrtainty Worksho 5 count rat ρ = 10,000 vnts r scond [s -1 ] uls width τ = 10 microsconds [s] normalisd rat ρτ = 0.1 [] 25 masurmnts with 1 million counts ach

6 Random art of uncrtainty BIPM, 17 St 2007 Uncrtainty Worksho 6 25 masurmnts with 1 million counts ach Poisson statisitics on masurmnt: u/n = 1/ N = 0.1% 25 masurmnts: u/n = 1/ 25N = 0.02% (random) statistical uncrtainty is insignificant focus on systmatic sourcs of rror

7 Thr cass BIPM, 17 St 2007 Uncrtainty Worksho 7 - no corrction for count loss du to dad tim - corrction by invrsion of throughut curv - liv-tim counting

8 Count loss through il-u BIPM, 17 St 2007 Uncrtainty Worksho 8 1 ρ = s -1 τ = 10 μs Rτ R ρτ = ρ loss through il-u ρτ no corrction => rror = = 9.5% ε ρt) ρt ( ρτ = 1

9 Count loss corrction by invrsion of throughut curv BIPM, 17 St 2007 Uncrtainty Worksho 9 ρ = R x(ρτ ) R = ρ ρτ τ = 10 μs ± 1 μs τ = not wll known not constant (uls-hight dndnt) => rror = = 1% Rτ ρτ ( t) ρσ( τ ) σ ρ ρt 1

10 Imosition of artificial dad tim BIPM, 17 St 2007 Uncrtainty Worksho 10 non-xtnding dad tim R = 1+ ρ ρτ n xtnding dad tim R = ρ ρτ

11 BIPM, 17 St 2007 Uncrtainty Worksho 11 Ral-Tim Mod : invrsion of throughut curv 0.6 non-xtnding dad tim Rτ 0.4 ρ = 1 R Rτ n ρτ + random comonnt + unc. roagation σ(τ n ) + cascad ffct

12 BIPM, 17 St 2007 Uncrtainty Worksho 12 Cascad il-u + non-xtnding dad tim Pil-u rolongs dad tim R = ρτ ρ + ρ(τ n τ ) instad of additional count loss through il-u R = 1+ ρ ρτ n non-xtnding dad tim

13 BIPM, 17 St 2007 Uncrtainty Worksho 13 Ral-Tim Mod : rror by nglcting cascad ffct 0.6 non-xtnding dad tim 0.4 ρ = R 1- Rτ n ρτ ρτ Rτ by itration (undr)- stimat of ρ rality ρτ

14 Count loss corrction by invrsion of throughut curv BIPM, 17 St 2007 Uncrtainty Worksho 14 non-xtnding dad tim τ = 10 μs ± 1 μs τ n = 15 μs ± 0.15 μs + random comonnt = 0.107% σ(ρt) = 1 Rt + roagation unc. τ n = 0.15% σ(ρt) ρt = ρτ n σ( τ τ n n ) + cascad ffct = 0.51% ( ρτ 1 ρτ ε ρt) ρt 1

15 BIPM, 17 St 2007 Uncrtainty Worksho 15 Cascad il-u + xtnding dad tim Pil-u liminats closly sacd vnts and rducs dad tim R = -ρτ ρ (1 P loss ) P loss = robability count loss by xtnding dad tim instad of count gain through il-u R = ρ ρτ xtnding dad tim

16 BIPM, 17 St 2007 Uncrtainty Worksho 16 Ral-Tim Mod : invrsion of throughut curv 0.6 xtnding dad tim 0.4 ρ = R ρτ by itration Rτ ρτ + random comonnt + unc. roagation σ(τ ) + cascad ffct

17 BIPM, 17 St 2007 Uncrtainty Worksho 17 Ral-Tim Mod : rror by nglcting cascad ffct 0.6 xtnding dad tim 0.4 ρ ρτ R = 1 P loss by itration Rτ 0.2 rality (ovr)- stimat of ρ P loss = J j= 1 [ ρ( τ jτ j! ) ρτ ] j ρτ

18 Count loss corrction by invrsion of throughut curv BIPM, 17 St 2007 Uncrtainty Worksho 18 xtnding dad tim τ = 10 μs ± 1 μs τ = 15 μs ± 0.15 μs + random comonnt = 0.11% σ(ρt) = 1 Rt 1 2ρτ (1 ρτ ρτ ) 2 + roagation unc. τ = 0.17% σ(ρt) ρt = ρτ 1 ρτ σ( τ) τ + cascad ffct = 0.44% ε ρt) ρt ρ( τ τ ) (1 P 1 ρτ loss ) ρτ (

19 BIPM, 17 St 2007 Uncrtainty Worksho 19 Liv-tim tchniqu K track of liv tim of systm at fixd frquncy R = ρ Liv Tim Ral Tim Liv Tim Dad Tim

20 BIPM, 17 St 2007 Uncrtainty Worksho 20 Cascad il-u + non-xtnding dad tim Liv-tim tchniqu undrstimats count rat ρ ρ = R Ral Tim Liv Tim ρτ ρτ by itration instad of unaccountd dad tim ρ = R Ral Tim Liv Tim non-xtnding dad tim

21 Count loss corrction by liv-tim tchniqu BIPM, 17 St 2007 Uncrtainty Worksho 21 non-xtnding dad tim τ = 10 μs ± 1 μs τ n = 15 μs + random comonnt = 0.107% σ(ρt) = 1 Rt + roagation unc. τ n 0% + cascad ffct = 0.51% ( ρτ 1 ρτ ε ρt) ρt 1

22 BIPM, 17 St 2007 Uncrtainty Worksho 22 Cascad il-u + xtnding dad tim Liv-tim tchniqu (slightly) undrstimats count rat ρ R ρ 1 P loss x Ral Tim LivTim Rτ by itration instad of unaccountd dad tim ρ = R Ral Tim Liv Tim xtnding dad tim

23 Count loss corrction by liv-tim tchniqu BIPM, 17 St 2007 Uncrtainty Worksho 23 xtnding dad tim τ = 10 μs ± 1 μs τ = 15 μs + random comonnt = 0.11% σ(ρt) = 1 Rt + roagation unc. τ 0% + cascad ffct = 0.17% ε( ρt) ρt 1+ ρτ ρτ τ τ

24 Al. Radiat. Isot. 66 (2008) 941 BIPM, 17 St 2007 Uncrtainty Worksho 24 influnc of cascad on corrctd count rat rror 'loss-corrctd' count rat du to cascad, ε(ρ) 20% 10% 0% -10% τ /τ n =τ /τ =2/3 EDT, RT NEDT, LT or RT EDT, LT incoming count rat ρτ

25 Uncrtainty aftr mathmatical corrction for cascad ffct BIPM, 17 St 2007 Uncrtainty Worksho 25 roagation of uncrtainty on uls width τ = 10 μs ± 1 μs τ = 15 μs non-xtnding dad tim 0.1% xtnding dad tim 0.01%

26 BIPM, 17 St 2007 Uncrtainty Worksho 26 Elctronic solution for liv-tim tchniqu Logical OR of dad tim and il-u non-xtnding dad tim account for xtra dad tim ρ = R Ral Tim Liv Tim xtnding dad tim

27 Homwork BIPM, 17 St 2007 Uncrtainty Worksho 27 Dos th lctronic solution liminat all systmatic rrors of nuclar counting? What is th influnc of th finit rsolution of th intrnal liv-tim clock on th dad-tim corrction?

28 BIPM, 17 St 2007 Uncrtainty Worksho 28 Conclusion: How to rduc cascad ffct? * Aly liv-tim tchniqu, using a logical OR btwn gnratd dad tim and uls width or * Aly mathmatical corrction factors on obsrvd count rats or * K count rat blow 0.04/τ (.g. ρ<4000 s -1 for τ =10 μs)

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