CARIOCA Dead-time & inefficiency - UPDATE

1. CARIOCA Dead-time &inefficiency - UPDATE M2 station hasbeenreanalysed from the Davide measurementsat 20 MHz BC of countingrates on the bi-gap physicalchannelcounters at 4 luminosities ~ (0.4 - 0.6 - 0.8 - 1) x 1033 PROCEDURE • Measureinefficiency of particlecounting • Extract the inefficiencyfraction due to CARIOCA dead-time δ • Evaluate (by MC) the δ valuegeneratingsuchinefficiency • From thisδ,evaluate the inefficiencywewillhaveat 40 MHz Allthis per region/readoutseparately G. Martellotti, G. Penso, D. Pinci

2. Inefficiency of particlecounting • The inefficiency of the FE channelasparticlecounterismeasured by the differencebetween the measured rate R* and the rate of hittingparticlesRpart. • Rpartisnotknownbutitscales with luminosityL • 2 measurements are made at L1 and L2 > L1 • The ratioρ = (R2*/R1*) (L1/ L2) as a function of R2*- R1* • measures with goodapproximation the inefficiency of a channelwhen the channelcounting rate is R* = R2*- R1 * DEFINITIONS: Ro = BC rate = 20MHz (in a 0.7 fraction of time - 1262 BC/orbit) Rpart = rate of particleshittingeach Pad (notknown) R*= rate of Pad counting (Pad not in dead-time) Note that the rates RD* measured per secondby Davide have to be rescaled to R*=RD*/0.7 whencompared to Ro=20 MHz

3. Inefficiency of particle counting Countingefficiency R* = R2* -R1* (GHz) The countinginefficiecyis due to 2 effects: # Non nullprobability of >1 particlehitting the samepad in the same BC (granularityeffect)  rate of padhit R < Rpartthisisnot a detector inefficiency # When the padis hit (rate R) ithas a probabilityto be in the CARIOCA dead-time δ  R*=R(1-δR*)  thisis a detector inefficiency Ifwewant to evaluatethe detector inefficiency (due to CARIOCA dead-time) from the counting rate, wehave to ‘’subtract’’ the granularityeffectcalculating R starting from Rpart

4. GRANULARITY EFFECT can be calculated in terms of m and w k = number of interactions in the BC m = average number of interactions per BC Poissonian of k Pk = exp(-m) mk/ k! n = number of particles on the Pad w= average pad occupancy for 1 interaction when occurring k interactions in the BC <n>= k w Poissonian of n Pn = exp(-kw) (kw)n/n! Probability of pad hit in the case of k interactions = 1-exp(-kw) Overall probability of Pad-on (1 – Po)= Sk=1… exp(-m) mk/ k! (1-exp(-kw)) = 1 - exp{-m[1-exp(-w)]} A channel hit in average by mw particles/BC will have a particle rate Rpart = mw Ro and a lower rate of Pad-on R = (1–Po) Ro

5. Ro = 20 MHz, Rpart = μωRo ω = Rpart/Roμ. • Wedon’tknowω butit can be quitewellapproximated by ω ≈ R*/Roμ • With thisωwecalculateR = Ro (1-Po) and write the dead-time formula R*/R = (1 - δR*) Giventwomeasurementsatdifferentluminositywe can calculate the ratio ρ = (R2*/R1*) (R1/ R2) = (1 - δR2*)/(1 - δR1*) where R1 and R2 are calculated with the sameω and the twodifferentμ1, μ2 Neglectingquadratictermsρ≈ 1 – δ(R2* - R1*) • Plottingρ versus (R2* - R1*) we can directlymeasureδ • Eventually, usingthisδvalue, we can recalculateω and make an iterationto improve the δvalue

6. inefficiency due to CARIOCA dead-time R1* measuredat L1 = 0.6 x 1033 R2* measuredat L2 = 0.4 x 1033 • Ifwe express the rate in GeV, the slopeisexpressed in nano seconds • effective dead-time δeffdue to the CARIOCA dead-time folded with the time BC sequence and the detector time response (bigap time response and dead-time variance) L1-L2 efficiency R* = R2* -R1* (GHz) R* = R (1- δeffR*) The inefficiencyat R* isδeffR*

7. # Channelsnothaving a meaningfullmeasurements for all the luminosities are eliminated # A fewmeasurementstoo far from the meanvalue are eliminated # The averagein bins of R2* – R1* can be performed  Linear Fit Apparently a change in luminosity of few per mill SLOPE = effective dead-time δeff = 48.5 ns efficiency GHz R* = R2* -R1* R* = R2* -R1*

8. At a first look the slopesobtained for the otherluminositycombinationsappear to be consistent (a more detailedcomparisonis in progress) Luminosity = (4-6, 4-8, 4-10, 6-8, 6-10, 8-10) x 10 32 δeff = (48.5, 50.1, 47.9, 48.6, 49.6, 46.9 )ns Averagevalueδeff ≈ 48±1.5 ns Structures are visible – to be interpretedas due to significantlydifferentδvalues for differentcases(regions – wires – cathodes). Wemayalsohaveslightchangesof luminosityduring the measurements of data samplesused Nextstepisto analyseseparatelythe different ‘’regions’’

9. L1-L2 Region R1 • Short leverarmwhenanalysingonlyoneregion • Analysethe combinationL1-L4 • Neverthelesswe can saythat • The slopeδeffissignificantlydifferent in differentregions. Itishigher for cathodesthan for wires • # Thisis due to the differentcapacitancebutalso to the hit quality (differentaveragechargedeposited) • # slightlydifferentextrapolations to zero. Possibly a change in luminosity of few per mill in between the measurements for wires and cathodes δeff 64ns δeff 65ns efficiency δeff 44ns δeff 51ns

10. L1-L2 Region R2 Evenshorterleverarmfor R2 Certainlytoo short for R3 R4 to measure a meaningfulslope  AnalyseL1-L4 δeff53ns δeff53ns δeff R1 cathodes64-65 ns R1 wires44-51ns R2 cathodes53 ns R2 wires46-50ns δeff46ns δeff50ns

11. Toy Monte Carlo Given # a value of CARIOCA dead time δcar (meanvalueand variance) # the time response of the bi-gap chamberσt # the BC rate = 20 MHz or 40 MHz • Inefficiency due to δiscalculated (expressed in terms of effective dead time δeff)

12. ASSUMED : bi-gap gaussianresponseσt = 5ns δcar = 70 ± 11 ns (gaussian) BCR = 20 MHz BC structure PreviousBCscontributing to dead time Current BC

13. For each <δcar> assumed (with itsvariance) MC  inefficiency Simple gaussianshapeshavebeenassumed for the time fluctuations. The maincontribution to the smoothingcomes from the δcar varianceassumed to increase with the δcar value. From the Rieglermeasurements I wouldsaythat the realbehaviouris in between the two last hypoteses (nearer to the last one). BCR = 20 MHz σt = 5ns σδcar= δcar /6 σt = 0 σδcar = 0 σt = 4 ns σδcar= δcar/10 δeff (ns) inefficiency DT eletctronics (ns) δcar (ns)

14. BCR = 20 MHz For each‘’inefficiency’’ δeffmeasured in a region, δcar isevaluated Ifδeff ~ 50 ns the δcar isnotverywelldetermined. σt = 5ns σδcar = δcar/6 σt = 4nsσδcar = δcar/10 R1 cathodes R2 cathodes δeff (ns) Averageallregions δcar (ns) δcar (ns)

15. For BCR = 40 MHzwith anyreasonableassumption on time fluctuations (in particular for the δcar variance) wewillhave a sufficientsmoothing inefficiencywill be ~ proportional to CARIOCA dead-time - δeff ~ δcar -12.5 ns σt = 4ns, σδcar = δcar /10 σt = 5ns, σδcar = δcar /6 δeff (ns) inefficiency δcar (ns)

16. ‘’PROVISIONAL’’ Summarytable Station M2 δeff (20 MHz)δcarioca δeff (40MHz) Average on allregions 48ns 67-73ns 54-61ns • R1 cathodes 64-65ns 90-95ns 77-83ns • R1 wires44-51ns ? 60-80ns 47-68ns • R2 cathodes 53ns 76-85ns 63-73ns • R2 wires46-50ns ? • R3 ? • R4 ? Inefficiencyat a rate R (measured in GHz) isobtained from the dead-time formula R*= R(1 -δeff R*) A reliableerror estimate isneeded Furtheranalysisisneeded of the samples with largerleverarm: L1-L4

17. Summary # Inefficiency of physicalchannels due to CARIOCA dead time ismeasured from countingrates in terms of an effectiveδeff # preliminaryresults indicate that : 1) The averageδeffis of the order of 50ns 2)δeffissignificantlydifferent for differentregions/readouts. Itishigher in R1 (and for cathodesishigherthan for wires) – Assuming an averageδcarseems to be a crude approximation (optimistic for the innerregion) 3) From the δeff, the (larger) CARIOCA dead time (δcar) isevaluatedwith a toy MC makingsimpleassumptions on itsvariance and on the bi-gap time response. 4) Whengoingat 40 MHz BCR, wewillhave a (larger) inefficiencywellapproximated by a δeff≈δcar – 12.5 ns  The inefficiency of R1 cathodesisvery high. At the high ratesforeseen for future, itseemsthatinefficiencywill be too high to work with the END of wires and cathodes # With the muon FE counters, carefullmeasurementswouldallow to monitor relative luminosities with very high precision