ATLAS NOTE - Τομέας Φυσικής · ATLAS NOTE November 25, 2015 2 3 Gas Leak Test...

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1 ATLAS NOTE November 25, 2015 2 Gas Leak Test Prototype Setup for the NSW Micromegas Multiplets: 3 Implementation and Calibration Technique 4 T. Alexopoulos a , E. Gazis a , S. Maltezos 1a 5 a National Technical University of Athens 6 Abstract 7 A prototype setup implemented for the Gas Leak Test of the NSW Micromegas Multiplets is 8 described in this work. Because this test is crucial for the stable operation of the Micromegas 9 modules, we have combined two methods: a conventional one based on the pressure decay 10 rate (PDR) and an alternative, but novel one, based on the flow rate loss (FRL). Both methods 11 have been tested by using emulated leak branches based on the idea of using home made 12 impedances and specific-low cost medical hypodermic needles. The gas leak rate of a certain 13 number of such leak branches have measured by connecting them to the flow stream pipe. 14 The obtained measurements by both methods are also given and are compared by means 15 of their consistency, and as well as, of their statistical and systematic errors. We present 16 a phenomenon of volume expansion strain, observed during the gas leak test of a small 17 size Micromegas. Its eect on the measured leak rate by the pressure decay method was 18 unsuspectingly very high and has been deeply studied. 19 20 1 Corresponding author © Copyright 2015 CERN for the benefit of the ATLAS Collaboration. Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

Transcript of ATLAS NOTE - Τομέας Φυσικής · ATLAS NOTE November 25, 2015 2 3 Gas Leak Test...

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ATLAS NOTENovember 25, 2015

2

Gas Leak Test Prototype Setup for the NSW Micromegas Multiplets:3

Implementation and Calibration Technique4

T. Alexopoulosa, E. Gazisa, S. Maltezos1a5

aNational Technical University of Athens6

Abstract7

A prototype setup implemented for the Gas Leak Test of the NSW Micromegas Multiplets is8

described in this work. Because this test is crucial for the stable operation of the Micromegas9

modules, we have combined two methods: a conventional one based on the pressure decay10

rate (PDR) and an alternative, but novel one, based on the flow rate loss (FRL). Both methods11

have been tested by using emulated leak branches based on the idea of using home made12

impedances and specific-low cost medical hypodermic needles. The gas leak rate of a certain13

number of such leak branches have measured by connecting them to the flow stream pipe.14

The obtained measurements by both methods are also given and are compared by means15

of their consistency, and as well as, of their statistical and systematic errors. We present16

a phenomenon of volume expansion strain, observed during the gas leak test of a small17

size Micromegas. Its effect on the measured leak rate by the pressure decay method was18

unsuspectingly very high and has been deeply studied.19

20

1Corresponding author© Copyright 2015 CERN for the benefit of the ATLAS Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

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1 Introduction21

The mass production of the Micromegas modules (MM)[1] for the New Small Wheel (NSW) upgrade22

phase I of the ATLAS muon spectrometer [2] has to be include quality checking and quality assurance23

individual tests. One of them is the gas leak test (GLT) which is crucial for the stable operation of the24

detectors. According to the NSW requirements a general rule for the leak rates of the modules have25

specified: the leak rate has to be 10−5 × V per minute, where V is the volume of the module. The26

obtained limits differ because of the different volumes. However, the pressure (gauge pressure) of the27

main test schedule has to be specified. In addition, when a Multiplet (four modules in back-to-back28

orientation)is created, the gas mixture can flow among the four modules. This lead to the necessity for29

testing the complete Multiplet and not the Modules alone. This fact makes the GLT more complicate30

because the transient gas flow effects have to be taken into account. In this work we present the design31

and the instrumentation for implemented two methods, the conventional “Pressure Decay Rate” (PDR)32

and a new proposed method we call “Flow Rate Loss” (FRL) [3]. The former is based on the ideal gas33

law and the latter on the mass conservation law. The most noticeable difference concerns the flow rate34

during the tests. In PDR method, the Multiplet under test is isolated from the stream line for a certain35

time and thus the flow rate is by definition zero. In FRL the flow rate is different than zero, relatively36

low and stable (undisturbed) during the test. In both methods, the gauge pressure is the fundamental37

parameter in this test because its strong effect on the leak rate. In our prototype setup we have chosen as38

basis 1 mbar but we have also results in a wide range of pressures. The gas we used was air (nitrogen39

with 21 % oxygen)and also pure argon. The argon could be appropriate for the GLT because its leak rate40

is very close to the one expected with the nominal mixture, Ar + 7%CO2.41

2 Methodology of data analysis42

2.1 Model uncertainty in PDR method43

In PDR method the main idea is to measure experimentally the pressure decay rate and analyzing this as44

a function of time to determine the leak rate QL, due an hypothetical rate loss of gas molecules dn/dt. In45

Ref.[6], its application for the Muon MDT chamber gas tightness test, is described in details.46

According to Ideal Gas Law:47

d(PV)dt

= RsTdmdt⇒ V0

P0

dPdt= −QL (1)

where Rs is the specific gas constant and m is the mass of the gas in the volume V0. However, the48

leak rate QL depends only on the absolute pressures inside the unit under test (UUT) and the ambient’s49

pressure. In general, for constant ambient absolute pressure P0 is a function of the gauge pressure p ≡ pg50

of the UUT, that is, QL = g(P, P0) = g(P0 + p, P0), where p = P − P0 ⇒ dP = dp. If P − P0 ≪ P0 the51

leak rate depends approximately on the gauge pressure, that is QL = f (p). As a result, the above Eq. 1 is52

written:53

V0

P0

dpdt= − f (p)⇒ dP

f (p)= −P0

V0dt ⇒

! p

p0

dp′

f (p′)= −P0

V0t (2)

From the above integral we have to calculate the pressure p as a function of time (pressure decay),54

1

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p(t), and then the leak rate at t = 0 as follows:55

QL,0 = f (p0) = f (p(0)) =V0

P0

"""""dpdt

"""""t=0

(3)

But the function QL = f (p) describing the flow by an unknown leak orifice or channel, by means56

of their geometrical shape and dimensions, is also unknown. Therefore, having the experimental57

data points for p(t) we have to fit the appropriate theoretical model without any hint for that.58

It is evident that a model uncertainty is unavoidable. To minimize the systematic error in the data59

analysis we have to fit the most probable to occurred theoretical models which are categorized as follows:60

61

a) Constant flow rate, independent of pressure, that is,QL = QL,0 = const. This is met only in62

“choked” flow cases (discussed in section 4) and it is the most simple theoretical model for determining63

the leak rate given by:64

QL,0 = |λa|V0

P0(4)

where λa is the constant slope of the pressure in time ∀t.65

66

b) The flow rate is a linear function of pressure, that is, QL = sb p. This is met in laminar flow67

cases, like the viscous leak channels with Reynolds number smaller than 2300. Substituting the function68

f (p) = sb p in the Eq. 2 and after integration we obtain the following exponential function:69

p(t) = p0e−P0V0

sbt (5)

and the leak rate is given by:70

QL,0 = |λb|V0

P0(6)

where λb = −sb p0P0V0

is the slope of pressure function at t = 0.71

If the leak rate is considerably low and in short time period the absolute value of the exponent in Eq.572

should be x = P0V0

sbt << 1. If it is the case we can apply the approximation e−x ≈ 1 − x for x << 1 and73

thus the Eq. 5 becomes:74

p(t) = p0

#1 − P0

V0sbt

$(7)

and the leak rate should be:75

QL,0 = sb p0P0

V0= |λb|

V0

P0(8)

The later expression is identical to that of Eq. 6 and it holds, not only for t = 0, but in a76

reasonable-short time period leading to faster and more simple data analysis.77

c) The flow rate is a function of pressure in n-th power, that is, QL = sc pn, where 0.5 ≤ n < 1.78

The value n = 0.5 is met in turbulent flow cases of viscous leak channels or orifices (quadratic79

relationship between pressure and flow rate) while a real building envelope will lie somewhere in80

between. Substituting the function f (p) = sc pn in the Eq. 2 and after integration we obtain:81

p1−n(t) = p1−no − scPo

Vot (9)

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QL,0 = sc pn0 = |λc| pn

0V0

P0(10)

where λc = −scP0V0

is the constant slope of pressure function p1−n(t),∀t.82

83

However, the actual leaking mechanism should be more or less complicate with arbitrary geometrical84

and dynamical parameters. For this reason the optimal fitting model has to investigated in each tested85

Micromegas Multiplets. The associated model uncertainty should cause a systematic error. The case (a)86

pertains higher pressures than that we use. The cases (b) and (c)can be the basis of the data analysis87

procedure aiming to minimize the systematic error. Below, we calculate the model uncertainty if we88

assume the case (a) instead of the actual (b) and vice versa. Let us assume n = 1/2. Then, the ratio of89

the determined leak rates in (c) and (b) cases is:90

QcL,0

QbL,0=λc p0

P0V0

λbP0V0

=

√pp0 − p0

∆t% dp

dt

&t=0

(11)

For a derivative in finite time we can have, ∆t%dp

dt

&t=0≈ p − p0 ! 0 and the ration of the leak rates91

becomes:92

QcL,0

QbL,0=

√pp0 − p0

p − p0=

11 +

'p/p0

(12)

For an average derivative using a finite pressure variation tending to zero, we obtain the following93

limit or the ratio:94

re = limp→p0

√p0(√p − √p0

)

p − p0= lim

p→p0

12

*p0

p=

12

(13)

This result means that, if we analyze the data assuming a laminar flow, model of case (b) while95

the actual leak channel corresponds to a turbulent flow, model of case (c), the error factor tends to 1/2.96

Therefore, there is a risk to overestimate the leak rate by a factor of 2. A similar conclusion should97

be pointed out in the reverse hypothesis, analyzing the model of case (c) while the actual leak channel98

corresponds to model case (b) where the error factor tends to 2 having a risk to underestimate the leak99

rate by a factor of 1/2. Considering a general exponent n the limit of re is:100

δn = limp→p0

re = limp→p0

(1 − n)pn0 p−n = 1 − n (14)

The model uncertainty due to unknown leak source and mechanism is: δ(1−n) = ∓δn and for n = 1/2101

we obtain:102

limp→p0

re = ∓12

(15)

Based on the above investigation, the data analysis in PDR method is proposed to be performed103

following the steps described below:104

1. Perform a non-linear fit to the data (with error to each point) trying with the exponential model105

and then with the model of f (p) = sc√p.106

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2. Calculate the resulting chi square per d.o.f. for both trials (models). Evaluate the goodness of the107

two fits and choose the best of them. If both models are not adequate (acceptable) continue with108

the last step. Otherwise keep the better of two and calculate the leak rate.109

3. Perform a non-linear fit to the data (with error to each point) trying with a polynomial110

second-degree model and evaluate the resulting chi square per d.o.f.111

The best fit, by means of the above criteria, is the most reliable for determining the leak rate by using112

the corresponding formula given by the optimal model found at t = 0, QL = f (p(0)) = f (p0).113

2.2 Temperature compensation in PDR method114

During a gas leak test by the PDR method a temperature variation is unavoidable and thus it is necessary115

to monitor it. Its variation affects on the pressure drop causing incorrect determination of the leak rate116

without a kind of its compensation. Let us consider the Ideal Gas Law and calculate the pressure drop117

assuming a simultaneous temperature variation:118

d(PV)dt

= RsTdmdt+ mRs

dTdt

(16)

Setting, P = p + P0 ⇒ p = P − P0 and RsT = P0ρ0

rearranging the terms in the equation we obtain:119

V0dpdt= RsTρ0

dVdt+ ρ0V0Rs

dTdt⇒ V0

P0

dpdt− V0

TdTdt=

dVdt= − f (p) (17)

Additionally, in practice, the variations of T are very small compared to the initial one, T0 and120

thus in the Eq. 17 we can set approximately T0 instead of T . Using also the equality θ in oC: dθ =121

d(T − 273.15) = dT , we obtain:122

V0

P0

dpdt− V0

T0

dθdt=

dVdt= − f (p) (18)

In addition, in order to have an approximate but applicable result, we assume that dθdt = constant in123

a short time period close to t = 0. Defining also, qθ = V0T0

dθdt and assuming that it is constant during the124

pressure drop, we have:125

V0

P0

dpdt− qθ = − f (p) (19)

Integrating by separating variables:126

! p

p0

dp′

f (p′) − qθ= −P0

V0t (20)

Assuming laminar flow and thus the flow rate being linear function of pressure, that is, QL = sp, we127

obtain:128

! p

p0

dp′

sp′ − qθ= −P0

V0t ⇒

! p

p0

dp′

p′ − qθs= −s

P0

V0t ⇒ p =

qθs+

+p0 −

qθs

,e−

sp0V0

t (21)

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Finally, based on the measured pressure drop, the leak rate can be determined by the the following129

formula including the temperature compensation:130

QL,0 = f (p0) = f (p(0)) =""""""qθ −

V0

P0

-dpdt

.

t=0

"""""" (22)

If dθdt < 0 ⇒ qθ < 0 then, without temperature compensation the leak rate is overestimated. In131

contrary, if dθdt > 0⇒ qθ > 0 then, without temperature compensation the leak rate is underestimated.132

2.3 “Volume compliance” effect in PDR method133

If a testing chamber has a degree of elasticity, that is after its pressurization it appears a slight134

expansion/contraction. In this case the PDR method becomes noticeably risking for the measured leak135

rate. This can be explained based on the Ideal Gas Law:136

−P0QL =d(pV)

dt= V0

dpdt+ P0

dVdt

(23)

In the Eq. 1 we can use the quantity “volume compliance” defined as, cv = dVdt . But it should be more137

practical to normalize it in order to be dimensionless and thus measuring relative quantities. This can be138

done defining, c, (where 0c ≤ 1)in the following way:139

c =dpP0

dVV0

(24)

From Eq. 26 and 24 we obtain:140

−P0QL = V0 (1 + c)dpdt

(25)

or141

V0

P0

dpdt= − QL

(1 + c)(26)

142

143

From the last equation we can conclude that the pressure drop rate is much lower for a given leak144

rate by a factor 11+c which varies in the range [0, 1]. Let us now correlate the compliance with the Youngs145

modulus, E. According to the definition of c we have, c = P0E .146

Therefore, the is essentially the reciprocal of the Youngs modulus normalized to and measures a kind147

of “Volume Expansion Strain” (VES). During a gas leak test by the PDR method, even a slight volume148

expansion of the chamber, could cause an associated underestimation of the leak rate according to the149

above mechanism. The VES can be measured experimentally by the help of a calibration procedure by150

the FRL method.151

2.4 Systematic error in FRL method152

The FRL method and has been described in [3] together with its sensitivity and the statistical153

uncertainties. In this subsection we discuss the main source of the systematic error is the coefficient154

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b of the calibration curve of the mass flow sensors. According the associated data analysis the leak rate155

is determined by:156

QL =1b1

-(VA

0,in − VA0,out

)− b1

b2

(VB

0,in − VB0,out

).(27)

The fraction b1/b2 has to be consider very close to 1 because the manufacturer gives only one set of157

calibration points. On the other hand, the comparison test given again by the manufacturer shows a slight158

difference among several samples of sensors. Thus, we can conclude that the difference between b1 and159

b2 has an upper limit equal to the repeatability upper bound (1 % F.S. in our case). Consequently, the160

ratio b1/b2 affects the systematic error at a level of 1 % F.S. while the b1 affects at a level of the absolute161

accuracy of the sensors which is 5 %. This systematic error can be further reduced if we calibrate the162

sensors by using more accurate mass flowmeters.163

Figure 1: The prototype setup for combined use of PDR and FRL methods. The abbreviations means,MFS: mass flow sensor, DM: differential manometer, DVM: digital voltmeter, FCR: flow controlregulator anv V: valve.

3 The overall prototype setup164

According to the [3], the design of the prototype GLT setup is based mainly on two mass flow sensors,165

OMRON D6F-P0001A1, appropriately selected to have low full scale flow rate, namely 0-6 L/h. In166

this range the repeatability given as 1% F.S. becomes sufficiently low, that is, 0.06 L/h. This value167

is given as an upper limit describing the behavior of a number of tested samples. According to our168

experience the repeatability of this MFS, calculated in rms, is in the level of 0.0006 L/h. The MFSs169

6

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Figure 2: A photograph of a general view of theprototype setup. The two well-tight referencetubes are also shown at the top of the image.

Figure 3: A photograph of three medicalhypodermic needles, used for the gas leakcalibration, inserted to a pipe of polyethylene.By using the thinner needle, 32G, we canaccomplish any leak rate in the range ofinterest.

are insensible in temperature variations in wide the range, from -10 to 60 oC. Its systematic error could170

come only from slope b of its fitted calibration curve. For the differential sugnal from MFSs we use a171

Digital Multimeter, High Performance 6 1/2 digits from Keithley (Multimeter 2000). In the setup we172

use two digital differential manometers, Digitron 2021P, with two full ranges 0-20 mbar and 0-130 mbar,173

accuracy 0.03 mbar and precision 0.01 mbar. Two well tight stainless steel tube of 1.05 L in volume174

are used as a) control volume in PDR method and b) reference volume for recording the atmospheric175

pressure variations during the pressure decay. A diagram of the prototype setup is given in Fig. 2.176

The measurement procedure for both methods presuppose to reach a steady state condition of gas177

flow before starting the measurement. The required time period depends mainly on the UUT volume178

and has to be confirmed during the tests of the real Micromegas Multiplets. In PDR method, after the179

steady state and isolating the equilibrium along the isolated volumes (the UUT and the associated pipes180

and components) has to be accomplished. In FRL method which the steady state condition of gas flow is181

being accomplished the correct pressure of the test has to be adjusted.182

4 Evaluation and calibration technique183

4.1 Pressure dependence of the leak rate184

According to the theoretical calculations for the leak orifices and channels the leak rate, in principle,185

depends on the pressure difference between the tested volume and the ambient pressure (this difference186

constitutes the gauge pressure). Regardless of the detailed relationship of leak rate with gauge pressure,187

the important remark is that for low pressure values this dependence is strong. A study of this dependence188

has been done using medical needles (see how we use them in Fig. 3). The leak rate has been measured189

using a needle of type 28G (D = 184 µm) and the results are illustrated in Fig. 4. We also measured190

another type of needle, 27G, and an orifice (of D = 413 µm). In a narrow range of pressure variation191

we can assume approximately linear dependence and thus the relative variations in leak rate and pressure192

could be considered the same. Consequently, the GLT has to be defined according to the gauge pressure193

we choose. Because the gases are compressible fluids, increasing the absolute pressure will increase the194

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volume leak flow rate until the gas velocity reaches the speed of sound and the flow becomes “choked”.195

Beyond this critical point, further increase of the absolute pressure doesn’t increase the volume leak rate.196

This critical absolute pressure corresponds to a pressure ratio between the volume and the ambient equal197

to 1.886 bar. This can be translated to a gauge pressure of 1.886 − 1.0132 ≈ 0.873 bar.198

Figure 4: Experimentally obtained plot of the leak rate of a calibrated needle (28G) as a function of thegauge pressure. The leak rate of this needle is close to the acceptance limit set for the LM MP. The solidline is a polynomial fit to the data.

4.2 Calibration by individual medical needles199

We have performed two individual measurements of leak rate, with both methods, by using the two with200

smaller diameter calibrated needles, that is, the 31G-CN1 and 32G-CN1. By using PDR we obtained the201

pressure drop decay of 31G-CN, in conjunction with a well -tight reference tube having volume of 1.05202

L while the atmospheric fluctuations have been compensated by using a differential manometer. The203

resulting plot is shown in Fig. 5. By fitting a line, with errors, to the first five data points we found the204

line equation, p = −10.2t + 1.13, in the units used in the plot (s for time and mbar for pressure). The205

overall error in the slope is 10 %, as minimum, because of the model uncertainty. A similar measurement206

and analysis procedure has been used for the pressure decay of needle 32G-CN1 shown in Fig. 7. The207

corresponding line equation was p = −5.04t+1.13 with an overall error in the slope, 11 %, as minimum.208

We can see by inspection that both pressure decay curves, close to t = 0, exhibit a general trend of linear209

behavior as approximately might be happened in a viscous leak channel like a needle. The same needles210

has been also measured by the FRL method, see Fig. 6 and Fig. 8 respectively. In the plots the small211

positive difference in flow rate corresponds to the demanded leak rate loss. The results in leak rate are212

summarized in Table 1. We have to note that while the lasting time of PDR procedure was about 10 min,213

the lasting time of FRL procedure was only a few seconds.214

It is also interesting to observe the small fluctuations in the data points coming from the repeatability215

variation. The rms of these fluctuations (around 0.0006 L/h) is 100 times smaller than the upper limit216

8

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Figure 5: Pressure decay plot obtained experimentally with the calibrated neeedle 31G-CN1. A line hasbeen fitted to the first five data points from 1 mbar and below.

Figure 6: The flow rates measured in the input and output with the calibrated neeedle 31G-CN1connected in the stream line.

9

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Figure 7: Pressure decay plot obtained experimentally with the calibrated neeedle 32G-CN1. A line hasbeen fitted to the first five data points from 1 mbar and below.

Figure 8: The flow rates measured in the input and output with the calibrated neeedle 31G-CN1connected in the stream line.

given by the manufacturer (1 % F.S. or equivalently 0.06 L/h). In fact, this a is very promising result217

proved that when operating in very low flow rates we can profit a much better repeatability.218

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Needle ID — Method PDR FRL31G - CN1 0.0107 ± 10% syst. (min) 0.0114 ± 8 stat. % ± 1.5% syst.32G - CN1 0.0053 ± 11% syst. (min) 0.0058 ± 15 stat. % ± 1.5% syst.

Table 1: Leak rate results obtained by both GLT methods, PDR and FRL by using emulated leak ofcalibrated needles.

5 Overview of experimental results - “Leak Ruler”219

The investigation of the detection limit of our setup was feasible by using medical (hypodermic) needles220

of the series 27G, 28G, 30G, 31G, 32G. Their precision in diameter is 19 µm (which corresponds to about221

from 9 % to 18 %). However, we are interesting only for their particular flow rate as we can measure222

with much better accuracy it by our setup. The needles are simply inserted in the side of a plastic pipe.223

As we confirmed experimentally, there is not any observable leak between the needle and the side of the224

tube. These needles constitute the emulated leak branches useful for calibration the gas GLT setup of225

Micromegas Multiplets (at CERN or at other test sites). We have measured them one-by-one with air and226

by the FRL method. The obtained results are illustrated in a plot which in the horizontal axis has the leak227

rate divided by the acceptance limit of LM1 Multiplet while in the vertical one has the obtained leak rate228

it self. This plot we call “Leak Ruler” because of its usefulness to give two information simultaneously.229

This plot is shown in Fig.9.230

Figure 9: The plot with the “Leak Ruler” in the region of acceptance limit and below this. The firstmeasured calibrated needles are indicated with N-XXCN where XX represents the corresponding Gcode.

A certain number of calibrated needles are going to be measured systematically with air, and as well231

as, with argon creating a complete calibration set.232

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Conclusions233

In this work we implement the methods we considered as appropriate for the gas leak test of Micromegas234

Multiplets for NSW, that is, the pressure decay rate (PDR) and the flow rate loss (FRL). For evaluation235

and calibration of both method we introduced the technique of the Leak Branches based on medical236

needles. The combined gas leak methods have been implemented in a unified prototype setup.237

Our experimental measurements using the calibrated leak branches have been confirmed a sensitivity238

corresponding to leak rates much lower than the NSW acceptance limit. We also detected and explained239

the high sensitivity of the PDR method to the “volume compliance” of a small Micromegas chamber of240

TMM type. Furthermore, we investigated the data analysis model uncertainty of the PDR method having241

in mind the Micromegas Multiplets. The proposed FRL method has been successfully tested and seems242

reliable, fast, accurate and insensible to the temperature variations. A progress have been done in the243

noise reduction based on Lock-in Amplifier technique and the data acquisition and control subsystem244

dedicated to gas leak test. Our prototype setup, as first-level PDR/FRL configuration, can be used in245

the BB5 Lab. For a noticeable upgrade for a second-level configuration, more precise mass flowmeters246

found in the market, should be proposed.247

Acknowledgments248

We would like to thank our colleagues in MAMMA collaboration for the useful private communications249

and discussions for this project.250

The present work was co-funded by the European Union (European Social Fund ESF) and Greek national251

funds through the Operational Program ”Education and Lifelong Learning” of the National Strategic252

Reference Framework (NSRF) 2007-2013, ARISTEIA-1893-ATLAS MICROMEGAS.253

References254

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