A Study of Back Diffusion in the ATLAS Muon Spectrometer Gas

System

Gordon Berman

University of Michigan

Advisors: Bing Zhou, Dan Levin, and Zhengguo Zhao

The ATLAS Detector

ganesh.physics.lsa.umich.edu/~atlas/

The Muon Gas System• Supply drift gas (93% Ar, 7% CO2) to 1194 Monitored

Drift Chambers, containing 371,488 tubes, keeping them at a pressure of 3 atmospheres

• Tubes specified to leak at a rate of less than 10-8 L*Bar/Sec

• Back-diffusion of contaminants (N2, O2, H2O) into the tubes limited to 100 parts per million (ppm)

• ATLAS specs assume that the leak rate equals the contamination rate

Question:What is the contamination rate resulting from a typicalchamber leak?

Why Do We Care?

• Contaminants alter the time-space function of an MDT, causing a degradation in resolution

• Contaminants also “eat up” drift electrons, which results in a smaller signal and less efficiency, as well as reduced resolution

• Leak checking is very costly in terms of time, money, and expertise—especially with the stringent ATLAS leak specifications.

TDC spectra

Gas with air is fasterGas with air is faster

Cerutti, et al.17 June 2002

My Project for the SummerMy Project for the Summer

• Calculate the contamination rate for a common leak geometry

• i.e.--fibers or dirt in O-rings, pinched O-rings, defective O-rings (notice a pattern?)

• Create a model describing worst case scenarios and use its results as an upper limit

• Consider the impact of relaxing the ATLAS leak specifications

My Model’s Assumptions

1) Perfectly cylindrical leak pathway used to model a leak caused by a fiber or hair

2) As a N2 or O2 molecule traverses the pathway, it will run into many “effective cross sections” of Argon gas

3) The molecule will bounce back and forth until it is either ejected or it passes through the cylindrical leak pathway

4) Very few collisions between the contamination molecules

5) All collisions are classical (elastic)6) It should serve as an upper-bound

What an Effective Cross-Section Is (Kind of)

Ar

Probability of N2 Passing Through 1 X-Section ~ 99.866%Number of X-Sections per mm ~ 422,000

Passage of an N2 particle

0

10000

20000

30000

0 0.2 0.4 0.6 0.8 1

Position (mm)

Tim

e S

tep

s

Distribution of Maximum States for N2 molecules in 3 atm of Ar (Each Bin = 8,440 X-Sections)

1

10

100

1000

10000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Maximum X-Section Reached

# N

2 m

ole

cule

s

Calculation of Contamination RateUsing the simulated diffusion rate (D):

# Molecules diffusing into tube per second = NC

NC = A * *D, where = p*(2m*kT)-1/2

Contamination Composition (by mass) = CC = (NC*mC) / ((NAr– NL) * mAr + NC * mC )

A = cross-sectional area of the leak

mC = mass of 1 contaminant molecule

mAr= mass of 1 Argon atom

NL = # of Argon molecules escaping from the leak

Simulation Results• For Rleak=5 m , Lleak = 1 mm, LMDT=2.16m (similar

to a small fiber):

• Rate of Passage in N2, O2 molecules ~ .16 +/- .002 %

• Leads to an N2 Contamination Rate of: ~ 15.3 ppm per leak*day (by mass)

• And an O2 Contamination Rate of: ~ 3.10 ppm per leak*day (by mass)

• Total Estimated Contamination RateTotal Estimated Contamination Rate ~ 20 ppm per leak*day~ 20 ppm per leak*day

Conclusions• Having a leak at this level should not bring the

contamination level of a given tube to above ATLAS specifications (100 ppm)

• This is because the gas will be flushed at a rate of about 1 volume per day and will be replaced at a rate of about 1 volume per 10 days

• Also, the simulation assumes conditions worse than an actual leak would create

• Hence, the ATLAS leak specifications can be relaxed by at least a factor of 5 (most likely by a factor of 10) from a contamination perspective.

• A more accurate back diffusion estimate can be determined through empirical measurements – a study is currently in progress at UM (Dan Levin)

Acknowledgements

• Bing Zhou, Dan Levin, Zhengguo Zhao, Rudi Thun, and the rest of the University of Michigan ATLAS Group

• Homer Neal, Jean Krisch, and Tom Dershem for organizing the U. of Michigan CERN REU Program

• The National Science Foundation• Ford Motor Company• The CERN Summer Students Program

References

-Andrews, F. Equilibrium Statistical Mechanics, 2nd ed. (Wiley, New York, 1975).

-Cerutti, F. “MDT Performance with Air Contamination.”17 June 2002.

-Crank, J. The Mathematics of Diffusion, 2nd ed. (Oxford Science Publications, Oxford, UK, 1975).

-Liboff, R. Kinetic Theory. (Prentice Hall, Englewood Cliffs, NJ, 1990).

-ATLAS Muon Spectrometer Technical Design Report. 25 May 1999.