13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 1 Gas Flow...

13/09/2005 Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain

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Gas Flow Modelling in Design of the Vacuum System

for of the Synchrotron Light Source

O.B. Malyshev

ASTeC Vacuum Science groupCCLRC Daresbury Laboratory,

Warrington WA4 4AD, UK


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Outline• Input parameters• Sources of gas in vacuum chamber• Interpretation of experimental data• SR from a dipole magnet • Desorption• Models• Pressure distributions


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Input parametersAn example of parameters as for diamond• Beam parameters: I=0.300 A, E=3 GeV• Required average pressure: <10-9 mbar • Beam vacuum chamber is uniform:

82 mm x 38 mm• SR from Dipole:

Ec = 8.37 keV, = 1.151017 photons/mrad

• SR from dipole on crotch-absorber: = ~6.01018 photons (approximate value)


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Sources of gas in the SLS vacuum system

• Leaks

• Residual gas

• Thermal outgassing

• Photon stimulated desorption


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Sources of Gas in a Vacuum System: Thermal Desorption

Thermal desorption

(or thermal outgassing) means:– Molecules adsorbed on the surface

(initially or after the air venting) and desorbing when vacuum chamber is pumped

– Molecules diffusing through the bulk material of the vacuum chamber, entering the surface and desorbing from it

Outgassing rate depends on many factors: choice of material, cleaning procedure, pumping time, etc...

AirVacuum


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Sources of Gas in a Vacuum System: PSD

e-

H2

H2

H2O

CO2

CH4

CO

Photon stimulated desorption (PSD) is one of the most important sources of gas in the presence of SR.

Gas molecules may be desorbed from a surface when and where photoelectrons leave and arrive at a surface

e-

The same as thermal desorption, PSD depends on:

• Choice of material • Cleaning procedure• History of material• Pumping time

Additionally it depends on

• Energy of photons• Photon flux• Integral photon dose• Temperature


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Sources of Gas in a Vacuum System: PSD

Photodesorption yields, (molecules/photon), as a function of accumulated photon dose, D, for different materials measured up to certain doses, these results are extrapolated for use in the design of new machines

PSD yield for CO for prebaked and in-situ baked stainless steel vacuum chambers. Yields for doses higher then 1023 photons/m (1 to 10 Amphrs for diamond) are extrapolations.

165.0,00

D

D

Photodesorption yield at room temperature as function of accumulated photon dose can be described as:


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Sources of Gas in a Vacuum System: ESD

F. Billard, N. Hilleret, G. Vorlaufer. Some Results on the Electron Induced Desorption Yield of OFHC Copper. Vacuum Technical Note 00-32, December 2000, CERN, Geneva

Electron stimulated desorption (ESD) can be a significant gas source in a vacuum system in a number of cases when the electrons bombard the surface.

The same as thermal desorption and PSD, ESD depends on:

• Choice of material • Cleaning procedure• History of material• Pumping time

Additionally it depends on:

• Energy of electrons impacting the surface

• Electron flux to the surface

• Integral electron dose• Temperature


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Vacuum chamber without an ante-chamber

• SR directly irradiate the strip with width a

a

b

e-beamSR


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• Some photons are reflected

a

b

e-beamSR


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• Photo-electrons are emitted and hit a vacuum chamber uniformly (for round tube)

a

b

e-beamSR


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• Photo-electrons are emitted and hit a vacuum chamber uniformly (for round tube)

• Gas molecules are desorbed where the electrons emitted and where they hit the wall

a

b

e-beamSR


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• In the presence of dipole field B the gas desorption most of electrons hit the wall near the intensively irradiated strip a

• Switching B on and off change the distribution of the electrons hitting the wall and therefore gas desorption.

a

b

e-beamSR

B


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Effect of magnetic field on photo-desorption

PAC-1993, p.3876


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• If the directly irradiated strip is narrow: a << b, then conditioned very fast.

• Initially a0 = b0 qa>>qb

• After some short time there will be: a << b and qaqb

• I.e. gas desorption is quite uniform radially

a

b

e-beamSR


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Vacuum chamber with an ante-chamber

• Part of SR directly irradiate the strips above and below the slot to the antechamber

• Photoelectrons may be repelled by the beam into the ante-chamber

• Some photons are backscattered from the crotch absorber to the ante-chamber

• Photoelectrons from the crotch absorber are distributed inside the antechamber


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Intensive conditioning


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Intensive conditioning

No conditioning 0


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Vacuum chamber with an anti-chamber

• There is distributed photon stimulated desorption in the vacuum chamber with an ante-chamber

• The lower photon and photo-electron flux onto the vacuum chamber walls lead to lower initial desorption flux but cause lower beam conditioning and therefore very little or no benefit in long term

• Meanwhile the antechamber is essential to let SR out => crotch absorber vacuum chambers.


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SR from a dipole magnet


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Photodesorption from a stainless steel vacuum chamber

pre-baked VC: pre-baked at 200C for 24 hrs (but not baked in-situ) in-situ baked: baked in-situ at 200C for 48 hrs[1] C.L. Foerster, et al, J.Vac.Sci.Technol A8(3) (1990) 2856[2] C. Herbeaux, et al, J.Vac.Sci.Technol A17(2) (1999) 635Extrapolation above Dmax!

D-0.66 D-0.95


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Photodesorption yield as a function of distance from a dipole magnet

•Initial desorption yields after ex-situ baking is 20 times better than after in-situ baking of vacuum chamber;• Desorption yields are similar in both chambers after 100 Ah conditioning and vary along the vacuum chamber


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Desorption flux as a function of distance from a dipole magnet

I.e. the photon flux may differ in about 104 times but after shot conditioning (1Ah) the difference in ougassing is less than factor 10.


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Models

• Analytical 1D diffusion model• Monte-Carlo simulations (3D)• Method of angular coefficient (2D and 3D)


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A model of dynamic desorption processes in a beam vacuum chamber (1)

2

2

dz

nducnq

dt

dnV

where z is the longitudinal axis of the vacuum chamber; n is the gas volume density; V is the vacuum chamber volume; q is the gas desorption flux; c is the distributed pumping speed

Gas desorption q consists of two main sources: thermal and photon stimulated desorption:

Fq twhere t is the thermal desorption yield,

F is the vacuum chamber surface area, is the photon stimulated desorption yield,

is the synchrotron radiation photon flux.

The equations of gas dynamic balance inside a vacuum chamber:


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In the quasi-equilibrium state when the condition V dn/dt = 0 is satisfied:

02

2

qcndz

ndu

This second order differential equation for the function n(z) has two solutions:

where the constants C1 and C2 depend on the boundary conditions.

0)(

02

)(

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212

cforeCeC

c

qzn

cforCzCzu

qzn

zu

c

b

zu

c

b

aa


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All vacuum chamber along the beam can be fragmented on N elements with c = 0 and c > 0. Every i-th element lying between longitudinal co-ordinates zi-1 and zi will be described by above

equations with two unknowns C1i and C2i. The boundary

conditions are and

A system of 2N–2 equations with 2N–2 unknowns which can be easily solved.

iiii znzn 1 zznzzn iiii )()( 1

.


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Comparison between models

model Diffusion Monte-Carlo

Accuracy 1D simplified model 3D accurate model

Complicate shape

Not accurate Accurate

Long structures

Short time calculations Very long calculations

Optimisation Easy to change and calculate

Time consuming modelling and calculations

Molecular beaming

Does not consider Accurate

Use Good knowledge of gas dynamic is essential


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Monte-Carlo for modelling pumping port


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Pressure profile along the arc

Comparison between the analytical methodology and a Monte-Carlo simulation (MOLFLOW written by R. Kersevan) for some elements of the diamond vacuum chamber


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Pressure profile along the arc after 100 Ahrs beam conditioning

Average pressure

without a beam:

<Pt> = 110-9 mbar

due to SR photons only:

<P> =110-9 mbar

Sum (i.e with a beam):

<Pdin> = <Pt> + <P

>=

= 210-9 mbar


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Pressure profile along front ends after 30 Ahrs beam conditioning


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Example of pressure profile


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Example of pressure profile

Pumping unitsGas injection


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Conclusions

• Vacuum chamber without an ante-chamber is not necessary need in-situ baking (but requires ex-situ one).

• Vacuum chamber with an ante-chamber needs in-situ baking • There are different methods to calculate the pressure profile,

choice of method or their combination depends on task, timescale, required accuracy, etc.

• There are no computing programme to optimise the design of vacuum chamber – each machine quite unique and there are many ways of optimisation.

• There is a lack of data for photo-desorption at high photon dose (above 1023 photons/m).


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Thank you!

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 1 Gas Flow...

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Transcript of 13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 1 Gas Flow...