13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 1 Gas Flow Modelling in Design of the Vacuum System for of the Synchrotron Light Source O.B. Malyshev ASTeC Vacuum Science group CCLRC Daresbury Laboratory, Warrington WA4 4AD, UK

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 2 Outline Input parameters Sources of gas in vacuum chamber Interpretation of experimental data SR from a dipole magnet Desorption Models Pressure distributions

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 3 Input parameters An 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: E c = 8.37 keV,  = 1.15  photons/mrad SR from dipole on crotch-absorber:  = ~6.0  photons (approximate value)

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 4 Sources of gas in the SLS vacuum system Leaks Residual gas Thermal outgassing Photon stimulated desorption

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 5 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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 6 Sources of Gas in a Vacuum System: PSD  e-e- H2H2 H2H2 H2OH2O CO 2 CH 4 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-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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 7 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 photons/m (1 to 10 Amp  hrs for diamond) are extrapolations. Photodesorption yield at room temperature as function of accumulated photon dose can be described as:

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 8 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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 9 Vacuum chamber without an ante-chamber SR directly irradiate the strip with width a a b e-beam SR

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 10 Vacuum chamber without an ante-chamber SR directly irradiate the strip with width a Some photons are reflected a b e-beam SR

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 11 Vacuum chamber without an ante-chamber SR directly irradiate the strip with width a Some photons are reflected Photo-electrons are emitted and hit a vacuum chamber uniformly (for round tube) a b e-beam SR

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 12 Vacuum chamber without an ante-chamber SR directly irradiate the strip with width a Some photons are reflected 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-beam SR

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 13 Vacuum chamber without an ante-chamber 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-beam SR B

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 14 Effect of magnetic field on photo-desorption PAC-1993, p.3876

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 15 Vacuum chamber without an ante-chamber If the directly irradiated strip is narrow: a << b, then conditioned very fast. Initially  a0 =  b0  q a >>q b After some short time there will be:  a <<  b and q a  q b I.e. gas desorption is quite uniform radially a b e-beam SR

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 16 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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 17 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 Intensive conditioning

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 18 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 Intensive conditioning No conditioning    0

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 19 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.

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 20 SR from a dipole magnet

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 21 Photodesorption from a stainless steel vacuum chamber pre-baked VC: pre-baked at 200  C for 24 hrs (but not baked in-situ) in-situ baked: baked in-situ at 200  C 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) 635 Extrapolation above Dmax!   D   D -0.95

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 22 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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 23 Desorption flux as a function of distance from a dipole magnet I.e. the photon flux may differ in about 10 4 times but after shot conditioning (1Ah) the difference in ougassing is less than factor 10.

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 24 Models Analytical 1D diffusion model Monte-Carlo simulations (3D) Method of angular coefficient (2D and 3D)

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 25 A model of dynamic desorption processes in a beam vacuum chamber (1) 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: where  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:

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 26 A model of dynamic desorption processes in a beam vacuum chamber (2) In the quasi-equilibrium state when the condition V dn/dt = 0 is satisfied: This second order differential equation for the function n(z) has two solutions: where the constants C 1 and C 2 depend on the boundary conditions.

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 27 A model of dynamic desorption processes in a beam vacuum chamber (3) 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 z i-1 and z i will be described by above equations with two unknowns C 1i and C 2i. The boundary conditions are and A system of 2N–2 equations with 2N–2 unknowns which can be easily solved..

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 28 Comparison between models modelDiffusionMonte-Carlo Accuracy1D simplified model3D accurate model Complicate shape Not accurateAccurate Long structures Short time calculationsVery long calculations OptimisationEasy to change and calculate Time consuming modelling and calculations Molecular beaming Does not considerAccurate UseGood knowledge of gas dynamic is essential

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 29 Monte-Carlo for modelling pumping port

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 30 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

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 31 Pressure profile along the arc after 100 A  hrs beam conditioning Average pressure without a beam: = 1  mbar due to SR photons only: =1  mbar Sum (i.e with a beam): = + = = 2  mbar

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 32 Pressure profile along front ends after 30 A  hrs beam conditioning

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 33 Example of pressure profile

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 34 Example of pressure profile Pumping units Gas injection

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 35 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 photons/m).

13/09/2005Vacuum Systems for Synchrotron Light Sources Workshop, Barcelona, Spain 36 Thank you!