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Design modelling and measured performance of the vacuum system of the Diamond Light Source storage ring
Vacuum 86 (2012) 1692e1696
Contents lists available at SciVerse ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Design modelling and measured performance of the vacuum system of the Diamond Light Source storage ring O.B. Malyshev a, M.P. Cox b, * a b
Accelerator Science and Technology Centre, STFC Daresbury Laboratory, Warrington, Cheshire WA4 4AD, UK Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 October 2011 Received in revised form 2 March 2012 Accepted 4 March 2012
A one-dimensional diffusion model of the Diamond Light Source storage ring vacuum system is described and its predictions are compared with actual measured static (without beam) and dynamic (with beam) pressures over more than 2000 A h of beam conditioning at 3 GeV. An average specific thermal outgassing yield of 1$1011 mbar l/(s cm2) during initial beam circulation is obtained, which reduces to 2$1012 mbar l/(s cm2) after an accumulated beam dose of 1000 A h and an elapsed time of 769 days. In the presence of stored electron beam, the pressure rises as expected due to photon stimulated desorption (PSD). The PSD yield reduces with beam dose according to a (2/3) power law as was applied in the model. Predicted and measured dynamic pressures generally agree within a factor of 2 over the whole range of beam conditioning dose studied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Gas flow modelling Photon stimulated desorption Synchrotron light source Storage ring
1. Introduction The UK national synchrotron facility, Diamond Light Source (Diamond), has been operating with circulating 3 GeV electron beam in the storage ring since September 2006. It generates synchrotron radiation from infra-red to X-rays for a wide range of applications in biology, physics, chemistry and medical research. The Diamond 3 GeV electron storage ring is 561.6 m in circumference. It consists of 24 cells with 24 identical achromat (arc) sections each 17.35 m long and 24 straight sections (6 8.3 m long plus 18 5.3 m long), 21 of which are dedicated for insertion devices which are progressively being installed as the machine development continues. The remaining 3 straight sections are currently dedicated for radio frequency (RF) systems, injection and beam diagnostics. According to the design objective, the storage ring should achieve an operating pressure of 109 mbar (CO equivalent) or lower with 300 mA of stored beam after 100 A h of beam conditioning. The operating pressure is critical both for the lifetime of the stored beam and to control the Gas Bremsstrahlung radiation. In-situ bakeout is limited to the storage ring straight sections and front ends; the storage ring arcs are not bakeable insitu. Details of the vacuum vessel cleaning, bakeout and installation have been published elsewhere [1].
* Corresponding author. Tel.: þ44 1235 778061. E-mail address: [email protected] (M.P. Cox). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2012.03.015
The technical design, including the vacuum system design, was summarized in 2002 in the Diamond Design Report [2]. Some details of the vacuum system design and modelling were also published elsewhere [3e5]. In order to understand the design parameters and to refine the design model and parameters for future projects and upgrades, this paper compares the design performance of the vacuum system based on model studies with the actual measured performance. During the detailed engineering and construction stage after publication of the Diamond Design Report some relatively minor changes were made to the vacuum system design and these have been incorporated into a revised model presented here. Aspects of the measured performance of the Diamond storage ring vacuum system have already been reported [6] at an earlier stage in the beam conditioning process. For the purposes of comparison with the design model, more detailed measured data extending over 2000 A h of beam conditioning has been extracted from the data archive and analysed. 2. Diamond storage ring modelling Modelling of a complex vacuum system such as the Diamond storage ring comprises several stages: Selecting a method of modelling Building a model and identifying required parameters Analyzing available experimental data and adopting them for use in the model
O.B. Malyshev, M.P. Cox / Vacuum 86 (2012) 1692e1696
Analyzing the results of the modelling Comparison of the modelling results with measurements of the real machine performance. 2.1. Model When vacuum vessel drawings and desorption rate at every point on the surface are known and pump locations and pumping characteristics are defined, then the most accurate vacuum system modelling result can be obtained with the Test Particle Monte-Carlo (TPMC) code; for example, MOLFLOW written by R. Kersevan allows the building of accurate models of accelerator vacuum vessels. However, building the TPMC model and modifying it during design optimization is a time consuming process. The calculations with the code also require long computing time. Another possibility is a diffusion model [2,3]. This is a onedimensional (1D) model based on the equation of gas dynamic balance inside a vacuum vessel:
V
dP d2 P ¼ q cP þ u 2 ; dt dz
(1)
where P [mbar] is the local gas pressure at position z [m] on the longitudinal axis of the vacuum vessel; V [m2] is the specific vacuum vessel volume per unit of vacuum vessel length; q ¼ htF/ L þ hgG/kBT [mbar m2/s] is the gas desorption flux per unit of vacuum vessel length where ht [mbar m/s] is the thermal outgassing rate, F [m2] is the vacuum vessel wall surface area, L [m] is the vacuum vessel length, hg [molecule/photon] is the photon stimulated desorption yield, G [photon/(s m)] is the incident synchrotron radiation (SR) photon flux, kB is the Boltzmann constant [J/K] and T [K] is the gas temperature; c ¼ rAmesh v=ð4LÞ [m2/s] is the distributed pumping speed, r is the capture factor for the pump including a pumping port and associated screening mesh, Amesh [m2] is the effective mesh area, v [m/s] is the mean molecular speed. u ¼ Ac$D [m4/s] is the specific vacuum vessel molecular gas flow conductance per unit axial length, Ac is the vacuum vessel cross-section; D is the Knudsen diffusion coefficient. Two solutions of equation (1) exist in the quasi-equilibrium state when the condition V dP/dt ¼ 0 is satisfied and also assuming that the parameters are independent of z. A vacuum vessel without a pumping port (when c ¼ 0) is described with equation:
q P z ¼ z2 þ C1a z þ C2a ; 2u
(2)
and a vacuum vessel with a non-zero distributed pumping speed (i.e. c > 0), for example a pumping port covered with a mesh, is described as a vacuum vessel with a distributed pump:
q P z ¼ þ C1b e c
rffiffiffi rffiffiffi c c z z u þC e u ; 2b
(3)
where the constants C1 and C2 depend on the boundary conditions. The effective pumping speed was calculated for each pumping port separately with a TPMC code and was used in the diffusion model as uniformly distributed along a length equal to the overall length of the pumping port. The vacuum vessel along the beam can in practice be considered as being divided into N longitudinal elements, each with c ¼ 0 or c > 0. Every ith element lying between longitudinal coordinates zi1 and zi will be described by equation (2) or (3) with two unknowns C1i and C2i. The inter-element boundary conditions are taken as Pi(zi) ¼ Piþ1(zi) (single-valued pressure) and vPi(zi)/vz ¼ vPiþ1(zi)/vz (zero net gas flow e assuming the conductances of the two
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elements are the same). There are several possible ways to write the boundary conditions for the first and the last elements. When the model includes the entire storage ring or its periodic parts, the periodic condition can be used (i.e. P1(z0) ¼ PN(zN) and vP1(z0)/ vz ¼ vPN(zN)/vz). However, during the design and optimisation work the periodic condition is not always fulfilled, and a simplification was applied where the first and the last elements have the same boundary conditions at both ends, i.e.: P1(z0) ¼ P1(z1) and vP1(z0)/ vz ¼ vP1(z1)/vz for the first element and PN(zN1) ¼ PN(zN) and vPN(zN1)/vz ¼ vPN(zN)/vz for the last one. The error due to simplified boundary conditions at the extremes of the modelled vacuum vessel has only a small influence on the calculated pressure distribution provided the first and the last elements are relatively short and the vacuum conductance of these elements is smaller than their pumping speed. These criteria are met at the location of vacuum pumps at the extremes of the arcs. In this case C1i ¼ C2i for i ¼ 1 and i ¼ N. Now for the N elements of the vacuum vessel we have a system of 2Ne2 equations with 2Ne2 unknowns, which can be easily solved with a numerical calculation package such as Mathcad. The above analysis is strictly correct only in the limit of axially symmetric long vacuum vessels of uniform cross-section. For some parts of Diamond storage ring, this is approximately the case. However, this 1D analysis could be far from reality in the wide dipole magnet vacuum vessel. To assure the validity of these calculations, corroborating TPMC simulations were performed for some elements of the Diamond vacuum vessel [2]. No significant differences were found between the results of the 1D analysis described above and the TPMC simulations for most of vacuum vessel elements; some minor differences were found for dipole vacuum vessels: up to 10% for longitudinally averaged pressure along the beam path and up to 50% for local pressure along the beam path. This comparison showed that the 1D analytical method was sufficiently accurate for optimisation of the pressure profiles and the average pressure during the design of the Diamond vacuum system. The 1D analytical method is much faster, more convenient and more flexible than TPMC for calculations where many iterations in input parameters are required. Results for the updated vacuum system design were already published [4,5]. 2.2. Input data All materials used to build accelerators, such as stainless steel or copper, desorb gas into the vacuum system. This thermal desorption determines the base pressure in the storage ring without beam (static pressure). Thermal desorption is described by an outgassing rate ht. The assumption based on experience from the Daresbury Synchrotron Radiation Source (information courtesy of R.J. Reid) was that for an ex-situ baked vacuum vessel which has been briefly vented to air and re-pumped, an outgassing rate of about 109 mbar l/(s cm2) for H2 and 1010 mbar l/(s cm2) for CO (in units commonly used in the vacuum community) will be reached after a few hours pumping, thereafter decreasing exponentially with additional pumping time. A value of outgassing rate two orders of magnitude lower should easily be obtained for carefully chosen and well-prepared materials after a few hundred hours of pumping at room temperature [7]. Since the cross-section of beam-gas interaction increases with atomic number squared [8] while the vacuum system conductance is greater for light gas species, the beam losses due to collisions with H2 and CO (two main gases presented in residual gas spectrum of accelerators) are quite comparable; therefore a single gas model with the CO equivalent can be used. The values used in the model are shown in Table 1.
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Table 1 Predicted and measured thermal desorption yields and average pressure without beam in the Diamond storage ring after various times. Elapsed time (days)
Dose (A h)
ht [mbar l/(s cm2)] used in the model
Average calculated pressure without beam [mbar]
Average measured pressure without beam [mbar]
ht [mbar l/(s cm2)] calculated from measurements
0 3.2 24.2 52.6 178.8 769.0
0 0.1 1 10 100 1000
1.0$1010 e e e 1.0$1012 e
1.1$108 e e e 1.1$1010 e
1$109 8$1010 5$1010 4$1010 3$1010 2$1010
9.1$1012 7.4$1012 4.5$1012 3.6$1012 2.7$1012 1.8$1012
In the presence of beam, in the initial stages of beam conditioning, the main source of gas is photon stimulated desorption (PSD) from vacuum-facing surfaces caused by synchrotron radiation (SR). PSD yields have been experimentally studied in many research centres. The most appropriate results for Diamond are in papers [9e12]. A detailed analysis of the available data was reported in Ref. [2,3]. In general, the PSD yield, hg, for a vacuum vessel decreases with photon dose proportionally to Da, where D [photons/m] is the integrated photon dose to which it has been exposed. At room temperature, the exponent a for very low photon doses is close to zero. After this initial period it then increases and reaches a constant value which lies somewhere between 2/3 a 1. Experimental data is lacking for large enough doses D required to simulation reasonable beam conditioning times at Diamond; the extrapolation of the data fitting curve assuming constant a had to be made over three orders of magnitude and may lead to a significant error. The pessimistic limit value a ¼ 2/3 [9] was used in the model to guarantee meeting the required vacuum specifications. A larger value of a ¼ 1 [10] would predict a significantly smaller value of PSD yield and lower operating pressure for longer beam conditioning time. The initial PSD yield of an ex-situ baked vacuum vessel as used at Diamond is higher than for an in-situ baked vessel but is much lower than for an unbaked vessel [9e11]. However, at very high photon doses there is no significant difference between baked and unbaked vacuum vessels [10]. Before applying these published values to the Diamond model one should compare the set-up and the samples used for the published studies with the materials and processing of the vacuum vessels used at Diamond. The experiments in [9] and [10] for example were performed with tubular samples with known diameter; the Diamond storage ring cross-section, in contrast, is non-circular and varies along the ring. To take this into account, the beam dose for the model was normalised using the ratio of the cross-sectional circumferences of the reference samples and those of the storage ring vacuum vessels, because the reflected and scattered photons and photoelectrons stimulate desorption from entire the cross-sectional surface area. The data in [11] was obtained from SR power absorbers made of oxygen-free highconductivity (OFHC) copper and these results were applied to model the Diamond crotch absorbers which are also made of OFHC copper. By applying these and similar principles it is possible to estimate the PSD yield as a function of photon dose for all the different vessel cross-sections found in the Diamond storage ring. Another complication is that different parts of vacuum system of Diamond storage ring are irradiated with different intensities of SR photon flux. That means that, during operation, the accumulated photon dose will be different for different parts of the vacuum system. The parts where the photon flux is higher are subject to a higher dose and therefore the PSD yield reduces more quickly with conditioning time. The model used here includes this effect and calculates the photon stimulated gas desorption flux q ¼ hgG/
(kBT) as a function of the longitudinal coordinate along the beam path. Finally, it is known that from manufacturers’ catalogues and lab measurements, the pumping speed of the sputter ion pumps is reduced by w30% between 108 and 109 mbar (see, for example Ref. [13]). This effect was also included in calculations. 2.3. Results of modelling The initial calculations were presented in Ref. [3]. However, the as-built Diamond storage ring design differed slightly from the assumptions made at that design stage as a result of engineering factors: the sputter ion pump ducts have an additional elbow that reduces pumping speed; titanium sublimation pumps, although installed, were not routinely activated and gas loads to and from attached front end and beamline vacuum systems were not considered. All these differences were implemented in a corrected model presented here. The results for thermal desorption are shown in Table 1, where the column 1 shows the elapsed time since first beam circulation at 3 GeV. Individual vacuum sections have different total pumping times as the storage ring was installed over a period of one year. Column 2 shows the beam dose. Columns 3 and 4 show corresponding values of thermal desorption yield used in the model and the average pressure calculated with these yields. The latter can be compared to the measured pressures in column 5; the ratio of measured and calculated pressures allows calculation of the actual thermal desorption yields achieved in Diamond storage ring (column 6). Modelling results for pressure in the presence of the beam are shown in Fig. 1 for two cases: the model published in the Design
Fig. 1. Longitudinally averaged dynamic pressure along the storage ring arcs as predicted from the model.
O.B. Malyshev, M.P. Cox / Vacuum 86 (2012) 1692e1696
Study [2] and a corrected model corresponding to the actually installed design. The normalized dynamic pressure Pd/I is plotted as a function of accumulated dose, where Pd ¼ P Pt, P and Pt are the average pressures along the arcs in the Diamond storage ring with or without the beam and I is the stored beam current. There is a significant (factor 3e5) difference between two modelling results for low accumulated doses that comes mainly from the difference in effective pumping speed used in the two models. However, the difference reduces for higher doses and is negligible (<25%) for 100 A h and still meets the design specification: 109 mbar at 300 mA circulating beam. Therefore modifications to the design after the Design Study did not significantly compromise the vacuum system performance in respect to the specification. As well as comparing calculations and measurements of the longitudinally spatially averaged pressure around the storage ring the model allows comparison of the pressure distribution measured at a number of discrete gauge locations. This will be discussed further in the following sections. 3. Analysis of the measured data The Diamond storage ring is well equipped with gauges and residual gas analysers (RGAs): four inverted magnetron gauges (MKS Instruments type 422) are installed in each of 24 storage ring arcs along the beam path, and two or more gauges used along each straight section used for the insertion devices, injection and RF. There are also typically 3 RGAs fitted per storage ring cell. The data from all gauges and RGAs were logged at appropriate intervals to a central archive via the Diamond control system. The layout of a standard Diamond storage ring cell is shown in Fig. 2. Gauges SRnnA-01 and SRnnA-04 (where nn is the cell number ranging from 01 to 24) are located respectively near the non-evaporable getter (NEG) pump at the start and end of each arc. Gauges SRnnA-02 and SRnnA-03 are located near the two dipole magnet crotch photon absorbers. Gauges SRnnS-01 and SRnnS-02 are located in the straight sections. The measurements for each gauge logged with an interval of 1 h were analysed following a standard procedure. Firstly the pressure with no beam, Pt, which depends on thermal outgassing, was analysed as a function of accumulated dose. The pressure readings varied somewhat from cell to cell around the storage ring. This is because the storage ring was installed cell-by-cell over a period of nearly a year and, therefore, different sections had been under vacuum conditions for very different times and had rather different thermal outgassing rates. To even out this variation, the average pressure was taken overall gauges in all 24 cells and this is shown in Table 1 for different accumulated doses. The dynamic pressure Pd was then calculated for all data recorded in the presence of beam using formula Pd ¼ P Pt, and normalized by the beam current I. Finally the average of similarlylocated gauges from each of the 24 cells was calculated, excluding outliers from faulty data. These measured pressures for each of six gauge positions (S1, S2, A1, A2, A3 and A4 in Fig. 2) were compared with pressures predicted by the model. The measured and
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predicted pressures for gauge position A2 are plotted in Fig. 3, where red crosses show the 24 cell average of Gauge SRnnA-02 measurements, green triangles show the pressure predicted by the model at the gauge position and blue circles are average calculated pressure along the storage ring (the same as the ‘corrected model’ in Fig. 1). The results for other gauge locations look very similar. The measured Pd/I data are 2e3 times lower than predicted values for low accumulated doses (less than 0.1 A h); all three plots converge at higher doses and differences can be neglected for doses greater than 100 A h. 4. Discussion Comparison of measurements from the Diamond storage ring with the model described in Table 1 demonstrates that an average specific thermal outgassing yield of about 1$1011 mbar l/(s cm2) was reached before the first beam was injected to the storage ring. In the last sections to be installed and which had been under vacuum for the least amount of time, agreement is better with a measured specific thermal outgassing yield of about 1$1010 mbar l/(s cm2). After an elapsed time of 769 days and beam conditioning dose of 1000 A h, the average specific thermal outgassing yield reduces by a factor of 5e2$1012 mbar l/(s cm2). From the available data, the relative influence of elapsed time and beam conditioning on this reduction cannot be separated. The values of specific thermal outgassing yield measured on Diamond storage ring can now be used with confidence for design of other ex-situ baked accelerators. There is good agreement between the predicted and measured values of pressure increase due to PSD and its dependence on beam dose. It can also be seen that the PSD yield reduces proportionally to D2/3, exactly as applied in the model (see Section 2.2). Local differences between predicted and measured pressures at the gauge location can be explained by shortcomings of applying a 1D model in situations where the pressure may vary across the width of a complex shape vacuum vessel such as a dipole vessel. Also there is uncertainty as to how far literature data on outgassing rates and PSD yields generally obtained from well-characterised materials is applicable to the technical construction materials used at Diamond. Furthermore it was necessary to extrapolate published material data by three orders of magnitude to higher beam dose. Another reason for this discrepancy is that all pressure measurements reported here were made with total pressure gauges, which have different sensitivities for different gas species but do not allow distinguish between them. It is also important to mention here that the model assumes the gas behaves in molecular flow similarly to CO, while the RGA indicates that the residual gas is dominated by hydrogen in the absence of stored beam but with significant contributions from CO, CO2 and CH4 during the beam conditioning process. In reality, the gas flow conductivity of the beam vacuum vessel and pumping ports, pumping speed of pumps and gauge sensitivity scales as M0.5 where M is the molecular mass of the gas. So uncertainties and changes in gas composition could
Fig. 2. Layout of 22.65 m long Diamond storage ring section (5.3 m straight plus achromat) used for the modelling showing the location of the pressure gauges S1 ¼ SRnnS-01, S2 ¼ SRnnS-02, A1 ¼ SRnnA-01, A2 ¼ SRnnA-02, A3 ¼ SRnnA-03 and A4 ¼ SRnnA-04. D1 and D2 are the two bending (dipole) magnets.
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predicted the behaviour of the Diamond storage ring correctly and accurately enough to develop and optimise the designs. The local dynamic pressures obtained from the model agree with pressures measured in the Diamond storage ring within a factor 2. This relatively small discrepancy for such a large, complicated vacuum system has four main contributions:
Fig. 3. Pressure vs accumulated dose. Comparison of modelling results and measurements for dipole vessel with gauge SRnnA-02.
1. A 1D model has been used which ignores the lateral extent of the vacuum vessel and cannot predict the local pressure as accurately as it predicts the longitudinal spatially averaged pressure. 2. The molecular flow model assumes the gas is CO equivalent instead of including the real gas species distribution. 3. Total pressure gauges have different sensitivity for gas species in vacuum system. 4. Vacuum vessel wall material properties may vary due to different manufacturers, cleaning and pre-treatments including bakeout and pumping time. References
also play a role in explaining the differences between the model and measured pressures. 5. Conclusions For the first time, predicted and measured pressures in an electron storage ring from beginning of operation up to more than 2000 A h beam dose were systematically compared. The contributions of thermal and photon stimulated desorption were analysed as a function of dose. The initial thermal desorption was correctly estimated in the model for the last installed section but overestimated for the average overall sections by a factor of 10. The average specific thermal outgassing yield w1$1011 mbar l/(s cm2) was reached before the first beam was injected into the storage ring, therefore this value can now be used with confidence for other ex-situ baked machines. After 1000 A h conditioning it reduces by a factor 5 only. The measured PSD yield reduces with accumulated dose proportionally to D2/3, exactly as applied in the model. These results prove that the applied PSD model and vacuum gas dynamic models
[1] Cox MP, Boussier B, Bryan S, Macdonald BF, Shiers HS. In: Proceedings of the 2006 European Particle Accelerator Conference (EPAC’06) June 2006. pp. 3332e3334. [2] Diamond synchrotron light source: report of the design specification. Warrington, Cheshire, UK: CCLRC, Daresbury Laboratory; June 2003. [3] Malyshev OB, Al-Dmour E, Herbert JD, Reid RJ. In: Proceedings of the 2002 European Particle Accelerator Conference (EPAC’02) June 2002. pp. 2571e2573. [4] Malyshev OB, Macdonald BF. Diamond internal report TDI-VAC-SR-REP-0001. Didcot, UK: Diamond Light Source; June 2003. 14 pages. [5] Herbert JD, Malyshev OB, Middleman KJ, Reid RJ. Vacuum 2004;73:219e24. [6] Cox MP, Boussier B, Bryan S, Macdonald BF, Shiers HS. J Phys Conf Ser 2008; 100:092011. [7] Calder R, Levin G. Brit J Appl Phys 1967;18:1459e72. [8] Chao AW, Tigner M, editors. Handbook of accelerator physics and engineering. World Scientific; 1999. p. 215. [9] Foerster CL, Halama H, Lanni C. J Vac Sci Technol A 1990;8:2856e9. [10] Herbeaux C, Marin P, Baglin V, Gröbner O. J Vac Sci Technol A 1999;17: 635e43. [11] Anashin V, Bulygin A, Kraemer D, Malyshev O, Mironenko L, Pyata E, et al. In: Proceedings of the 1998 European Particle Accelerator Conference (EPAC’98) June 1998. pp. 2163e2165. [12] Malyshev OB. The study of photodesorption processes in the prototypes of vacuum chambers for superconducting super colliders. Ph.D. thesis (in Russian); 1995. Novosibirsk, Russia. [13] Audi M. Vacuum 1988;38:669.
Contents lists available at SciVerse ScienceDirect
Vacuum journal homepage: www.elsevier.com/locate/vacuum
Design modelling and measured performance of the vacuum system of the Diamond Light Source storage ring O.B. Malyshev a, M.P. Cox b, * a b
Accelerator Science and Technology Centre, STFC Daresbury Laboratory, Warrington, Cheshire WA4 4AD, UK Diamond Light Source Ltd, Harwell Science and Innovation Campus, Didcot, Oxfordshire OX11 0DE, UK
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 October 2011 Received in revised form 2 March 2012 Accepted 4 March 2012
A one-dimensional diffusion model of the Diamond Light Source storage ring vacuum system is described and its predictions are compared with actual measured static (without beam) and dynamic (with beam) pressures over more than 2000 A h of beam conditioning at 3 GeV. An average specific thermal outgassing yield of 1$1011 mbar l/(s cm2) during initial beam circulation is obtained, which reduces to 2$1012 mbar l/(s cm2) after an accumulated beam dose of 1000 A h and an elapsed time of 769 days. In the presence of stored electron beam, the pressure rises as expected due to photon stimulated desorption (PSD). The PSD yield reduces with beam dose according to a (2/3) power law as was applied in the model. Predicted and measured dynamic pressures generally agree within a factor of 2 over the whole range of beam conditioning dose studied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Gas flow modelling Photon stimulated desorption Synchrotron light source Storage ring
1. Introduction The UK national synchrotron facility, Diamond Light Source (Diamond), has been operating with circulating 3 GeV electron beam in the storage ring since September 2006. It generates synchrotron radiation from infra-red to X-rays for a wide range of applications in biology, physics, chemistry and medical research. The Diamond 3 GeV electron storage ring is 561.6 m in circumference. It consists of 24 cells with 24 identical achromat (arc) sections each 17.35 m long and 24 straight sections (6 8.3 m long plus 18 5.3 m long), 21 of which are dedicated for insertion devices which are progressively being installed as the machine development continues. The remaining 3 straight sections are currently dedicated for radio frequency (RF) systems, injection and beam diagnostics. According to the design objective, the storage ring should achieve an operating pressure of 109 mbar (CO equivalent) or lower with 300 mA of stored beam after 100 A h of beam conditioning. The operating pressure is critical both for the lifetime of the stored beam and to control the Gas Bremsstrahlung radiation. In-situ bakeout is limited to the storage ring straight sections and front ends; the storage ring arcs are not bakeable insitu. Details of the vacuum vessel cleaning, bakeout and installation have been published elsewhere [1].
* Corresponding author. Tel.: þ44 1235 778061. E-mail address: [email protected] (M.P. Cox). 0042-207X/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2012.03.015
The technical design, including the vacuum system design, was summarized in 2002 in the Diamond Design Report [2]. Some details of the vacuum system design and modelling were also published elsewhere [3e5]. In order to understand the design parameters and to refine the design model and parameters for future projects and upgrades, this paper compares the design performance of the vacuum system based on model studies with the actual measured performance. During the detailed engineering and construction stage after publication of the Diamond Design Report some relatively minor changes were made to the vacuum system design and these have been incorporated into a revised model presented here. Aspects of the measured performance of the Diamond storage ring vacuum system have already been reported [6] at an earlier stage in the beam conditioning process. For the purposes of comparison with the design model, more detailed measured data extending over 2000 A h of beam conditioning has been extracted from the data archive and analysed. 2. Diamond storage ring modelling Modelling of a complex vacuum system such as the Diamond storage ring comprises several stages: Selecting a method of modelling Building a model and identifying required parameters Analyzing available experimental data and adopting them for use in the model
O.B. Malyshev, M.P. Cox / Vacuum 86 (2012) 1692e1696
Analyzing the results of the modelling Comparison of the modelling results with measurements of the real machine performance. 2.1. Model When vacuum vessel drawings and desorption rate at every point on the surface are known and pump locations and pumping characteristics are defined, then the most accurate vacuum system modelling result can be obtained with the Test Particle Monte-Carlo (TPMC) code; for example, MOLFLOW written by R. Kersevan allows the building of accurate models of accelerator vacuum vessels. However, building the TPMC model and modifying it during design optimization is a time consuming process. The calculations with the code also require long computing time. Another possibility is a diffusion model [2,3]. This is a onedimensional (1D) model based on the equation of gas dynamic balance inside a vacuum vessel:
V
dP d2 P ¼ q cP þ u 2 ; dt dz
(1)
where P [mbar] is the local gas pressure at position z [m] on the longitudinal axis of the vacuum vessel; V [m2] is the specific vacuum vessel volume per unit of vacuum vessel length; q ¼ htF/ L þ hgG/kBT [mbar m2/s] is the gas desorption flux per unit of vacuum vessel length where ht [mbar m/s] is the thermal outgassing rate, F [m2] is the vacuum vessel wall surface area, L [m] is the vacuum vessel length, hg [molecule/photon] is the photon stimulated desorption yield, G [photon/(s m)] is the incident synchrotron radiation (SR) photon flux, kB is the Boltzmann constant [J/K] and T [K] is the gas temperature; c ¼ rAmesh v=ð4LÞ [m2/s] is the distributed pumping speed, r is the capture factor for the pump including a pumping port and associated screening mesh, Amesh [m2] is the effective mesh area, v [m/s] is the mean molecular speed. u ¼ Ac$D [m4/s] is the specific vacuum vessel molecular gas flow conductance per unit axial length, Ac is the vacuum vessel cross-section; D is the Knudsen diffusion coefficient. Two solutions of equation (1) exist in the quasi-equilibrium state when the condition V dP/dt ¼ 0 is satisfied and also assuming that the parameters are independent of z. A vacuum vessel without a pumping port (when c ¼ 0) is described with equation:
q P z ¼ z2 þ C1a z þ C2a ; 2u
(2)
and a vacuum vessel with a non-zero distributed pumping speed (i.e. c > 0), for example a pumping port covered with a mesh, is described as a vacuum vessel with a distributed pump:
q P z ¼ þ C1b e c
rffiffiffi rffiffiffi c c z z u þC e u ; 2b
(3)
where the constants C1 and C2 depend on the boundary conditions. The effective pumping speed was calculated for each pumping port separately with a TPMC code and was used in the diffusion model as uniformly distributed along a length equal to the overall length of the pumping port. The vacuum vessel along the beam can in practice be considered as being divided into N longitudinal elements, each with c ¼ 0 or c > 0. Every ith element lying between longitudinal coordinates zi1 and zi will be described by equation (2) or (3) with two unknowns C1i and C2i. The inter-element boundary conditions are taken as Pi(zi) ¼ Piþ1(zi) (single-valued pressure) and vPi(zi)/vz ¼ vPiþ1(zi)/vz (zero net gas flow e assuming the conductances of the two
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elements are the same). There are several possible ways to write the boundary conditions for the first and the last elements. When the model includes the entire storage ring or its periodic parts, the periodic condition can be used (i.e. P1(z0) ¼ PN(zN) and vP1(z0)/ vz ¼ vPN(zN)/vz). However, during the design and optimisation work the periodic condition is not always fulfilled, and a simplification was applied where the first and the last elements have the same boundary conditions at both ends, i.e.: P1(z0) ¼ P1(z1) and vP1(z0)/ vz ¼ vP1(z1)/vz for the first element and PN(zN1) ¼ PN(zN) and vPN(zN1)/vz ¼ vPN(zN)/vz for the last one. The error due to simplified boundary conditions at the extremes of the modelled vacuum vessel has only a small influence on the calculated pressure distribution provided the first and the last elements are relatively short and the vacuum conductance of these elements is smaller than their pumping speed. These criteria are met at the location of vacuum pumps at the extremes of the arcs. In this case C1i ¼ C2i for i ¼ 1 and i ¼ N. Now for the N elements of the vacuum vessel we have a system of 2Ne2 equations with 2Ne2 unknowns, which can be easily solved with a numerical calculation package such as Mathcad. The above analysis is strictly correct only in the limit of axially symmetric long vacuum vessels of uniform cross-section. For some parts of Diamond storage ring, this is approximately the case. However, this 1D analysis could be far from reality in the wide dipole magnet vacuum vessel. To assure the validity of these calculations, corroborating TPMC simulations were performed for some elements of the Diamond vacuum vessel [2]. No significant differences were found between the results of the 1D analysis described above and the TPMC simulations for most of vacuum vessel elements; some minor differences were found for dipole vacuum vessels: up to 10% for longitudinally averaged pressure along the beam path and up to 50% for local pressure along the beam path. This comparison showed that the 1D analytical method was sufficiently accurate for optimisation of the pressure profiles and the average pressure during the design of the Diamond vacuum system. The 1D analytical method is much faster, more convenient and more flexible than TPMC for calculations where many iterations in input parameters are required. Results for the updated vacuum system design were already published [4,5]. 2.2. Input data All materials used to build accelerators, such as stainless steel or copper, desorb gas into the vacuum system. This thermal desorption determines the base pressure in the storage ring without beam (static pressure). Thermal desorption is described by an outgassing rate ht. The assumption based on experience from the Daresbury Synchrotron Radiation Source (information courtesy of R.J. Reid) was that for an ex-situ baked vacuum vessel which has been briefly vented to air and re-pumped, an outgassing rate of about 109 mbar l/(s cm2) for H2 and 1010 mbar l/(s cm2) for CO (in units commonly used in the vacuum community) will be reached after a few hours pumping, thereafter decreasing exponentially with additional pumping time. A value of outgassing rate two orders of magnitude lower should easily be obtained for carefully chosen and well-prepared materials after a few hundred hours of pumping at room temperature [7]. Since the cross-section of beam-gas interaction increases with atomic number squared [8] while the vacuum system conductance is greater for light gas species, the beam losses due to collisions with H2 and CO (two main gases presented in residual gas spectrum of accelerators) are quite comparable; therefore a single gas model with the CO equivalent can be used. The values used in the model are shown in Table 1.
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Table 1 Predicted and measured thermal desorption yields and average pressure without beam in the Diamond storage ring after various times. Elapsed time (days)
Dose (A h)
ht [mbar l/(s cm2)] used in the model
Average calculated pressure without beam [mbar]
Average measured pressure without beam [mbar]
ht [mbar l/(s cm2)] calculated from measurements
0 3.2 24.2 52.6 178.8 769.0
0 0.1 1 10 100 1000
1.0$1010 e e e 1.0$1012 e
1.1$108 e e e 1.1$1010 e
1$109 8$1010 5$1010 4$1010 3$1010 2$1010
9.1$1012 7.4$1012 4.5$1012 3.6$1012 2.7$1012 1.8$1012
In the presence of beam, in the initial stages of beam conditioning, the main source of gas is photon stimulated desorption (PSD) from vacuum-facing surfaces caused by synchrotron radiation (SR). PSD yields have been experimentally studied in many research centres. The most appropriate results for Diamond are in papers [9e12]. A detailed analysis of the available data was reported in Ref. [2,3]. In general, the PSD yield, hg, for a vacuum vessel decreases with photon dose proportionally to Da, where D [photons/m] is the integrated photon dose to which it has been exposed. At room temperature, the exponent a for very low photon doses is close to zero. After this initial period it then increases and reaches a constant value which lies somewhere between 2/3 a 1. Experimental data is lacking for large enough doses D required to simulation reasonable beam conditioning times at Diamond; the extrapolation of the data fitting curve assuming constant a had to be made over three orders of magnitude and may lead to a significant error. The pessimistic limit value a ¼ 2/3 [9] was used in the model to guarantee meeting the required vacuum specifications. A larger value of a ¼ 1 [10] would predict a significantly smaller value of PSD yield and lower operating pressure for longer beam conditioning time. The initial PSD yield of an ex-situ baked vacuum vessel as used at Diamond is higher than for an in-situ baked vessel but is much lower than for an unbaked vessel [9e11]. However, at very high photon doses there is no significant difference between baked and unbaked vacuum vessels [10]. Before applying these published values to the Diamond model one should compare the set-up and the samples used for the published studies with the materials and processing of the vacuum vessels used at Diamond. The experiments in [9] and [10] for example were performed with tubular samples with known diameter; the Diamond storage ring cross-section, in contrast, is non-circular and varies along the ring. To take this into account, the beam dose for the model was normalised using the ratio of the cross-sectional circumferences of the reference samples and those of the storage ring vacuum vessels, because the reflected and scattered photons and photoelectrons stimulate desorption from entire the cross-sectional surface area. The data in [11] was obtained from SR power absorbers made of oxygen-free highconductivity (OFHC) copper and these results were applied to model the Diamond crotch absorbers which are also made of OFHC copper. By applying these and similar principles it is possible to estimate the PSD yield as a function of photon dose for all the different vessel cross-sections found in the Diamond storage ring. Another complication is that different parts of vacuum system of Diamond storage ring are irradiated with different intensities of SR photon flux. That means that, during operation, the accumulated photon dose will be different for different parts of the vacuum system. The parts where the photon flux is higher are subject to a higher dose and therefore the PSD yield reduces more quickly with conditioning time. The model used here includes this effect and calculates the photon stimulated gas desorption flux q ¼ hgG/
(kBT) as a function of the longitudinal coordinate along the beam path. Finally, it is known that from manufacturers’ catalogues and lab measurements, the pumping speed of the sputter ion pumps is reduced by w30% between 108 and 109 mbar (see, for example Ref. [13]). This effect was also included in calculations. 2.3. Results of modelling The initial calculations were presented in Ref. [3]. However, the as-built Diamond storage ring design differed slightly from the assumptions made at that design stage as a result of engineering factors: the sputter ion pump ducts have an additional elbow that reduces pumping speed; titanium sublimation pumps, although installed, were not routinely activated and gas loads to and from attached front end and beamline vacuum systems were not considered. All these differences were implemented in a corrected model presented here. The results for thermal desorption are shown in Table 1, where the column 1 shows the elapsed time since first beam circulation at 3 GeV. Individual vacuum sections have different total pumping times as the storage ring was installed over a period of one year. Column 2 shows the beam dose. Columns 3 and 4 show corresponding values of thermal desorption yield used in the model and the average pressure calculated with these yields. The latter can be compared to the measured pressures in column 5; the ratio of measured and calculated pressures allows calculation of the actual thermal desorption yields achieved in Diamond storage ring (column 6). Modelling results for pressure in the presence of the beam are shown in Fig. 1 for two cases: the model published in the Design
Fig. 1. Longitudinally averaged dynamic pressure along the storage ring arcs as predicted from the model.
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Study [2] and a corrected model corresponding to the actually installed design. The normalized dynamic pressure Pd/I is plotted as a function of accumulated dose, where Pd ¼ P Pt, P and Pt are the average pressures along the arcs in the Diamond storage ring with or without the beam and I is the stored beam current. There is a significant (factor 3e5) difference between two modelling results for low accumulated doses that comes mainly from the difference in effective pumping speed used in the two models. However, the difference reduces for higher doses and is negligible (<25%) for 100 A h and still meets the design specification: 109 mbar at 300 mA circulating beam. Therefore modifications to the design after the Design Study did not significantly compromise the vacuum system performance in respect to the specification. As well as comparing calculations and measurements of the longitudinally spatially averaged pressure around the storage ring the model allows comparison of the pressure distribution measured at a number of discrete gauge locations. This will be discussed further in the following sections. 3. Analysis of the measured data The Diamond storage ring is well equipped with gauges and residual gas analysers (RGAs): four inverted magnetron gauges (MKS Instruments type 422) are installed in each of 24 storage ring arcs along the beam path, and two or more gauges used along each straight section used for the insertion devices, injection and RF. There are also typically 3 RGAs fitted per storage ring cell. The data from all gauges and RGAs were logged at appropriate intervals to a central archive via the Diamond control system. The layout of a standard Diamond storage ring cell is shown in Fig. 2. Gauges SRnnA-01 and SRnnA-04 (where nn is the cell number ranging from 01 to 24) are located respectively near the non-evaporable getter (NEG) pump at the start and end of each arc. Gauges SRnnA-02 and SRnnA-03 are located near the two dipole magnet crotch photon absorbers. Gauges SRnnS-01 and SRnnS-02 are located in the straight sections. The measurements for each gauge logged with an interval of 1 h were analysed following a standard procedure. Firstly the pressure with no beam, Pt, which depends on thermal outgassing, was analysed as a function of accumulated dose. The pressure readings varied somewhat from cell to cell around the storage ring. This is because the storage ring was installed cell-by-cell over a period of nearly a year and, therefore, different sections had been under vacuum conditions for very different times and had rather different thermal outgassing rates. To even out this variation, the average pressure was taken overall gauges in all 24 cells and this is shown in Table 1 for different accumulated doses. The dynamic pressure Pd was then calculated for all data recorded in the presence of beam using formula Pd ¼ P Pt, and normalized by the beam current I. Finally the average of similarlylocated gauges from each of the 24 cells was calculated, excluding outliers from faulty data. These measured pressures for each of six gauge positions (S1, S2, A1, A2, A3 and A4 in Fig. 2) were compared with pressures predicted by the model. The measured and
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predicted pressures for gauge position A2 are plotted in Fig. 3, where red crosses show the 24 cell average of Gauge SRnnA-02 measurements, green triangles show the pressure predicted by the model at the gauge position and blue circles are average calculated pressure along the storage ring (the same as the ‘corrected model’ in Fig. 1). The results for other gauge locations look very similar. The measured Pd/I data are 2e3 times lower than predicted values for low accumulated doses (less than 0.1 A h); all three plots converge at higher doses and differences can be neglected for doses greater than 100 A h. 4. Discussion Comparison of measurements from the Diamond storage ring with the model described in Table 1 demonstrates that an average specific thermal outgassing yield of about 1$1011 mbar l/(s cm2) was reached before the first beam was injected to the storage ring. In the last sections to be installed and which had been under vacuum for the least amount of time, agreement is better with a measured specific thermal outgassing yield of about 1$1010 mbar l/(s cm2). After an elapsed time of 769 days and beam conditioning dose of 1000 A h, the average specific thermal outgassing yield reduces by a factor of 5e2$1012 mbar l/(s cm2). From the available data, the relative influence of elapsed time and beam conditioning on this reduction cannot be separated. The values of specific thermal outgassing yield measured on Diamond storage ring can now be used with confidence for design of other ex-situ baked accelerators. There is good agreement between the predicted and measured values of pressure increase due to PSD and its dependence on beam dose. It can also be seen that the PSD yield reduces proportionally to D2/3, exactly as applied in the model (see Section 2.2). Local differences between predicted and measured pressures at the gauge location can be explained by shortcomings of applying a 1D model in situations where the pressure may vary across the width of a complex shape vacuum vessel such as a dipole vessel. Also there is uncertainty as to how far literature data on outgassing rates and PSD yields generally obtained from well-characterised materials is applicable to the technical construction materials used at Diamond. Furthermore it was necessary to extrapolate published material data by three orders of magnitude to higher beam dose. Another reason for this discrepancy is that all pressure measurements reported here were made with total pressure gauges, which have different sensitivities for different gas species but do not allow distinguish between them. It is also important to mention here that the model assumes the gas behaves in molecular flow similarly to CO, while the RGA indicates that the residual gas is dominated by hydrogen in the absence of stored beam but with significant contributions from CO, CO2 and CH4 during the beam conditioning process. In reality, the gas flow conductivity of the beam vacuum vessel and pumping ports, pumping speed of pumps and gauge sensitivity scales as M0.5 where M is the molecular mass of the gas. So uncertainties and changes in gas composition could
Fig. 2. Layout of 22.65 m long Diamond storage ring section (5.3 m straight plus achromat) used for the modelling showing the location of the pressure gauges S1 ¼ SRnnS-01, S2 ¼ SRnnS-02, A1 ¼ SRnnA-01, A2 ¼ SRnnA-02, A3 ¼ SRnnA-03 and A4 ¼ SRnnA-04. D1 and D2 are the two bending (dipole) magnets.
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predicted the behaviour of the Diamond storage ring correctly and accurately enough to develop and optimise the designs. The local dynamic pressures obtained from the model agree with pressures measured in the Diamond storage ring within a factor 2. This relatively small discrepancy for such a large, complicated vacuum system has four main contributions:
Fig. 3. Pressure vs accumulated dose. Comparison of modelling results and measurements for dipole vessel with gauge SRnnA-02.
1. A 1D model has been used which ignores the lateral extent of the vacuum vessel and cannot predict the local pressure as accurately as it predicts the longitudinal spatially averaged pressure. 2. The molecular flow model assumes the gas is CO equivalent instead of including the real gas species distribution. 3. Total pressure gauges have different sensitivity for gas species in vacuum system. 4. Vacuum vessel wall material properties may vary due to different manufacturers, cleaning and pre-treatments including bakeout and pumping time. References
also play a role in explaining the differences between the model and measured pressures. 5. Conclusions For the first time, predicted and measured pressures in an electron storage ring from beginning of operation up to more than 2000 A h beam dose were systematically compared. The contributions of thermal and photon stimulated desorption were analysed as a function of dose. The initial thermal desorption was correctly estimated in the model for the last installed section but overestimated for the average overall sections by a factor of 10. The average specific thermal outgassing yield w1$1011 mbar l/(s cm2) was reached before the first beam was injected into the storage ring, therefore this value can now be used with confidence for other ex-situ baked machines. After 1000 A h conditioning it reduces by a factor 5 only. The measured PSD yield reduces with accumulated dose proportionally to D2/3, exactly as applied in the model. These results prove that the applied PSD model and vacuum gas dynamic models
[1] Cox MP, Boussier B, Bryan S, Macdonald BF, Shiers HS. In: Proceedings of the 2006 European Particle Accelerator Conference (EPAC’06) June 2006. pp. 3332e3334. [2] Diamond synchrotron light source: report of the design specification. Warrington, Cheshire, UK: CCLRC, Daresbury Laboratory; June 2003. [3] Malyshev OB, Al-Dmour E, Herbert JD, Reid RJ. In: Proceedings of the 2002 European Particle Accelerator Conference (EPAC’02) June 2002. pp. 2571e2573. [4] Malyshev OB, Macdonald BF. Diamond internal report TDI-VAC-SR-REP-0001. Didcot, UK: Diamond Light Source; June 2003. 14 pages. [5] Herbert JD, Malyshev OB, Middleman KJ, Reid RJ. Vacuum 2004;73:219e24. [6] Cox MP, Boussier B, Bryan S, Macdonald BF, Shiers HS. J Phys Conf Ser 2008; 100:092011. [7] Calder R, Levin G. Brit J Appl Phys 1967;18:1459e72. [8] Chao AW, Tigner M, editors. Handbook of accelerator physics and engineering. World Scientific; 1999. p. 215. [9] Foerster CL, Halama H, Lanni C. J Vac Sci Technol A 1990;8:2856e9. [10] Herbeaux C, Marin P, Baglin V, Gröbner O. J Vac Sci Technol A 1999;17: 635e43. [11] Anashin V, Bulygin A, Kraemer D, Malyshev O, Mironenko L, Pyata E, et al. In: Proceedings of the 1998 European Particle Accelerator Conference (EPAC’98) June 1998. pp. 2163e2165. [12] Malyshev OB. The study of photodesorption processes in the prototypes of vacuum chambers for superconducting super colliders. Ph.D. thesis (in Russian); 1995. Novosibirsk, Russia. [13] Audi M. Vacuum 1988;38:669.