Vacuum 85 (2011) 1165e1169
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A transparent vacuum window for high-intensity pulsed beams Michael Monteil a, *, Juan Blanco a, b, Raymond Veness a a b
CERN, CH-1211, Geneva 23, Switzerland EPFL, CH-1015, Lausanne, Switzerland
a r t i c l e i n f o
a b s t r a c t
Article history: Accepted 7 December 2010
The HiRadMat (High-Radiation to Materials) facility [1] will allow testing of accelerator components, in particular those of the Large Hadron Collider (LHC) at CERN, under the impact of high-intensity pulsed beams. To reach this intensity range, the beam will be focused on a focal point where the target to be tested is located. A 60 mm aperture vacuum window will separate the vacuum of the beam line which is kept under high vacuum 108 mbar, from the test area which is at atmospheric pressure. This window has to resist collapse due to beam passage. The high-intensity of the beam means that typical materials used for standard vacuum windows (such as stainless steel, aluminium and titanium alloy) cannot endure the energy deposition induced by the beam passage. Therefore, a vacuum window has been designed to maintain the differential pressure whilst resisting collapse due to the beam impact on the window. In this paper, we will present calculations of the energy transfer from beam to window, the design of the window and associated mechanical calculations. Ó 2011 Elsevier Ltd. All rights reserved.
Keywords: Vacuum window Beryllium Particle accelerator FEM
1. Introduction The CERN’s TT66 vacuum beam line is designed to transport LHC type proton and ion beams to the HiRadMat facility. The beam is focused onto the objects to test at the HiRadMat experimental area. The beam line must be capable of providing a beam size between s ¼ 0.1 mm and s ¼ 0.2 mm at different focal point positions in the experimental area. The imposed functional specification [2], requires a vacuum window to isolate the beam line vacuum from the experimental area which is kept under atmospheric pressure at the interface to the beam line. This window has to maintain the required differential pressure, and also to cope with the repeated dynamic thermal load of the beam of 4.9$1013 protons per pulse at 1/18 Hz and 440 GeV. The beam properties at the window location are shown in Table 1.
2. Energy deposition In passing through matter, particles ionize and excite the atoms they encounter. A part of the beam energy E, is transferred to the matter. The energy lost by the beam in this way is called stopping power (dE/dx). Particles gradually lose energy in many small steps
while passing through matter. FLUKA [3] calculations were done in order to obtain the energy deposited by the HiRadMat proton beam in different materials commonly used for vacuum windows. The thickness of the window was chosen to be significantly smaller than the nuclear interaction length and radiation length in the material so that only ionization and excitation losses occur. Low-Z materials are preferable as the stopping power scales with Z. Table 2 shows the four candidate low-Z materials. Calculations were done for protons, as the energy deposited by ions is a factor of two smaller than for ions. FLUKA calculates the energy deposition on the window given the beam profile and the energy. Results were normalized per beam particle. Then the results were scaled with the intensity of the beam to reach the energy deposited by a maximal pulse of 288 bunches (Np ¼ 4.9$1013 protons). This energy was then analytically integrated using the heat capacity, to get the punctual and conservative temperature increase. Energies and maximum temperatures results are shown in Table 2. Among the four low-Z materials, only beryllium and Carbon Fibre reinforced Carbon (CeC) do not exceed the acceptable temperature, the value of which depends on the window material. The temperature distribution in the plane of the window perpendicular to the beam direction can be fitted by a Gaussian model as expected due to the beam profile; shown in Eq. (1)
* Corresponding author. Tel.: þ41 22 76 78693. E-mail address:
[email protected] (M. Monteil). 0042-207X/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.vacuum.2011.03.016
TðrÞ ¼ Troom þ ðTmax Troom Þ$e
1 $r 2 2$s2beam
(1)
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Table 1 HiRadMat beam properties at the window location. Parameter
Symbol
Protons
Beam energy Max. bunch intensity Maximal number of bunches per pulse Max. pulse intensity Bunch spacing Beam size RMS bunch length Pulse length Number of pulses per cycle Cycle length
E Nb nmax
440 [GeV] 497 [GeV] 1.7$1011 [protons] 7$107 [ions] 288 52
Np ¼ nmax$Nb 4.9$1013 [protons] 25 [ns] 0.5 [mm] 11.24 [cm] 7.2 [ms] tp 1 18 [s]
Dtb sbeam sz
Ions
3.64$109 [ions] 100 [ns] 0.5 [mm] 11.24 [cm] 5.2 [ms] 1 13,2 [s]
Table 2 Energy deposited by a HiRadMat proton pulse and associated maximum integrated temperature; results from FLUKA. Material
Energy [GeV/cm3/proton]
[ C]
CeC 1501G Beryllium PF-60 Titanium Grade 5 Aluchrom Ò
0.40 0.58 0.62 1.03
623 497 1411 1591
Table 3 Comparison between results from FLUKA and analytical results from the formula in Eq. (1). Source
Method
Temp. Max [ C]
FLUKA results Formula [4]
Hottest point (dE/dx) (total stopping power)
497 481
where r [mm], is the radius from the centre of the beam impact, Tamb [ C] the room temperature, Tmax [ C] the maximal temperature given in Table 2 and T [ C] the temperature at a radius r [mm] from the centre.
In addition, an analytical formula [4] shown in Eq. (2) was used to estimate the temperature increase from the total stopping power (dE/dx) [GeV/cm] and the beam profile (2ps2beam) in a material irradiated by a particle beam. Table 3 compares results from the analytical method that is more realistic, as it calculates a temperature over a defined volume (2ps2beamdx), to the results obtained using FLUKA results, that is punctual and thus more pessimistic. The analytical formula to evaluate the temperature rise in a material irradiated by a particle beam is:
DTinst ¼
Np dE $ r$dx 2$p$C$s2beam
(2)
Where DTinst, is the temperature variation, (dE/dx) is the stopping power of the beryllium, r [g/cm3] the beryllium density and C [J/g/ C] its specific heat capacity. The design of HiRadMat window will take into account the highest temperature Tmax ¼ 497 C, given by the numerical FLUKA analysis.
3. Conceptual design With respect to temperature considerations, CeC and beryllium are the only suitable materials for the window. For the selection of a vacuum window, other constraints apply. There is no UHV leak tight form of carbon existing in industry and beryllium is a fragile and toxic material with high restrictions on use at CERN. The proposed solution consists of using a 0.5 cm-thick (<< radiation length of 29 cm for CeC material) CeC plate (grade SIGRABOND 1501G from SGL Carbon) which is quite a porous material (coefficient of permeability of 5$102 cm2/s) to support the 103 mbar differential pressure load due to its high mechanical properties. A 0.254 mm-thick, leak tight, beryllium foil (grade PF-60 from Brush-Wellman) is laid on this CeC plate, thereby maintaining vacuum to 108 mbar. This foil is diffusion bonded on a ISO-CF
Fig. 1. Assembly of the window.
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Fig. 2. Geometry of the ANSYS model.
DN63 flange. The beryllium foil has been supplied as an assembly with the flange leak tight better than 1.0$109 mbar l s1. During the leak-detection test, the window has been plasticized leaving a residual convex shape of about 0.4 mm. The beryllium foil will be installed on the high pressure side of the window, since the outgassing rate of the CeC is low (1.33$108 mbar l s1 cm2 without bake-out and 1.33$1011 mbar l s1 cm2 with a 24 h-long bake-out at 300 C) [5]. The design is such that while under vacuum, the beryllium is partially flattered on the CeC plate. Fig. 1 shows the HiRadMat window design. To prevent any oxidation of the beryllium foil at high temperature, a 0.5 mm Ti þ 0.5 mm Nb coating has been made on the atmospheric side of the foil.
As long as the beryllium foil is partially supported by the thick CeC plate, the main load at the centre of the foil comes from the thermal stress, as presented in the following paragraph. 4. Mechanical design 4.1. Numerical study of thermal and pressure load stresses The window must withstand the DP ¼ 103 mbar differential pressure and the thermal stresses induced by the HiRadMat beam. A static finite element method was used to estimate stresses in the CeC plate and in the beryllium foil.
Fig. 3. Stress in the beryllium foil partially flattered on the CeC plate with a 105 Pa load.
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Fig. 4. Stress/strength ratio in the beryllium foil partially flattened on the CeC plate with a 105 Pa load.
This simulation was done in ANSYS Workbench v12.0.1, using APDL command lines to define element types, material properties and post-processing results. The geometry is presented in Fig. 2. The material properties model used for the beryllium foil is Multi-linear Kinematic Hardening (MKIN) with plasticity behaviour. Both MKIN data and CTE data are a function of the temperature T (r) given in Eq. (1) The mechanical stress induced under DP ¼ 103 mbar, in the foil which is partially laid on the CeC plate are presented in Fig. 3. Fig. 4 shows the ratio s (t)/Us (T) where, s (T) [MPa], is the stress in the beryllium foil at the temperature T [ C], and Us (T) is the ultimate strength at the same temperature. The mechanical stresses induced under DP ¼ 103 mbar, in the foil which is partially laid on the CeC plate with the thermal load induced by the HiRadMat proton beam are presented in Fig. 5. Fig. 6 shows the ratio s (t)/Us (T) where s (T) [MPa], is the stress in the beryllium foil at temperature T [ C], and Us (T), the ultimate strength at the same temperature.
Mechanical stress plots of the CeC plate are not shown in this paper. However, results show that the Tsaï-Wu coefficient for the CeC plate is 0.03 with pressure load only and 0.3 immediately after the beam passed through material. Table 4 presents the stress values. 4.2. Stresses induced by thermal shock-waves This paragraph will deals with thermal shock-waves into the beryllium window laid on the CeC plate using an analytical model [6]. The upper limits of the maximum central dynamic stresses are given by:
smax < 2
r0 E$a$DT ¼ 21MPa c$t0
(3)
Where smax is the maximal dynamic stress, r0 ¼ 0.5$103 m the heated region, c ¼ 15$103 m/s the speed of sound in beryllium,
Fig. 5. Stress in the beryllium foil partially flattered on the CeC plate with a 105 Pa load at the end of a HiRadMat proton pulse.
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Fig. 6. Stress/strength ratio in the beryllium foil partially flattened on the CeC plate with a 105 Pa load at the end of a HiRadMat proton pulse.
Table 4 Results from the FEM calculation. Component
Load
smax [MPa]
s (T)/Us (T)
Tsaï-Wu
beryllium foil beryllium foil CeC plate CeC plate
pressure pressure þ beam pressure pressure þ beam
354 381 3 32
0.69 0.88 e e
e e 0.03 0.3
t0 ¼ tp ¼ 7.2$106 s the heating period (or pulse length), R ¼ 0.035 m the radius of the window, E ¼ 303 GPa the elasticity modulus of beryllium, a ¼ 156 m/(m C) its thermal expansion coefficient and DT ¼ 472 C the instantaneous temperature rise. This is valid for a circular window where c$t0 > r0 and r0 < < R which is the case in this study. The upper limit of the thermal shock-wave stresses, estimated by Eq. (3) shows that the maximum central dynamic stress is negligible compare to the thermal stresses. Furthermore, in the HiRadMat design, the foil is laid on the CeC plate, which provides some support to the foil which makes the results of Eq. (3) a conservative estimate of the real dynamic thermal stress. 5. Conclusions The HiRadMat facility test will use a particularly high-intensity focused beam that no vacuum window currently present at CERN
can endure. In this paper, the different design steps from the beam properties to the mechanical calculation to finally reach a final design of a vacuum window which will withstand the beam and the differential pressure load of 105 Pa were described. The highly transparent CeC plate supports the fragile beryllium window and reduces the consequences of any failure of the beryllium. This window will be manufactured by the end of 2010 and installed at the beginning of 2011. Acknowledgements The authors would like to thank all members of the HiRadMat project team for their help. References [1] Assmann R, Bertarelli A, Efthymiopoulos I, Goddard B, Hessler C, Markiewicz T, et al. Specification for a test facility with high power LHC type beam, http://lhccollimation-project.web.cern.ch/lhc-collimation-project/HiRadMat/tt60-specout.doc. [2] Hessler C. “Design requirements for the TT66 exit window”, CERN-EDMS1078222. [3] Fassó A, Ferrari A, Ranft J, Sala PR. “FLUKA: status and prospective for hadronic applications”, Proc. MonteCarlo 2000 conference, Lisbon, 2001. [4] Ferrari A, Ziemann V. EUROTeV-Report-2008e009. [5] Deville T, Versolatto B. “Mesure de degasage de composites Carbone-Carbone”, CERN-LHC-VAC-TN-98e22. [6] Sievers P. “Elastic stress waves in matter due to rapid heating by an intense high-energy particle beam” CERN-CM-P00065112, p. 13.