Very Large Hadron Collider Beam Screen Design. Preliminary Investigation of Space Requirements

Transcription

1 TD July 1999 Very Large Hadron Collider Beam Screen Design Preliminary Investigation of Sace Requirements P. Bauer, C. Darve, T. Peterson Fermilab, Technical Division, T&D Deartment B. Jenninger Cern -Division VAC Grou Keywords:, beam screen, synchrotron radiation, suerconducting magnets, suercritical helium 1) Introduction As art of the R&D for a Very Large Hadron Collider (1 TeV), high field magnets are being designed at Fermilab. A ten- or more fold increase in synchrotron radiation heat load from the design to a hyothetical design is a serious issue, which will definitely require searate vacuum and beam-screen studies. However, it would be desirable for the first magnet rototyes to have a cold-bore, which can match all ossible vacuum and heat evacuation systems being brought forward by such studies. We therefore scaled the current state of the art beam screen design to a 5/5TeV machine. The aim of the study is to determine if in rincile such a beam-screen design could coe with the strong heat loads. In case the design has to be scaled to the higher heat load, the question of the sace requirements of such an uscaled beamscreen design arises. 1

2 2) Beam Screen Design The high-energy roton beams of the Large Hadron Collider (), a suerconducting accelerator cooled by suerfluid helium at 1.9 K, will induce heat loads into the cryogenic system through several mechanisms: synchrotron radiation from bending the beam image currents in the resistive wall of the tube (featuring the anomalous skineffect [1] ) inelastic scattering by residual gas molecules acceleration of hotoemitted electrons by the beam electrical field ( electron cloud instability or multiacting [2] ). These heat loads will be interceted by an inner shield (beam screen, see figure 1), searated from the beam tube. The double ie design [3] imroves the Carnot efficiency of the cooling scheme because the beam screen is ket at a higher temerature (5 K-2 K) than the magnet cold bore (1.9 K). Furthermore, being at a higher temerature it acts as an intermediate temerature baffle for the cryoum constituted by the 1.9 K surface of the magnet cold bore, thus reventing desortion of the traed gas molecules and avoiding breakdown of the vacuum. The screen is cooled by forced flow (1-2g/s) suercritical helium (3 bar, 5-2 K) in two nonmagnetic stainless steel tubes, attached to the beam screen on to and bottom. The beam screen design [4] is based on a 1mm thick non-magnetic stainless steel tube with a round cross-section, flattened to and bottom. The sace between it and the surrounding 1.9 K cold bore is just sufficient for the cooling ies. The beam screen is centered within the cold bore by suorts. To minimize resistive wall heating the interior surface of the screen is covered by a thin (~5 µm) collaminated (by cold rolling) high urity coer layer. The uming slots are rounded and randomly distributed to Figure 1: The beam screen [3] ; avoid increased beam- 1 W. Chou, F. Ruggiero, Anomalous Skin Effect and Resistive Wall Heating, Project Note 2, Set O. Groebner, Beam Induced Multiacting Proceedings of the 1997 Particle Accelerator Conference, Yellow Book, Design Grou, CERN/AC/ P. Cruikshank, K. Artoos, F. Bertinelli, J.-C. Brunet, R. Calder, C. Camedel, I. Collins, J.-M. Dalin, B. Feral, O. Grobner, N. Kos, A. Mathewson, L. Nikitina, I. Nikitine, A. Poncet, C. Reymermier, G. Schneider, I. Sexton, S. Sgobba, R. Valbuena, R. Veness, Mechanical Design Asects of the Beam Screen, Project Reort 128, July

3 couling imedance and resonance effects. The extruded stainless steel cooling tubes are continuously laser-welded to the beam screen. Intensive R&D is dedicated to: the thermal behavior (cryogenic tests under heat load, flow instabilities), material studies (low suscetibility materials, welding technique, coer inlay technique, insulating suort materials), mechanical behavior of the beam screen (twisting, deformation due to weigth, contraction during cool-down, reaction to quench ressure), mirror current studies and vacuum issues (gas-desortion, cryouming). 2a) Heat Load The heat load data ublished by Cern [5] are listed in the following table (Table 1): De. on E De. on I Average nominal Average ultimate Peak nominal Peak ultimate Synchrotron radiation E 4 I Resistive wall heating I Multiacting hotoelectrons E I Total Table 1: Estimation of heat load into the beam screen [5]. Nominal conditions refer to E=7 TeV, I=536 ma, ultimate conditions are: E=7 TeV, I=848 ma. The maximum ermissible average heat load er beam is aroximately 1 W/m for the design. Multiacting has recently been identified as a serious roblem, which may result in heat loads exceeding the design limit. 3) Scaling the Beam Screen to the Heat Load 3a) Estimated heat loads of a configuration The heat load calcuations are based on the following machine characteristics: Energy er roton E 5 TeV Peak Luminosity L 1 34 cm -2 s -1 Circumference C 89 km Diole Field B 12.5 T Number of Bunches 2 Initial Nr. of Protons er Bunch 1.25x1 1 Number of rotons er beam N rot 2.5x1 14 Bunch Sacing 4.45m Beam Current (N rot ce/c).135a Table 2: machine arameters [6] 5 Project Reort 212, Suercritical Helium Cooling of the Beam Screens, E. Hatchadourian, P. Lebrun, L. Tavian, Cern, July M. Syhers, Accelerator Physics Issues in Future Hadron Colliders, Proceedings of the Symosion at the 1998 Annual Meeting of the American Physical Society in Columbus Ohio 3

4 The heat loads can be scaled to the values through their deendence on article energy, circumference (or magnetic field) and beam current using the following scaling laws for: -the synchrotron radiation heat load SR SR E = E 4 R R 2 I I, -the resistive wall heating heat load (no anomalous skin effect included and assuming that the bunch length is equal in the and the configuration) RW RW I I 2, -and the hotoelectron contribution (asuming that the hotoelectron yield is not increased by the higher critical hoton energy in the and with some uncertainty regarding the energy deendence - which could be as well ~E 2 or ~E 4 ). PE PE E = E I I 3 R R 2. Using these scaling laws combined with the machine/beam arameters in above table, the exected heat loads in a machine can be comuted. De. on E De. on R De. on I Average nominal Synchrotron radiation E 4 1/R 2 I 7.8 Resistive wall heating I 2.15 Multiacting hotoelectrons E 1/R 2 I 3.1 Table 3: Heat loads on a hyothetical -tye beam screen. Values are scaled from the average nominal conditions in Table 1. The uncertainty concerning the hotoelectron contribution is big. The synchrotron radiation is clearly the dominant source of heat load. Eventually it is feared that multiacting could become as well a dominant source of heat load in a tye machine. Furthermore a design based on a higher luminosity than 1-34 cm -2 s -1 will result in an even higher synchrotron radiation heat load. 3b) Cooling the beam screen The following describes the simlified steady state thermal model we use to describe the beam screen cooling. A chain of thermal resistances reresents the heat ath from the oint where the synchrotron radiation hits the screen to the cryogenic system. The arameters dominating the temerature rofile across the heat ath is the thermal 4

5 imedance of the steel between the coer on the inside of the beam screen and the cooling tube, and the forced convection heat transfer in the flowing helium (Figure 2). It is suosed that all other contributions (variations in the cross-section of the heat ath, the thermal imedance of the thin coer layer on the inside of the screen, the boundary layer Kaitza resistance) to the total temerature dro are negligible. Additionaly it has to be verified that the cooling caacity of the forced flow suercritical helium volume always matches the heating ower coming from the beam screen. We assumed that a unit length of the cryogenic system cooling the beam screen is 2 m. The helium temerature will vary along this length between T in and T out. Suerimosed to the longitudinal temerature rofile there will be a radial temerature rofile, which is the driving force of the convective heat transfer into the cryogen. We imosed that the longitudinal temerature difference in the cryogenic system along the 2 m should remain smaller or of the order of 3 K. Furthermore we imosed that the ressure dro along this length should remain within 25% of the system ressure. Presumably the strongest simlification lies within the fact, that we calculated the solutions at a oint along the line where the coolant temerature is the average of T in and T out. The stronger the longitudinal temerature difference in the system, the less valid is the model for the extremities of the cooling circuit. Q cond Q conv P bs R SS R He P He T bs T ct T Figure 2: Simlified thermal network model for the beam screen cooling: The incoming heating ower P bs is conducted through the steel ath (R SS ), transferred into the helium through forced convection (R He ) and finally transorted in the helium P He. The key temeratures along the ath are T bs, the beam screen temerature, T ct, the inner wall temerature of the cooling tube (and aroximately the radial eak temerature of the helium) and T the average helium temerature along the cryogenic system. 3c) The Otimum Beam Screen Temerature Prior to the calculation of the required beam screen cooling caacity, the thermodynamic otimum for the beam-screen or coolant temerature at the given rate of heat deosition was calculated. Therefore the ower er unit length of beam tube was comuted for beam screen and beam tube (considering conductive and radiative heat exchange) and both functions multilied by a Carnot-efficiency factor taking into account 5

6 the temerature of the screen and the tube. The cold bore (cb) temerature T cb was set to 4.2 K, the beam screen temerature T bs was chosen to be the free variable. d dt ( T ) tot bs 1 = tot = bs ( Tbs ) f ( T ) + cb( Tbs ) f ( Tcb ) f ( T) cb = T R T T η ( T ) C ( T T ) + C ( T T ) ( T ) = ( T ) bs W m = 1 bs cb 2σ bs cb bs bs The owers are in terms of Watts er meter of beam tube, T R is the room temerature, η the efficiency of the refrigerator (assumed to be.3), f(t) the Carnot-efficiency for refrigerators, C 1 a geometrical constant ( W/m/K 2.34 ) as measured at Cern for the suortless ( touching ) beam screen design [7], C 2 a geometrical function containing the emissivity of two arallel surfaces. is the exected heat load on the beam screen (see Table 3). P tot as a function of beam screen temerature is shown in the next lot. In the calculation of the Carnot efficiency of the beam screen cooling the initial temerature of the cryogenic fluid was assumed to be T bs -2K. cb bs 3K er m of magnet beam tube - cold bore conduction cooling thermal radiation 4.2 K beam screen beam screen temerature [K] Figure 3: Estimation of the total cooling ower (at room temerature) versus beam screen temerature (the cold bore temerature was fixed to 4.2 K) for a rojected beam screen heat load of 8 W/m. 7 D. Bozzini, P. Cruikshank, Ch. Darve, F. Dolizy, B. Jenninger, N. Kos, D. Willens, Heat Transfer Measurements on Beam Screens with and without Suorts, techn. Note - VAC in rearation, June

7 The thermodynamic otimum temerature is at a broad minimum around 1 K. Obviously the temerature of the coolant (which is in fact the relevant temerature at which the ower extraction occurs) is different from the beam screen temerature. Since the beam-screen temerature and the helium temerature are couled (see Figure 2), we are not free to choose them indeendently. Therefore it is required that the beam screen temerature and the helium temerature T are both within the broad minimum of the P tot curve. The tyical temerature difference T bs -T is roughly 2 K. Another asect of this calculation is that the total cold-bore heat load is mainly generated in the magnets (through beam- and raming loss) or through static heat leaks into the cryostat. The heat transferred from the beam screen to the cold bore is usually only a fraction of that heat load (tyically in the order of 4 mw/m). Assuming an additional.2 W/m cold bore heat load coming from the magnet oeration adds an offset of 5 W/m to tot in Figure 3. To kee the resistive wall heating load contribution small we rejected solutions with T bs >5 K (which is indeed an arbitrary number). Taking into account a tyical temerature difference of 2 K between the beam-screen and the incoming coolant, the beam-screen cooling will cost roughly 2 1 kw/m (~2 MW over the total ring) of lug in refrigeration ower. This figure corresonds to the double of the total refrigeration ower need of the. Although some solutions of the cooling roblem will be roosed in the following, they will not remove this issue of the tremendous cost of such a heat load at low beam screen temeratures. 3d) Results of the Modeling To solve the cooling roblem we sought a common solution to the basic set of equations mentioned above: a continuity equation for the heat flux from the sot hit by radiation to the cooling system and a global energy balance equation. The heat flux equation demands that the heat flux from the hot sot to the cooling tube Q cond and the flux being transferred into the helium Q conv meet at the incoming level of heat flux given by the beam screen heating ower P bs. The conductive heat transfer in the beam screen is of the Fourier-tye, using an integrated stainless steel thermal conductivity (k SS ) and a geometrical factor (S is the cross-sectional area of the heat ath over the full length of the beam screen cooling system), L the length of the beam screen cooling system (2 m) and l the length of the heat ath). Q cond T bs S W = k SS ll m T ct ( T) dt The cooling heat transfer-correlation is of the forced convection tye with the helium in the suercritical state. It is assumed that the flow is turbulent. The average helium temerature T and the eak temerature (assumed to be the wall temerature T ct ) are variables. N is the number of -tye cooling ies (design: 4.5 mm od,.4 mm wall thickness), A ct the inner cooling tube wall surface over the full length L of the cooling system, the heat transfer coefficient h calculated from the Nusselt-number at the initial helium temerature and the helium heat conductivity k. The contributors to the Nusselt number are the density ρ, the viscosity µ, the flow velocity ν, the hydraulic diameter of 7

8 the cooling tube (which is the inner diameter d ct ), the secific heat c and the heat conductivity k. v ( T) Q m = A ρ Act = N h L ( T) N s m conv ct ( T ) k ( T ) h = Nu d ct W m ( T )( T T ) Nu =.23Re Re = ρ Pr = µ d.8 Pr ct ( T ) v µ ( T ) c ( T ) ( T ) k( T ).4 The energy balance equation requires that the heat deosit on the beam screen has to be at least equal to the heat removal caacity of the helium. The heat removal caacity of the helium is calculated from the mass flow rate dm/dt, the temerature difference over the full length of the cryogenic system T out -T in, and the secific heat c, taken at the average longitudinal helium temerature in the system (T ). He = dm c dt 1 L W m ( T )( T T ) out in The solution is found iteratively from a first guess of N, dm/dt, T out, T in, T ct and T bs by satisfying the following conditions: Q conv (T ct )=Q cond (T ct )= bs < He with T ct being in agreement with its inut value T bs >T ct >T out bs ( Tin Tout ) L dm c T T T ( ) in out 2 L m ( ) dt mk ressure dro along the 2 m ie is smaller than 25% of the system ressure T bs <5 K T in as high as ossible to imrove thermodynamic efficiency The geometrical arameters are ket as in the design. A lot showing a ossible solution is shown in Figure 4. 8

9 5 45 cond 4 SS He Power bs onv He T ct [K] Figure 4: A ossible solution for the beam screen cooling (D in Table 5). Heat conduction along beam screen cond, forced convection heat transfer to helium conv, Heat load on beam screen bs and heat transort caacity of the helium He, all in W/m, as a function of the cooling tube wall temerature. The list of solutions in Table 5 (A-D) is not comlete. Only a few solutions are technologically feasable. It turns out that the most critical art of the oeration is the heat absortion caacity of the cryogenic system. T in T out T bs T ct T P D dm/dt N [K] [K] [K] [K] [K] [bar] [torr] [g/s] * A B C D Table 5: Possible solutions to the beam-screen cooling roblem. T in is the helium entry temerature, T out is the helium exit temerature (refering to the beam screen cryogenic system of length L=2 m), T bs is the beam screen temerature, T ct is the wall temerature of the cooling tube, T is the average helium temerature in the center of the tubes, P and D are the ressure and the ressure dro in the 2 m cryogenic system, dm/dt is the helium flow rate, N the number of cooling tubes (refering to tye cooling tubes with id=3.7 mm), * The first row refers to the design (with a heat load of <1 W/m). A is a baseline -solution. B, C and D are otimized for high T in (B), low beam screen temerature (C) and a small number of cooling tubes (D). All otimized solutions reach the technological limits in the other arameters. T ct 9

10 An excessive rise in helium temerature (limit ~.2 K/m) has to be avoided as well as a strong ressure dro. The cooling caacity of the system can be imroved in many ways: by increasing the number of cooling tubes, lowering the entry temerature of the helium, increasing the flow rate or increasing the oerating ressure (to kee the helium density high). All solutions in Table 5 oerate at the limit of technological feasibility: either very high flow rates exceeding 1 g/s, a big number of channels (>4), low helium temeratures or high beam screen temeratures are required. Other ossibilities to imrove the heat transfer correlation have not been considered here (e.g. the use of liquid hydrogen as cryogen). The use of suerfluid helium, although temting because of an in imroved heat transfer correlation, is not reasonable because of the low Carnot-efficiency at the temeratures below T λ. 3d) Sace Requirements for a Beam Screen Figure 6: Tye A (table 5) beam screen design: 8 tubes (3.7 mm id / 4.5 mm od), screen (44 mm id / 46 mm od) and cold bore (49 mm id / 52 mm od); The baseline design (A), resented in Table 5, oerates at a rather low T in, a relatively high T bs and still needs 8 -tye cooling tubes to coe with the synchrotronic heat load. Any otimization with resect to thermodynamic efficiency (increasing T in ) or decreasing T bs immediately requires a better cooling erformance. Therefore it is advisable to roject a number of tubes of 1 or even higher. Roughly estimating the sace requirement for one -tye cooling tube to ~2 mm 2, such that 1 tubes would require at least 2 1 mm 2. The extruded cooling ies (4.5 mm od) are considered as the limit of technology and therefore any further miniaturization has not been considered. The suortless beam screen design (49 mm cold bore id) has a total of 19 mm 2, with 15 mm 2 being available on to and bottom. The 2 times 4 cooling tubes could fit into these cavities. As well the 15-tube solution B could fit. A similar calculation for a hyothetical 45mm id cold bore magnet (36 mm vertical beam-screen dimension) reveals that the cavity has 83 mm 2, which can at best case house 2 times 4 tubes. It is not clear to which extent the filling of this cavity interferes with the cryoum-function. However, it is advisable to use only one duct having the shae of the cavity between beam screen and cold bore. The more efficient use of sace could make a 1 tube 45 mm bore design ossible. Furthermore, good surface to volume ratios can be achieved this way. The only way to oerate a -tye beam screen in a magnet with a smaller bore (<5 mm) is through the use of suercritical helium at higher ressure (see solution D). The hoo stress in a 2 bar -tye cooling tube would be ~2 MPa, which is tolerable. 1