The quadrupole magnets in the CLIC Test Facility II (CTF2) incorporate a water cooling circuit. In the frame-work of the CLIC stability study, the mechanical vibrations of the magnets were measured for different flows of cool-ing water. We present the results and compare them with simple theoretical estimates. It is shown that the vibra-tion requirements of the Compact LInear Collider (CLIC) quadrupoles with cooling water can basically be met

Assmann, R W

Coosemans, Williame

Redaelli, S

Schnell, Wolfgang

CERN Document Server

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN-SL DIVISIONCERN-SL-2002- 040 (AP)The Effect of Cooling Water on Magnet VibrationsS. Redaelli ,R.W. Aßmann, W. Coosemans, W. SchnellThe quadrupole magnets in the CLIC Test Facility II (CTF2) incorporate a watercooling circuit. In the frame-work of the CLIC stability study, the mechanicalvibrations of the magnets were measured for different flows of coolingwater.We present the results and compare them with simple theoretical estimates.    It is           shown that the vibra-tion requirements of the Compact LInear Collider (CLIC)quadrupoles with cooling water can basically be met.8th European Particle Accelerator Conference, 3-7 June 2002Paris, FranceCLIC Note 531Geneva, Switzerland26 June, 2002SL/DIV RepsTHE EFFECT OF COOLING WATER ON MAGNET VIBRATIONSS. Redaelli   , R.W. Aßmann, W. Coosemans, W. Schnell, CERN, Geneva, SwitzerlandAbstractThe quadrupole magnets in the CLIC Test Facility II(CTF2) incorporate a water cooling circuit. In the frame-work of the CLIC stability study, the mechanical vibrationsof the magnets were measured for different flows of cool-ing water. We present the results and compare them withsimple theoretical estimates. It is shown that the vibra-tion requirements of the Compact LInear Collider (CLIC)quadrupoles with cooling water can basically be met.1 INTRODUCTIONStabilization issues are one of the main concerns for thenew generation of Linear Colliders. For instance, toler-ances for uncorrelated RMS vertical motion above  Hzfor the linac quadrupoles of the Compact LInear Col-lider (CLIC) [1] are   nm [2]. The circulating waterused to cool the magnets is a source of mechanical vibra-tions. In the framework of the CLIC Stability Study, mea-surements have been done to quantify this effect for thequadrupoles of the CLIC Test Facility II (CTF2) [3], whichhave a similar design to the ones foreseen for the CLIClinac. In this paper we present the preliminary results ofquadrupole vibrations versus water flow. These measure-ments have been done by means of the active stabilisationsystem 	 , described in details in [4]. This sys-tem is used to isolate the motion of the quadrupole fromthe ground motion, but is not capable of damping vibra-tions generated by the quadrupole itself. It is thus suitablefor studies of water induced vibrations. Other studies aboutthe effect of the circulating water on RF structures havebeen done at SLAC, as reported in [5].2 EXPERIMENTAL SET-UPA scheme of our experimental setup and the cross sectionof the CTF2 quadrupole [6], with its transverse dimensions,are given in Fig. 1. Each quadrupole is 80 mm long, 6.7 kgweight and has four copper coils made of six rectangularcables, with a 3 mm diameter hole for the cooling water tocirculate. Each quadrupole has one feeding channel. Twomagnets forming a doublet sit on a common support plateand have independent water connections. The doublet usedin our measurements was connected to the regular Genevatap water system (pressure of about  bar). The water wasfirst brought from the tap to a 4 channel manifold and thento the quadrupoles with tubes of different diameter (seeFig. 1). The water volume rate was measured with a pre-cision of  %. The maximum water velocity in quadrupolePhD student of the University of Lausanne, Institut de Physique desHautes Energies (IPHE), Switzerland.L=6md=13mmL=1md=8mm       ﬀle on Stacis2000Geophonesﬁ ﬂ ﬃ   ! " #$&%('*)+),- ../1032 4 5687 93:<;2;=9> 03?9Figure 1: Cross section of the CTF2 quadrupole with itstransverse dimensions. In our measurements we used aquadrupole doublet installed as shown in the scheme.pipes was of about  m s @BA (the nominal value for the CTF2quadrupoles is C D m s @EA [6]).The doublet was fixed directly on top of a honeycombtable, which was supported by actively stabilised feet (seeFig. 1) [4]. Three triaxial geophones of the type describedin [4] ( FG Hz to HJI Hz frequency range) were fixed ontop of the doublet, on the table and on the floor. Geophonesprovide a measure of the mechanical vibration velocity ver-sus time. The power spectral density of the displacementsas a function of frequency, KMLONBP , is calculated from the dis-crete velocities. The RMS motion above a given NRQ is thenobtained as the integral of KMLONBP from NRQ to HRI Hz. Themeasurements were taken over night, to have the quietestbackground conditions. Data were acquired with a sam-pling time of ST SUSH s for about  minutes and the resultswere averaged over subsamples of I s.3 SIMPLE THEORYWater induced vibrations are thought to be induced bythe onset of turbulence in the water in the pipes. For alaminar motion, no vibrations should be generated sincethe water velocity at the internal wall of the pipe is zero.To estimate the water induced vibration the simplified ap-proach of [7] and the results of [8] are referred to. TheReynold’s number is defined as VXWZY\[^]J_`, where a isTable 1: Some parameter of the pipes at turbulent onset.Pipe VXW b [m] Flow [l/h] Nc [Hz]Tap d Manifold DUSeSUS ST SHR RfT  JS* IManif. d Quad DUSeSUS ST SUSeg  ST  DHhC iQuadrupole DUSeSUS ST SUSe RITj RiUgthe water velocity, b the pipe diameter, k = JSUl kg m @+l andm=ST gUinRS @+l kg m @BA s @EA the water density and dynamicviscosity. Turbulence occurs at around VoW =DUSUSeS , depend-ing for instance on the roughness of the pipe surface, onthe pipe shape and on the status of the water upstream ofthe pipe. The water motion will be assumed to be laminarupstream and downstream the pipe under consideration.Turbulent motion is characterised by domains where thewater has an eddy-like motion. These domains move withvelocity a and have the typical size of order of magnitudeof the pipe radius [8]. The lowest induced vibration fre-quency is expected to be of the order of NcpYqasrUb , whichis a frequency associated to coherence domains of lengthequal to the tube radius. In Table 1 the values N c at theturbulence onset are given for the different pipes of our ex-perimental setup (see Fig. 1). The estimate of the minimalvibration frequency N c gives the order of magnitude of thefrequency window where turbulence effects are expected.Here, the results from [7] are used to estimate turbulenceinduced quadrupole motion. The pressure drop along thepipe depends on aut as vxw = _y[zt]{}|, where{is the pipe lengthand |~ ST HJf*VXW@EA< =ST S  is obtained from empirical for-mulae [7]. Per quadrupole coil the value vxw =STjJf bar isfound. vxw equals the average fraction of energy densityconverted to irretrievable turbulent kinetic energy, kterD( is the instantaneous velocity). Assuming isotropy of tur-bulence and adding in quadrature the contributions of eachcoil and quadrupoles, the following expression is obtainedfor the RMS motion in the vertical  direction:RMSYq  c  qbDwaterŁTot|fwhere  water= RDT f g is the pipe water mass,ŁTot the totalmass of the object under investigation,  c= and  q=D thecoil and quadrupole number. In the pessimistic assumptionthat all the energy in concentrated around the Nc =eiU Hz (ateS l/h), for one isolated doublet the value  RMS ~ DJS nm isfound. As the doublet is rigidly fixed on the table, it seemsa better choice to define Ł Tot~hJSUS kg, which leads toRMS ~D nm.4 RESULTS OF THE MEASUREMENTSIn Fig. 2 and 3 typical power spectral densities of ver-tical displacements of the doublet are given for differentfrequency ranges and water flows. Measurements were re-peated on different days and showed a good reproducibility.The KML(NBP peaks of the doublet with no circulating water0 10 20 30 40 50 60 7010−1010−910−810−710−6Frequency [Hz] P(f) [µm2 /Hz]0 l/h   12.5 l/h45 l/h  55 l/h  Figure 2: Power spectral density of vertical displacementsvs.frequency as measured on top of the CTF2 doublet.100 150 200 250 30010−1210−1110−1010−9Frequency [Hz] P(f) [µm2 /Hz]0 l/h 40 l/h70 l/hFigure 3: Power spectral density of vertical displacementsvs.frequency as measured on top of the CTF2 doublet.are mostly induced by floor motion, damped by a factorbetween JS and JSUS by the stabilising support [4]. In thevertical direction a new peak at around i Hz is induced bystructural resonances of the quadrupoles.The JD* I l/h flow KMLONBP of Fig. 2 is superimposed on thezero flow line. This reflects the threshold nature of the tur-bulence onset. Turbulence is found for flows above aroundJI l/h only. The data of Table 1 suggest that the main sourceof turbulence in the few tens of Hz frequency range is thepipe from the tap to the manifold. The quadrupole pipes areexpected to affect frequency DUSeS Hz. The pipes from theswitch to the quadrupole can be important for flows aboveS l/h.Above the turbulence threshold, two main effects in-duced by the circulating water are observed. (1) Thereleased energy increases the overall noise level of thequadrupole vibrations. The existing peaks of KML(NBP get con-siderably amplified. This is for instance the case of thepeaks below RS Hz and for the one at around UhRS Hz (Fig. 2and 3). (2) A number of new peaks arise, which are notTable 2: Integrated RMS displacements above  Hz, DUS Hzand fUS Hz on floor, on doublet rigidly clamped to a hJSeS kgtable, for zero and operational water flow.Vertical displacementsN Floor Doublet DoubletS l/h US l/hHz * feD nm ST iUD nm C eS nmDUS Hz C Dei nm ST DH nm S*&hnmfUS Hz S* Sh nm ST SUI nm S* Sef nmHorizontal displacementsHz D* e nm ST UI nm C e nmDUS Hz S* nm STjJg nm S* geS nmfUS Hz S* Snm ST Snm S*&eh nmpresent without turbulence. This is the case for a strongpeak at JI Hz (appearing above  I l/h) and for broad peaksin the DUI - I Hz frequency range (see Fig. 2). In the higherfrequency range these features are even more remarkable:amplifications of the zero flow vibration level of up to JSeSUSand more are clearly shown in Fig. 3. Three new peaks ap-pear at~iUS Hz,~RgUS Hz and~DhJS Hz, both in ver-tical and horizontal directions, whose amplitude increasesfor increasing water flows. However, the vibrations abovefeS Hz contribute less than ST D nm to the total integrated mo-tion (see below).In Table, 2 some absolute values of the integrated RMSmotion of the doublet are given for  Hz, DeS Hz and fUS Hzand compared with the motion of the floor. For the CTF2operational water flow of US l/h, the vertical RMS motionabove  Hz is C  nm, which meets the limit tolerance forCLIC [4]. Similar values are found for the horizontal dis-placement, where the tolerance is less demanding. Thepure effect of the water is given by the difference in quadra-ture of the cases with and without flow. Above  Hz weobtain ST i nm, which is comparable with the theoretical es-timate assuming that the doublet and the table move as awhole. The water induced motion is strongly dependent onthe water flow. In Fig. 4 we show vibrations versus waterflow for different minimal frequencies. We find a maxi-mum vibration level at around fUS Hz. Interestingly, the vi-bration levels are lower at even higher water flows.Vibration measurements of a doublet mounted on itsCTF2-like alignment support, which was fixed on the sta-bilised table, have also been performed. The preliminaryresults show that the horizontal RMS motion above  Hzcan be amplified by a factor of D and more. A supportinternal resonance at h Hz [4] is considerably amplifiedby turbulence and is the main contribution to the increasedmotion. The vertical direction is not much affected by thealignment support, as also confirmed by in-situ measure-ments of the CTF2 quadrupoles.5 CONCLUSIONSPreliminary results of water induced vibrations of aCTF2 quadrupole doublet have been discussed. Measure-0 10 20 30 40 50 60 7000.511.522.533.54Water flow [l/h]Vertical RMS motion above  f min [nm] fmin = 4 Hz  fmin = 10 Hz fmin = 20 Hz fmin = 60 HzFigure 4: Vertical RMS motion above  Hz, JS Hz, DUS Hzand fUS Hz vs. water flow.ments have been done at constant pressure and in a widerange of water flows. Turbulence was found to be a thresh-old phenomenon that appears for water velocities in thequadrupole pipes above ST f m s @BA and induces an increaseof the magnet vibrations. The main source of the low fre-quency vibrations (up to fUS Hz) seems to be the turbulenceonset in the pipes feeding the quadrupoles rather than in thequadrupoles themselves. They are the main source of theoverall magnet RMS motion. Vibrations up to fUS Hz arealso the typical range of magnet and support internal reso-nances, which can be considerably enhanced by the energyreleased in water turbulent motion. The simplified theoryof [7] seems to give a good rough estimate of the frequencyrange of the turbulence induced vibrations and the order ofmagnitude of the RMS motion.The effect of water flow in CLIC type quadrupoles hasbeen quantified in detail. The results will feed into furtherdesign optimisation of the system (diameter of pipes, wa-ter velocity, support design,...). However, already the ini-tial measurements have achieved the CLIC linac toleranceswith nominal cooling water flow.The authors would like to acknowledge the members ofthe CLIC Stability Study Group, in particular N. Leros, fortheir support and for helpful discussions and also A. Seyriand H. Braun. G. Yvon and D. Gros did the installation ofthe water connections.6 REFERENCES[1] G. Guignard (Ed), et al., CERN 2000-008, Geneva (2000).[2] R. Aßmann, et al., PAC2001, Chicago (2001).[3] H.H. Braun, CLIC Note 441, Geneva, (2000).[4] R. Aßmann, et al., these proceedings.[5] F. Le Pimpec et al., these proceedings.[6] Tech. Spec. CERN/AT-MA/95-114/Rev.1, Geneva (1995).[7] W. Schnell, CLIC Note 468, Geneva (2001).[8] L. Landau and E.M. Lifschitz, Course of Theoretical PhysicsVol. VI, (Pergamon Press, London, 1959).

The effect of cooling water on magnet vibrations

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