Balmer JA

Holder D J

Owen H L

English

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MEASUREMENT OF GROUND VIBRATIONS AND CALCULATION OFTHEIR EFFECT ON THE DIAMOND LIGHT SOURCEJ.A.Balmer, D.J.Holder, H.L.Owen, CLRC Daresbury Laboratory, Warrington, U.K.AbstractDue to the very small beam emittances with which theyoperate, all 3rd generation synchrotron radiation sourcesare particularly concerned with the effects of groundmotion on accelerator components. Even smallmovements of magnetic elements of the accelerator,particularly the quadrupoles, will lead to problems withphoton beam stability.Using a state-of-the-art seismometer, measurementshave been made over the Daresbury Laboratory site,during both normal site operations and when the levels ofcultural and technical noise are particularly low.These measurements can then be used to inform thepreliminary design decisions being made for the 3 GeVsynchrotron radiation source, DIAMOND.The predicted effect of the measured ground vibrationson an example DIAMOND lattice is also presented. Theseresults can then be used in the design of systems tomollify vibration effects, such as magnet girders andfeedback damping.1 INTRODUCTION3rd generation synchrotron radiation sources are verysensitive to effects of ground motion. Small movements ofmagnetic elements of the accelerator, particularly thequadrupoles, will lead to problems with photon beamstability. For a synchrotron light source a typicalspecification can be given that the electron beam motionmust not exceed 10% of the beam size in either plane.This paper presents measurements of ground motion atDaresbury Laboratory and calculates its effect on anexample DIAMOND lattice.2 MAGNET MOTION2.1 The Effect Of Magnet MotionMisalignments in the storage ring elements insynchrotron light sources cause closed-orbit errors in theposition of the electron beam which must be corrected for.Vibration gives rise to deflections in the electron beam inthe same way that misalignments do, albeit the deflectionis transient. At higher frequencies the effect of vibration isto effectively degrade the brightness of the extractedphoton beams, whilst at lower frequencies the motion cancause noise problems in experimental detector systems;the break-point between these two regimes depends uponthe experiment. 2.2 Calculating the Beam Motion The effect of a particular type of element motion can bequantified by an amplification factor AsjsCOrmsrms=∆∆ , where ∆jrms is the rms change in some set of co-ordinates (i.e. position, tilt angle, roll angle, pitch angle),∆sCOrms is the resulting rms closed-orbit deviation andthe index s  refers to the plane under consideration(horizontal or vertical). For static deviations the threemain sources of closed-orbit error are:1. Transverse misalignment of quadrupoles2. Roll angle misalignment of dipoles3. Fractional field imperfection in the dipoles With ground vibration, the dominant effect will be toproduce lateral movements of the elements rather than toinduce rotations within them, so that only the first of thethree sources above is relevant. Assuming that vibration isdistributed randomly around the accelerator, the generatedorbit distortion at a particular location i  from a set of jquadrupoles with an rms vibration amplitude of ∆arms is ( )∑∆=∆jjjirmsiklQax βπβ 2sin22, where Q  is the betatron tune and ( )kl j  the integratedstrength of quadrupole j ; the calculation can beperformed in either the horizontal or vertical plane. Thisdistortion is then scaled by the beam size at theobservation point, given by σ εβ σ ηεi i i= + 2 2 ( ε  is the emittance, εσ the dispersion and iη  the energyspread). It can be shown that for lattices that are broadlysimilar to each other, the sensitivity of the beam tovibrations scales roughly as ∆ x Niiσ ε∝             (1) where N  is the number of quadrupoles in the lattice. Proceedings of EPAC 2000, Vienna, Austria23283 GROUND MOTION MEASUREMENTS3.1 Measurement MethodThe measurements presented in this paper were madeusing a Guralp CMG-3T seismometer [1]. This is anhermetically sealed three-axis device that produces adigitised voltage proportional to the velocity measured ineach axis. In each of the three axes (east-west, north-southand vertical) the position of an inverted pendulum iscapacitively measured; coils are then used to drive thependulum back to its centre position. The device output isdigitised, buffered and read out via an RS-232 link to a PCfor saving. The instrument was placed in a pitapproximately 1 m deep and covered with a temporaryshelter; the depth of excavation was sufficient to exposethe Bunter sandstone upon which the laboratory is built. Alayer of concrete was used to provide a uniform surfacefor the instrument.3.2 Analysis of MeasurementsIn general, the power spectral density (PSD) of a noisesignal is defined as ( ) ( )[ ]21lim2 fXTfSTx ∞→=where the Fourier transform of the noise signal is definedas( ) ( ) dtetxfX iftTTπ22/2/−−∫= .However, if as in our case the instrument used recordsvelocity then the displacement power spectral density canbe obtained from the velocity data by( ) ( )224 ffSfS vxπ=.This is because although displacement and velocity arerelated by dtdxv= , their Fourier harmonics are relatedby( ) ( )fXi ffV π2−= .MATLAB [2] was used t o apply the calibration,calculate the power spectral density (applying suitablewindowing and smoothing functions) and convert betweenvelocity and displacement using the relationships above.3.3 ResultsExample results of three measurements are shown inFig. 1. Samples were collected at a rate of 200 per secondand subsequently 217 samples were transformed to give thedisplacement power spectral density, shown here for thevertical axis only. The measurement locations wereadjacent to the building that houses the existingSynchrotron Radiation Source (SRS); on the edge of thesite adjacent to a busy road; and one measurement on aquiet part of the site taken during the night.1.E-111.E-101.E-091.E-081.E-071.E-061.E-051.E-041.E-031.E-021.E-011.E+001.E+010.1 1.0 10.0 100.0Frequency (Hz)QuietBoundaryNear SRS Figure 1: Displacement PSD measured at DaresburyLaboratoryIt can be clearly seen that the level of cultural noise,which is significant at frequencies above a few hertz andmuch of which emanates from outside of the site, dropsdramatically during the night time period. The proximityof the road adds a broad range of components above 10Hz, while specific peaks, some of which are due to theoperation of the SRS, are visible in all traces. An exampleof this technical noise would be the cryoplant compressorat around 18 Hz.4 EFFECT ON DIAMOND The magnitude of the vertical ground motion can becalculated from these measurements as ( ) ( )dffSfzffxrms ∫= max which gives the sum of the rms displacement observed forall frequencies above f. For the purposes of this calculation, the DIAMONDspecification is 24 cell, 3 GeV, with source pointspredominantly being within insertion devices (ID). Thespecification value for horizontal-vertical coupling inDIAMOND of 1 % is also assumed. However, several3rd-generation light sources are now operating with2329Proceedings of EPAC 2000, Vienna, Austriacoupling values as little as 0.3 %, and this would be asimilar goal for DIAMOND after a period of operation. DIAMOND has a combination of standard and long IDstraight sections. The beam sizes and calculatedamplification factors (for 1 % coupling) are shown inTable 1.  Table 1: Beam sizes and amplification factorsBeam size, σ (µm) Amplification FactorStraightType Horizontal Vertical Horizontal VerticalStandard 79.9 7.82 45 20Long 166 15.6 102 41  The movement of the beam for a particular rmsdisplacement, expressed as a percentage of beam size inthat plane, is approximately independent of straight type.Figure 2 shows the calculated vertical beam movements,expressed as a percentage of beam size based on the realground motion measurements presented earlier. For aDIAMOND storage ring of 150 m diameter on theDaresbury bedrock the quadrupoles will moveincoherently for frequencies above about 1.5 Hz, 001101001000100000.1 1.0 10.0 100.0Frequency (Hz)QuietBoundaryNear SRS increasing the beam movement by N compared to asingle quadrupole. Fig. 1 shows the beam movement inthe centre of the standard straights on DIAMOND thatwould be seen for each of the three sets of data, expressedas a percentage of the beam size.5 DISCUSSIONThe calculations show that 3rd-generation light sourcesare very sensitive to vibration, regardless of the exactlattice optics. Equation (1) shows that the sensitivity willbe increased still further if the lattice contains additionalcells; this is a fundamental consequence of the increasednumber of quadrupoles and the small emittance. Other 3rd-generation light sources have observed beamdisplacements from vibration, and have implementedfeedback systems to counteract this. While such a systemwill help to counteract this level of vibration, it isimportant to avoid the larger levels of vibration arisingfrom construction work or the movement of heavyequipment. This is because any feedback system by itsnature only reduces the initial amplitude vibration in aparticular frequency band by some factor (rather thaneliminating it completely), so the greater the initial levelof vibration the more residual vibration is still presentwhen the feedback system is active.The results in Figure 2 show that in order to obtainvertical electron beam motion of less than 10% of thebeam size then a feedback system will be required abovethe low frequency coherence limit (estimated at about 1.5Hz) to probably 15 Hz.In all aspects of the design careful consideration needsto be given to the effect on all structures and systems ofthe predicted levels of vibration which will beexperienced by the storage ring.REFERENCES[1] Guralp Systems Limited, 3 Midas House, CallevaPark, Aldermaston, Reading, Berks, U.K.[2] The MathWorks Limited, Matrix House, CowleyPark, Cambridge, U.K.Figure 2: Vertical beam movements, for the groundmotion data, assuming uncorrelated quadrupole motion.Proceedings of EPAC 2000, Vienna, Austria2330

Measurement of ground vibrations and calculation of their effect on the DIAMOND light source

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