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A novel electromagnetic design and a new manufacturing process for the cavity BPM (Beam Position Monitor)

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A novel electromagnetic design and a new manufacturing process for the cavity BPM (Beam Position Monitor)
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  A novel electromagnetic design and a new manufacturing process for thecavity BPM (Beam Position Monitor) Massimo Dal Forno a, n , Paolo Craievich b , Roberto Baruzzo c , Raffaele De Monte b , Mario Ferianis b ,Giuseppe Lamanna c , Roberto Vescovo a a Department of Industrial Engineering and Information Technology, University of Trieste, Italy b Sicrotrone Trieste S.C.p.A., Basovizza, Trieste, Italy c Cinel Strumenti Scientifici s.r.l., Vigonza, Padova, Italy a r t i c l e i n f o  Article history: Received 7 September 2011Received in revised form13 September 2011Accepted 22 September 2011Available online 3 October 2011 Keywords: Cavity beam position monitorBPMElectro-discharge machineEDM a b s t r a c t The Cavity Beam Position Monitor (BPM) is a beam diagnostic instrument which, in a seeded FreeElectron Laser (FEL), allows the measurement of the electron beam position in a non-destructive wayand with sub-micron resolution. It is composed by two resonant cavities called reference and positioncavity, respectively. The measurement exploits the dipole mode that arises when the electron bunchpasses off axis. In this paper we describe the Cavity BPM that has been designed and realized in thecontext of the FERMI@Elettra project [1]. New strategies have been adopted for the microwave design,for both the reference and the position cavities. Both cavities have been simulated by means of AnsoftHFSS [2] and CST Particle Studio [3], and have been realized using high precision lathe and wire-EDM (Electro-Discharge) machine, with a new technique that avoids the use of the sinker-EDM machine.Tuners have been used to accurately adjust the working frequencies for both cavities. The RFparameters have been estimated, and the modifications of the resonant frequencies produced bybrazing and tuning have been evaluated. Finally, the Cavity BPM has been installed and tested in thepresence of the electron beam. &  2011 Elsevier B.V. All rights reserved. 1. Introduction Cavity BPMs are employed in the context of the FERMI@Elettraproject as diagnostic devices for two free-electron laser beamlines,referred to as FEL 1 and FEL 2 [1]. Presently, 10 Cavity BPMs aresuccessfully installed in the FEL 1 beamline (Fig. 1). The workingfrequency is 6.5GHz (C-Band). The reference cavity adopts a newgeometry, which enables adjusting the antenna coupling withoutaffecting its resonant frequency. The waveguide-coaxial transitionsfor the position cavity have been designed in-house. The RF para-metersofthecavitieshavebeendeterminedbymeansofAnsoftHFSS[2], while the cavity output signal levels have been estimated usingthe CST Particle Studio [3]. The connectors have been directly brazedon the bulk of copper, and the length of the rectangular waveguidehas been properly chosen. Such improvements avoid the signalcontamination produced by parasitic resonance effects of the con-nectors, waveguides and other additional mechanical parts, experi-enced in previous designs [4,5]. The ‘‘Manufacturing’’ section reports a novel machining tech-nique that allows the Cavity BPM production with only the latheand with the wire-EDM (Electro-Discharge) Machine. No sinker-EDM machines have been employed. This new strategy allows aless costly and less time-consuming manufacturing process. Thecavities have been realized with the lathe and with the highprecision electro-discharge machine (EDM). The tolerances are 7 10 m m for both the turning and the EDM. Such high precision inthe manufacturing process strongly reduces the crosstalk effectbetween the orthogonal ports of the position cavity, and only aslight tuning of the resonant frequencies is needed. A system of fine tuners is used in both the reference and the position cavitiesto adjust the resonant frequency with high precision. After thefabrication, a workbench inspection of all cavities has beenperformed with a vector network analyzer. Ten cavities havebeen installed and carefully tuned. The paper describes the RFmeasurements, and reports the test of a prototype performed inthe presence of electron beam. The effect of the temperature onthe resonant frequency has been analyzed in the last section. 2. The cavity BPM: theory and basic formulas When the electron beam interacts with the position cavity, thebeam wakefield excites the first resonant modes. To measure thebeam offset, the most interesting among these modes is the first Contents lists available at SciVerse ScienceDirectjournal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods inPhysics Research A 0168-9002/$-see front matter  &  2011 Elsevier B.V. All rights reserved.doi:10.1016/j.nima.2011.09.040 n Corresponding author. Tel.:  þ 39 040 375 8043. E-mail addresses:  massimo.dalforno@phd.units.it (M. Dal Forno),paolo.craievich@elettra.trieste.it (P. Craievich).Nuclear Instruments and Methods in Physics Research A 662 (2012) 1–11  dipole mode ( TM  110 ). The reason is that, in its linear range, itsintensity is proportional to the beam offset. There are two dipolepolarizations, one that senses the ‘X’ beam offset, the other thatsenses the ‘Y’ beam offset.  2.1. Linearity range The Cavity BPM works in a satisfactory way, as a diagnostictool, only in the linear range, that is when the electron bunchtravels with a small offset with respect to the beam pipe axis. Thelinear range can be estimated by analyzing the following fieldfunctions of the  TM  110  mode in a cylindrical resonator: E   z  ¼ CJ  1  j 11 r R   cos ð f Þ H  r  ¼ iC  oe 0 R 2  j 211  J  1  j 11 r R   r   sin ð f Þ H  f ¼ iC  oe 0 R j 11  J  0 1  j 11 r R   cos ð f Þ ð 1 Þ where  J  1  is the Bessel function of the first kind of order one,  R  thecavity radius,  r   the radial position,  f  the angle and  C   an arbitraryconstant.By (1), in the linear range the intensity of the dipole mode isproportional to the bunch offset  r  . Expanding  J  1 ð  x Þ  as a Taylorseries, yields  J  1 ð  x Þ  x 2   x 3 16 þ ð 2 Þ We want to evaluate when the cubic term is no larger than 1%,5% or 10% of the linear one. For linearity in the range below 1%,the following inequality holds:  x 3 16 o 1100  x 2  ð 3 Þ which yields  x o 0 : 2, where  x ¼  j 11  r  = R ,  j 11 ¼ 3.8 and R ¼ 26.29 mm. This yields  r  o 1 : 5 mm.Table 1 summarizes the maximum beam offset that gives anon-linear term below 1%, 5% and 10% of the signal.  2.2. Output voltage on a matched load The energy losses of a bunch of charge  q  that crosses a pillboxcavity, for the  TM  010  mode and the  TM  110  mode, are given,respectively, by D U  010 ¼ q 2 k 010  ð TM  010 Þ D U  110 ¼ q 2 k 110  x 2 ð TM  110 Þ ð 4 Þ where  k 010  and  k 110  are the so called ‘‘loss factors’’, defined as k i 10 ¼  o i 10 2 RQ    i 10 ð 5 Þ where  i ¼ 0,1 (reference and position cavity, respectively), whilethe resistance  R  is meant to be the circuit resistance defined fromthe circuit theory, and not by the linac convention.The output power of the cavity is therefore (for the referenceand the position cavity, respectively) P  010 , ext  ¼  o 010 D U Q  ext  ¼  o 010 Q  ext  k 010 q 2 P  110 , ext  ¼  o 110 D U Q  ext  ¼  o 110 Q  ext  k 110 q 2  x 2 :  ð 6 Þ The output voltage on a matched  Z  0  load is therefore (for thereference and the position cavity, respectively) V  010 , out  ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Z  0 P  010 , ext  p   ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Z  0 o 010 Q  ext  k 010 r   qV  110 , out  ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Z  0 P  110 , ext  p   ¼  ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Z  0 o 110 Q  ext  k 110 r   qx  ð 7 Þ where the voltage has the meaning of maximum amplitude value,and not of rms value. 3. The electromagnetic design This section describes improvements and simulations per-formed for the Cavity BPMs. The reference and the positioncavities have been designed to have a high time constant  t , asthe RF frontend needs a long duration signal. In this way theneeded sampling frequency can be obtained using low costelectronic devices. On the other hand,  t  and the quality factorsof a cavity are related as follows: t ¼  2 Q  L o  ð 8 Þ where  o  is the angular frequency and  Q  L  is the loaded qualityfactor, given by1 Q  L ¼  1 Q  0 þ  1 Q  EXT  ð 9 Þ with  Q  0  and  Q  EXT   the internal and external quality factors,respectively. By (8), a high value of   t  is achieved with a highquality factor  Q  L . This requires a high  Q  EXT  , by (9), since the  Q  0 cannot be changed for a fixed material and frequency.Both the reference and the position cavities have beendesigned and analyzed with Ansoft HFSS [2] and CST ParticleStudio [3]. The parameters of interest are, for both cavities, theresonant frequencies, the internal and external  Q  , the ð R = Q  Þ ratio,the  b  coupling factor, the loss factor and the level of the outputsignals. The HFSS simulator has been used to analyze the RFparameters of the cavities, while the CST Particle Studio has beenused to estimate the output signals of the cavities. Fig. 1.  Photo of the cavity BPM.  Table 1 Linear range.Linear range (mm)1% 1.505% 3.3710% 4.74 M. Dal Forno et al. / Nuclear Instruments and Methods in Physics Research A 662 (2012) 1–11 2   3.1. The reference cavity For the reference cavity, we propose the geometry of  Fig. 2,which consists of a particular pillbox where the antenna ismounted in the protrusion.The depth of the antenna is related to the level of the desiredoutput signal. Precisely, the deeper the antenna penetration, thehigher the output signal. With this technique, it is possible toadjust the antenna length to obtain the desired output signal levelwithout affecting the resonant frequency of the cavity.The dimensions of the reference cavity are listed in Table 2.At first, we use HFSS to perform the simulations exploiting thesymmetry of the structure with respect to orthogonal planes,using the ‘‘eigenmode’’ and ‘‘driven modal’’ settings. The eigen-mode setting is used to estimate the resonant frequency of thecavity and the internal quality factor  Q  0 . The driven modal settingis used to estimate the reflection coefficient  S  11  of the output port,thus estimating the external quality factor and the output voltage.For a bunch charge of 1 nC, the RF parameters of the referencecavity are listed in Table 3.As a second step, we evaluated the output signal level with CSTParticle Studio, setting a bunch charge of 1 nC, with a bunchlength  s  z  ¼ 8 mm, and assuming the electron beam as travellingalong the beam pipe axis. Fig. 3 shows the simulated outputvoltage of the reference cavity.  3.2. The position cavity 3.2.1. The dipole mode of the position cavity The geometry of the position cavity is illustrated in Fig. 4.The dimensions of the position cavity are listed in Table 4.The bunch offset measurement exploits the dipole mode thatarises in the cavity when the beam passes off-axis. In order toobtain a high quality factor, such mode must be trapped in theresonant pillbox to avoid its propagation along the beam pipe.The beam pipe radius is  R BP  ¼ 10 mm, so its dominant mode ( TE  11 )has the following cut-off frequency:  f  TE  11  ¼  c  2 p  j 0 11 R BP   8 : 78 GHz  ð 10 Þ where  j 0 11  is the first zero of the derivative of the Bessel function of the first kind and first order.Since the dipole mode oscillates at the resonant frequency  f  RES  ¼ 6.5 GHz, by (10) it is under the cut-off of the beam pipe.Thus this mode is trapped in the cavity.As shown in Fig. 4, the signal is extracted from the cavity usingfour rectangular waveguides, which are coupled to the cavity withthe magnetic coupling described in Refs. [6–9]. The magnetic coupling allows the separation of the two dipole polarizations,one sensing the ‘X’ displacement, and the other sensing the ‘Y’displacement. Furthermore it allows the rejection of the unde-sired monopole mode, which cannot be used for the offsetmeasurement, and its intensity is independent of the beam offset.The rejection of the monopole mode is discussed in the nextsection.  3.2.2. The rejection of the monopole mode The monopole mode of the position cavity resonates at4.3 GHz, thus it is under cut-off both in the beam pipe and inthe waveguides. As a consequence, it remains trapped inside theposition cavity. Unfortunately, although it is under cut-off, itsintensity is much higher than the intensity of the dipole mode,when the beam travels close to the pipe axis. Thus, it must bemade small compared to the output port signals. In order do so,we exploit the following three expedients:   Use of the magnetic coupling between the position cavity andthe waveguide.   Use of the high-pass filtering in the rectangular waveguides.   Introduction of a band-pass filter centered at 6.5 GHz (which isthe resonant frequency of the dipole mode), placed in the RFfront-end.Note that the high-pass behavior of the rectangular wave-guides, coupled with the resonant cavity, contributes to themonopole rejection. In fact, for the designed dimensions, thecut-off frequency of such waveguides is  f  TE  10  ¼  c  2 a   5 GHz  ð 11 Þ where  c   is the speed of light in the vacuum, and  a ¼ 30 mm is themajor transversal dimension of the waveguide.  3.2.3. The waveguide-coaxial transition The electron beam excites the dipole mode signal in theposition cavity; thus such signal propagates along the fourrectangular waveguides and reaches two coaxial cables of theelectronic circuitry, which carry out the two output signals, onefor the X polarization and one for the Y polarization. This sectionfocuses on the waveguide-coaxial cable transition. The latter canbe realized by exploiting the electric or the magnetic couplingbetween the waveguide and the antenna, as discussed below. Fig. 2.  Geometry of the reference cavity, with the cross-section.  Table 2 Reference cavity dimensions.Cavity radius 18.36 mmCavity gap 9 mmBeam pipe radius 10 mm  Table 3 HFSS simulations for the reference cavity.HFSS simulations for the reference cavitySymmetryplanes90 1 (eigenmode)180 1 (eigenmode)180 1 (drivenmodal)Nosymmetries(driven modal)  f  RES   (MHz) 6481.1 6478.2 6477.4 6471.6 Q  0  6307 6255 – – S  11  – – 0.731 0.730 b  – – 0.155 0.156 ð R = Q  Þ 010  ð O ) 36.4 36.2 – – k 010  (V/nC) 741 737 – – Q  EXT   – – 40,355 40,100 P  OUT   at 1 nC(W)– – 0.74 0.75 V  OUT   at 1 nC (V) – – 8.62 8.64Convergence Very good Good Good Good# Tetrahedra 13,000 35,000 16,000 52,000 M. Dal Forno et al. / Nuclear Instruments and Methods in Physics Research A 662 (2012) 1–11  3   3.2.3.1. Electric coupling.  In the waveguide-antenna electriccoupling, the antenna is placed in the position corresponding tothe maximum of the electric field (Fig. 5). To do so, the waveguideis shortened, and the maximum of the  E  -field is  l = 4 away fromthe short circuit, thus catching the voltage antinode and thecurrent node, as is shown in Fig. 5. Furthermore, the antennamust not touch the base surface of the waveguide.This method requires to calculate three dimensions (Fig. 6):1. The antenna-closure distance  l c  , which is not exactly equal to l = 4, due to the antenna thickness.2. The antenna-lateral waveguide distance  l l .3. The antenna-bottom waveguide distance  l b .Unfortunately, the stringent tolerances on these three para-meters make this kind of coupler difficult to realize. As anexample, Fig. 7 shows the dependence of the  9 S  21 9  parameter on l b , obtained with an HFSS simulation.The sensitivity of   9 S  21 9  with respect to  l b  can be completelyavoided making use of the magnetic coupling, discussed below.  3.2.3.2. Magnetic coupling.  In the magnetic coupling the antennais connected to the bottom of the waveguide, in a point at which acurrent antinode and a voltage node occur. The magnetic fieldvariation induces a voltage in the antenna, which thereforereceives the signal. The latter is then sent to the electroniccircuitry. This alternative approach requires calculating twodimensions (Fig. 8): Fig. 3.  Output signal of the reference cavity. Fig. 4.  Geometry of the position cavity. Fig. 5.  Electric coupling scheme. Fig. 6.  Electric coupling transition. Fig. 7.  Sensitivity analysis of the antenna-bottom waveguide distance  l b . M. Dal Forno et al. / Nuclear Instruments and Methods in Physics Research A 662 (2012) 1–11 4  1. The antenna-closure distance  l c  .2. The antenna-lateral waveguide distance  l l .This coupling approach is more robust, because there are onlytwo tolerances, which are not critical. This transition has beendesigned and simulated with Ansoft HFSS. The antenna positionhas been chosen to maximize transmission from the waveguide tothe coaxial cable, in the frequency range of interest. This has beendone with a trial-and-error procedure, obtaining the dimensionslisted in Table 5.Fig. 9 shows the parameters 9 S  21 9 and 9 S  11 9 obtained with suchmagnetic coupling.In the previous prototypes the geometry of the antennaconnector produced a spurious resonant frequency, because thecomplicated interconnection system behaved like an additionalresonant cavity [4,5]. For this reason we introduced a new type of  antenna, which is simpler, directly brazed in the copper bulk, andnot generating parasitic resonances. Fig. 10 shows both types of connectors.  3.2.4. Resonance of the rectangular waveguides The four rectangular waveguides might behave as rectangularresonators, if mismatching in the waveguide-coaxial transitionoccurs, due to the residual power reflected by the waveguide-coaxial transition. The spurious modes thus generated have aresonant frequency that must be far away from that of the signalof interest. This can be obtained by suitably choosing the dimen-sions of each rectangular cavity. With reference to Fig. 11, thedesigned dimensions of the cavity are the following:  X  MAX  ¼ 53 mm,  Y  MAX  ¼ 30 mm,  Z  MAX  ¼ 6 mm.With this choice, the first four resonant frequencies are listedin Table 6.The position cavity dipole frequency is 6.5 GHz, which islocated between the  TE  101  and  TE  102  resonant frequencies. Thus,the resonances of the rectangular cavity do not affect the signal of  Fig. 9.  9 S  21 9 (a) and 9 S  11 9 (b) parameters of the waveguide-coaxial cable transition. Fig. 10.  Old connector (a) and new type of connector (b). Fig. 11.  Waveguide-coaxial transition. Fig. 8.  Magnetic coupling transition.  Table 4 Position cavity dimensions.Cavity radius 26.29 mmCavity gap 10 mmBeam pipe radius 10 mmCoupling WG 30  6 mmDistance WG to beam axis 19.39 mm  Table 5 Magnetic coupling dimensions. l c   31 mm l l  13 mmAntenna radius 0.5 mm M. Dal Forno et al. / Nuclear Instruments and Methods in Physics Research A 662 (2012) 1–11  5

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