In this paper we discuss longitudinal beam coupling impedance measurements performed with the coaxial wire method on a modified prototype of the SPS MKE kicker. The frequency dependent real and imaginary part of the distributed coupling impedance are obtained from the measured S-parameters by standard and improved log-formulae. A comparison with theoretical models and previous measurements is discussed as well

Caspers, Friedhelm

Mostacci, A

Tsutsui, H

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHCERN – SL DIVISIONCERN-SL-2000-071 (AP)Impedance Evaluation of the SPS MKE Kicker withTransition Pieces between Tank and Kicker ModuleF. Caspers, A. Mostacci   , and H. TsutsuiAbstractIn this paper we discuss longitudinal beam coupling impedance measurements per-formed with the coaxial wire method on a modified prototype of the SPS MKE kicker.The frequency dependent real and imaginary part of the distributed coupling impedanceare obtained from the measured S-parameters by standard and improved log-formulae. Acomparison with theoretical models and previous measurements is discussed as well.Geneva, Switzerland11th October 2000Also with Universita` di Roma “La Sapienza”, Roma, ItalySumitomo Heavy Industries, Ltd., Tokyo, JapanContents1 Introduction and Motivation 12 Measurements 13 Coupling Impedance from Measured S-Parameters 24 Conclusion 35 Acknowledgements 3i1 Introduction and MotivationRecently, some theoretical and experimental work has been devoted to estimating the longitudinal cou-pling impedance of the SPS MKE kicker. The main reason is the excessive heating that could prevent itfrom working. In fact when the ferrite reaches the Curie temperature, it loses all its magnetic properties.Analytical models have been worked out by L. Vos [1] and H. Tsutsui [2] and compared with sim-ulations. Measurements on a prototype were also performed to eventually asses the theoretical predic-tions [3]. A comprehensive summary of the conclusions and the open questions is reported in [4].To reduce the coupling between the kicker module and the cavity modes in the tank at mediumfrequencies, transition pieces were inserted inside the kicker tank to electrically connect the beam pipein the ferrite to the tank itself; a schematic design is given in Fig. 1, while Fig. 2 shows a front view of thetransition pieces. In this paper we report about measurements (analogous to [3]) on the modified kickerprototype (Sec. 2) and compare the longitudinal coupling impedance with previous results (Sec. 3).2 MeasurementsApplying the single wire measurement technique, a number of transmission measurements were carriedout on the modified SPS MKE kicker, with an experimental set as similar as possible to the set-updescribed in an earlier paper [3]. For practical reasons we used flat flanges (15 cm long) at the kickerbeam pipe port. The diameter of the wire was 0.5 mm.In order to improve the matching of this wire (seen from inside the tank with respect to the 50 coaxial cable) resistors were installed near either flange of the tank. The ohmic value of these lowinductance carbon resistors is simply determined by the relation: 	 . The characteristicimpedance  of a thin wire in the ferrite loaded structure (see Fig. 1 in [3]) can be approximated as ifit were an usual coaxial line (with a proper choice of the value of the outer diameter  [3]):ﬀﬂﬁ ﬃ  (1)The vertical (horizontal) aperture is 32 mm (140 mm); choosing     mm (and wire diameterﬃ! mm), then  is about 263  . Thus two matching resistors 1 of 	   "# were solderedat both ends of the wire (one in each flange). The remaining corrections were done during the dataanalysis.The raw data (obtained using a HP-8753D vector network analyser) are shown as dotted lines inFigs. 3–4 (with cable response calibration); each measurement contains 801 points, the IntermediateFrequency (IF) bandwidth is 100 Hz and the Test Port Power is set to 0 dBm. The length $ of the kicker(including the flanges) has been measured ( $% &ﬂ')(  ( m) and taken into account via the electricaldelay correction function of the instrument. Its value was subtracted in the phase display. Correctionprocedures have been subsequently applied to both amplitude and phase data; comparison between rawand corrected data are also shown in Figs. 3–4. For the amplitude of *,+.- , we had to subtract the lossesattributed to the matching resistors, which were simply obtained by taking the attenuation values at thelowest frequency point (around 100 kHz); they amount approximately 15 dB (that is in fact the distancebetween the solid and dotted lines in the upper part of Figs. 3–4). For the phase plots, we removedthe phase ambiguities of  . Note that some resonances lead to fast phase variation vs. frequency;they may coincide and be mistaken for  phase jumps attributed to the phase ambiguity. Such acorrection was not applied in [3] for frequencies beyond 1 GHz, since the interpretation of the data wastoo questionable; in the present case (see Fig. 4), it is done up to approximately 2 GHz. The correctionmight be possible also up to higher frequencies, but it is not done in this paper.1The exact value of each resistor should have been 213 / .1In the previous kicker set-up (no transition pieces), cavity modes resonating in the kicker tank didcontribute to fields on the beam axis (that is to the longitudinal coupling impedance) and the correspond-ing *,+.- is shown in Fig. 5 (dotted line). Comparing it to the *,+.- from the new design (Fig. 5, solid line),we can observe a reduction of transmission coefficient between 400 MHz and 800 MHz in the newerset-up. Note that with transition pieces there are much less resonances.3 Coupling Impedance from Measured S-ParametersTo evaluate the coupling impedance, we use the formulae for distributed impedance systems, alreadyapplied in [3, 4]; a more detailed explanation and derivation can be found in [5, 6]. First of all, the“standard” logarithmic formula is:0214356ﬂﬁ*789+.-*,:<;>=+.- ?(2)where DUT stands for Device Under Test while REF for REFerence measurement. Such a referencemeasurement in a smooth, homogeneous beam pipe has not been done for practical reasons. We as-sumed, instead, for the reference a lossless line of length $ (that is * :@;A=+.-6BDCFEGHJILK5$NM"OQP ). This delayhas been included in the raw data via the time delay correction function of the network analyser; thus,what is plotted in Figs. 3–5 is directly the ratio *,789+.-M"*:<;>=+.-. As pointed out by E. Shaposhnikova [7],it is very useful for accuracy enhancement to apply the “improved” log formula (see [4] and AppendixA),RTS>Uﬀ60V143(XW I<OK5$,YZﬁ*789+.-*,:@;A=+.- ?(3)instead of the standard one in particular when the impedance to be measured exceeds significantly thecharacteristic impedance  of the wire forming the coaxial line in the DUT. $Y is the length of theferrite module ( $,Y[ (]\ "^ mm) and O is the velocity of light.A comparison between the two formulae for the coupling impedance and the theoretical estimatedone in [2] is shown in Fig. 6. The real part agrees very well with the model, while the imaginary partdiffers substantially from the theoretical expectation for frequencies above 500 MHz. To understandthe reason, the theoretical coupling impedance is converted to the *,+.- using Eq. (3) (Fig. 7). From thefigure, it seems there are some mode(s) travelling through the kicker above 500 MHz. These mode(s)enhance the magnitude of the *,+.- about 20 dB, and reduces the phase with `_ab . Probably `_abphase jump by some mode(s) above 500 MHz caused large discrepancy of the imaginary part of thecoupling impedance. Two possibilities can be considered: 1) there are some waveguide modes insidethe beam aperture of the kicker module, 2) still there are some cavity modes excited. The first effectmay be small because in the theory all waveguide modes inside the beam aperture are included. Thesecond possibility may be reasonable because the measured data are somewhat in the middle of the oldmeasurement [3] and the theory (see Figs. 5, 7).It is interesting to compare the results from the old measurements [3] with the recent ones (obtainedwith the improved formula). For the real part, the low frequency contribution to the coupling impedanceshould be slightly bigger in the old kicker design (no transition pieces), as shown in Fig. 8; at higherfrequencies, we can see the opposite behaviour (Fig. 9). The behaviour at very low frequencies is shownin Fig. 10, using the “standard” formula ( 0V143 ).Figure 10 shows also that at very low frequencies (below 30 MHz) the theory developed in [2] is notreliable anymore. The approximation of considering an homogeneously distributed impedance systembreaks down at such frequencies. Another model to estimate the impedance of the RHIC injectionkicker (with a design similar to MKE kicker), has been proposed in [8]. It is based on a lumped elementequivalent circuit and predicts an impedance peak at low frequencies, similarly to Fig. 10.24 ConclusionWe have discussed the results of coaxial wire measurements on a newer set-up (with transition pieces)of the SPS MKE kicker. So far the transition pieces have not been used but they are foreseen to beinstalled in all the SPS kickers of this type.The transition pieces lower the coupling to the cavity modes in the kicker tank; they reduce (evenslightly) the coupling impedance (below 200 MHz) providing a by-pass for the image currents betweenthe kicker module and the tank.The measurements confirm well (much better than in the old set-up) the theoretical predictions forthe real part of the coupling impedance reported in [2]. Such a theory predicts (for a beam current of132 mA) a power dissipated in the kicker of about 35 W [4] and this may have a consequence on thefinal design of the kicker. Such calculated power is only based on the first 5 coherent lines (200 MHz,400 MHz, ...) of the bunch spectrum and doesn’t take into account the wide-band signals in betweenthese lines.Moreover there may be some interest in repeating the heat measurement (referred in [3]) with thetransition pieces installed. In fact the microwave energy passing through the kicker module in the oldconfiguration (no transition pieces of Fig. 1), might lead to an additional (but not “real”) heating of thethermo probes.5 AcknowledgementsThe authors would like to thank F. Ruggiero for helpful discussion and support, D. Brandt and L. Vosfor their valuable comments. The authors are also grateful to G. Schro¨der and L. Ducimetiere for thesupport and J. Guillot for the help with the mechanical set-up.References[1] L. Vos, Longitudinal impedance from ferrite, CERN-SL-2000-010 AP (2000).[2] H. Tsutsui, Some simplified models of ferrite kicker magnet for calculation of the longitudinalcoupling impedance, CERN-SL-2000-004 AP (2000).[3] F. Caspers, C. Gonzales, M. D’yachkov, E. Shaposhnikova and H. Tsutsui, Impedance measure-ment of the SPS MKE kicker by means of the coaxial wire method, PS-RF-Note 2000-004 (2000).[4] F. Caspers, SPS kicker impedance measurement and simulation, Proceedings of the workshop onSPS-LEP performance (Chamonix X), CERN-SL-2000-007 DI (2000), pp. 85–93.[5] V.G. Vaccaro, Coupling impedance measurements: an improved wire method, INFN/TC-94/023(1994).[6] L.S. Walling et al., Transmission line impedance measurements for an advanced hadron facility,NIM, A 281, 433 (1989).[7] E. Shaposhnikova: private communication (September 1999).[8] H. Hahn and A. Ratti, Equivalent circuit analysis of the RHIC injection kicker, BNL-AD/RHIC/RD-112 (1997).[9] E. Jensen, An Improved log-formula for homogeneously distributed impedance, PS/RF/Note 2000-001 (2000).[10] R.E. Collin, Foundations of microwave engineering, McGraw-Hill (1966).3Appendixc A Improved LOG FormulaThe improved LOG formula (Eq. (3)) used in the measurement is somewhat different from the formgiven by V.G. Vaccaro [5], which was further discussed by E. Jensen [9]:dfeghheji41k60V143(XWI<OK5$ﬂﬁ*,789+.-* :@;A=+.- (4)We derive the formula according to Vaccaro’s derivation.Figure 11 shows the schematic drawing of the coupling impedance measurement for the SPS MKEkicker. In our case the length of the ferrite block is $,Yl (ﬂ\ "^ m, while the total length of the DUTis $m 2.3101 m. For the sake of simplicity, we assume hno+p	hnq-rs . The matching resistorstL`uv are added at either end of the DUT. The experimental set-up is modelled (approximated)as a series of homogeneous transmission lines, each one with its own propagation constant ( w or xw ) andits characteristic impedance ( Hno+ , hnq- , xhn or u ).The Vector Network Analyser (VNA) measures the scattering transmission parameters of the overallsystem. The longitudinal coupling impedance depends (in a first approximation) only on the ferritemodule parameters (such as $,Y , xw and xhn ). According to [5], we getxwy w-zI@w{and xN6 xww?(5)where{is the longitudinal coupling impedance per unit length and w|K5M"O . To get the couplingimpedance, we need to calculate xw from measured data. Thus in the following we show the relationbetween xw and the (transmission) scattering parameters.Providing two semi-infinite transmission lines with characteristic impedance + and ,- , the trans-mission coefficient (from line 1 to line 2) can be written as [10]:}+~+W,- (6)A line can be assumed to be semi-infinite when the signal reflected by any possible termination isnegligible. This approximation is consistent with our configuration and we can use Eq. (6) to estimatethe transmission of a signal going from one block to the next one. The main approximation of thisreasoning is considering the transition region (namely $+ and $- ) as homogeneous transmission lines(and they are not, since their cross section changes).The transmission factor for each transition (going from the left to the right of Figure 11) are: From cable to transition region: Transmission factor is hM)G W uP , since  is chosen to beu . From transition region to ferrite block: Transmission factor is  qMG W xjP . In ferrite block: The waves at the entrance of the ferrite block are attenuated and becomeBgCfEGHJIxw$,Y&P times the original value at the exit of the block. From ferrite block to transition region: Transmission factor is xqMGWxjP . From transition region to the cable: Transmission factor is 1, if tu .The total transmission coefficient can be approximated as:*789+.-uuWBgCfEGHJI<w$+PWxBDCfEGIxw)$,Y"PxWxBgCfEGI<w$-P?(7)4having included the exponential factors BgCfE[GI<w$,ŁP ( (? ) for propagation inside the transitionregions. The transmission coefficient of the reference is*:<;A=+.-BgCfEGI<wG$+W$,YW$,-PjP (8)The coupling impedance RTS>U of the ferrite block is{$,Y . The value{can be obtained from *,+.- ,using Eqs. (5, 7, 8):{$,Y6ZﬁGP(XW Iw$,YﬂﬁGP?(9)whereﬂﬁGPvﬂﬁ*,789+.-* :<;A=+.-WﬂﬁuWuZﬁWxxWx (10)The transmission coefficient * 789+.-M"*:@;A=+.-is observed with VNA. The second term inﬂﬁGP is com-pensated off-line. In our case, this term corresponds to  ﬂ"GjGH"W6 ""PMT""P[(' dB. The thirdterm is neglected in the measurement.Ferrite module, length LfKicker tank, length LbeamaxisTransition piecesFigure 1: Schematic view of the kicker.5Figure 2: Frontal view of a transition piece: the beam pipe changes shape from rectangular (inside thekicker module) to circular (outside the kicker tank).60 200 400 600 800 1000−120−80−400|S 12| (dB)0 200 400 600 800 1000Frequency (MHz)−720−540−360−1800180arg(S12) (deg)Figure 3: Raw data (dotted line) and corrected *,+.- (solid line) (0–1 GHz). Amplitude and phase of*,+.- from a network analyser with electrical delay $a &'A(  ( m, cable calibration done, IF bandwidth100 Hz and test port power set to 0 dBm (801 points).The transmission coefficient *,+.- is noisy at high attenuation (below -80 dB) where many spurious effects(such as mechanical imperfections) start to be important.70 1000 2000 3000−120−80−400|S 12| (dB)0 1000 2000 3000Frequency (MHz)−900−720−540−360−1800180arg(S12) (deg)Figure 4: Raw data (dotted line) and corrected *,+.- (solid line) (0–3 GHz). Amplitude and phase of*,+.- from a network analyser with electrical delay $a &'A(  ( m, cable calibration done, IF bandwidth100 Hz and test port power set to 0 dBm (801 points).80 200 400 600 800 1000−120−80−400|S 12| (dB)OLDNEW0 200 400 600 800 1000Frequency (MHz)−2160−1440−7200arg(S12) (deg)NEWOLDFigure 5: Latest measured data (solid) compared with previous one (dotted) from [3]. The mechanicalmodifications discussed in Sec. 1 have changed significantly the transmission response between 400 and800 MHz.90 200 400 600 800 100002468Re(Z) (kΩ)TheoryZLOGZlog0 200 400 600 800 1000Frequency (MHz)−202468Im(Z) (kΩ)TheoryZLOGZlogFigure 6: The coupling impedance (0–1 GHz) calculated from measured data with the “improved”logarithmic formula RSAU of Eq. (3) (solid line) and with the “standard” logarithmic formula 0V143(dotted line). The dot-dashed line represents the theoretical estimate in [2]. Note that, except for verylow frequencies, resonances become visible around 500 MHz and higher, may be due to waveguidemodes inside the beam aperture of the kicker module.100 500 1000 1500−120−80−400|S 12| (dB)Theory0 500 1000 1500Frequency (MHz)−900−720−540−360−1800180arg(S12) (deg)TheoryFigure 7: Transmission parameter *,+.- as a function of frequency. The solid, dotted, and dot-dashedlines show the corrected data, raw data, and the theoretical data using Eq. (3), respectively.110 50 100 150 200 250 3000500100015002000NewOld    Figure 8: Real part (0–0.3 GHz) of the coupling impedance calculated from measured data with the“improved” logarithmic formula RSAU . The solid heavy line refers to the old measurements (no conesbetween the tank and the kicker module), while the thinner one is obtained from the new data. Thedashed line represents the expected result from the theory in [2].120 200 400 600 800 10000350070000 200 400 600 800 10000123 x 104New OldNew Old     ¡  Figure 9: Real and imaginary part (0–1 GHz) of the coupling impedance calculated from measured datawith the “improved” logarithmic formula RSAU . The solid thicker line refers to the old measurements(no cones between the tank and the kicker module), while the thinner one is obtained from the new data.The dashed line represents the expected result from the theory in [2].135 10 15 20 25 300100200300400500600¢ £¤ ¥ ¦Figure 10: Real part (0–30 MHz) of the coupling impedance calculated from measured data with the“standard” logarithmic formula 0V143 . The solid thicker line refers to the old measurement, while thethinner one is obtained from the new data. Dashed line represents the expected result from the theoryin [2]: such theory is not anymore applicable at those low frequencies. Raw data has been corrected toavoid low frequency *,+.- to be greater than unity.14§ ¨§ © ª§ ©§ © «§ ¨ª¬«Figure 11: Conceptual (“electrical”) drawing of the longitudinal coupling impedance measurementof ferrite kickers by coaxial wire method. Going from the left side to the right one, there is first atransmission line representing the cable ( w , u ), then the matching resistor  and the “transition”region of length $+ ( w , Hno+ ). The ferrite module ( xw , xu ) follows and then again a transition re-gion of length $- ( w , hnq- ), a matching resistor  and the cable ( w , u ). The kicker module has atotal length $­ $+ W $- W $,Y . The cable characteristic impedance is u® l . We assumeHno+XmhnQ-Jm"\"' .15

Impedance Evaluation of the SPS MKE Kicker with Transition Pieces between Tank and Kicker Module

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