20th IMEKO TC4 International Symposium and18th International Workshop on ADC Modelling and TestingResearch on Electric and Electronic Measurement for the Economic UpturnBenevento, Italy, September 15-17, 2014

RF coupling impedance measurements for particleaccelerator devices

Andrea Mostacci1,4, David Alesini2, Nicolò Biancacci3, Fritz Caspers3, Luca Ficcadenti4, JosephKuczerowski3, Mauro Migliorati1,4, Luigi Palumbo1,4, Benoit Salvant3, Bruno Spataro2

1Sapienza, SBAI Department, Via A. Scarpa 16, 00161 Roma, Italy.2INFN-LNF, Via E. Fermi, 40, Frascati (Roma), Italy.

3CERN, CH-1211 Geneva 23. Switzerland.4INFN-Roma, P.le Aldo Moro 2, 00161 Roma, Italy.

Abstract – Bench measurements nowadays representan important tool to estimate the coupling impedanceof any particle accelerator device. The well-knowntechnique based on the coaxial wire method allows toexcite in the device under test a field similar to theone generated by an ultra-relativistic point charge. Wediscuss the basics of the coaxial wire method and re-view the formulae widely used to convert measuredscattering parameters to longitudinal and transverseimpedance data. We review, as well, bead-pull tech-nique used in the design, construction and tuning ofmulti-cell accelerating structures. We discuss typicalmeasurement examples of interest for the CERN LargeHadron Collider as well as other state of the art particleaccelerator.

I. INTRODUCTIONThe interaction between a (relativistic) beam and its sur-

roundings is usually described in terms of longitudinaland transverse coupling impedance [1]. The longitudinalimpedance accounts for the energy lost by a point chargeq because of the wake field of a leading particle; assumingan infinitely long pipe, for a relativistic beam it is definedas

Z‖ = −1

q

∫ ∞

−∞Ez (r = 0;ω) exp

(jω

cz)dz (1)

where Ez is the longitudinal electric field and c is thespeed of light. Instead the transverse kick experienced bya particle because of deflecting fields excited by a leadingcharge, can be described in terms of the transverse cou-pling impedance

Z⊥ =j

q2

∫ ∞

−∞

F⊥ (r1, r2;ω)

r1exp

(jω

cz)dz (2)

where F⊥ is the transverse Lorentz force and r1 (r2)is the leading (trailing) particle position. Longitudinalimpedance is, therefore, measured in Ω while the trans-verse one in Ω/m.

After the introduction of the beam coupling impedanceconcept by V. Vaccaro it was realized soon that for highly

relativistic beams a very close similarity exists between theTEM like field of the charged particles and the field of awire in a coaxial structure. This is the basis and motivationof the coaxial wire method.

We review the early concepts of this method in orderto show the motivation; we show some issues (and ad-vantages) concerning the practical implementation of thoseconcepts with modern instruments and then eventually wediscuss some recent applications.

Longitudinal impedance measurements are straightfor-ward, but also transverse impedance measurements usingtwo wires carrying currents with opposite polarity were al-ready done on the late 70ths. The concept was extendedto the evaluation of dipole and quadrupolar impedances byapplying a single displaced wire and pair of wires.

We discuss the basis of those methods and present someexamples relevant for modern accelerator components.

II. THE COAXIAL WIRE METHODThe field of a relativistic point charge q in the free space

(or in a perfectly conducting beam pipe) is a TransverseElectric Magnetic (TEM) wave, namely it has only com-ponents transverse to the propagation direction (z-axis).The amplitude scales inversely with the distance r fromthe propagation axis and the propagation constant is ω/c.The fundamental mode of a coaxial wave guide is a TEMwave as well, with the same amplitude dependence on 1/rand the same propagation constant.

Therefore the excitation due to a relativistic beam in agiven Device Under Test (DUT) can be “simulated” by ex-citing a TEM field by means of a conductor placed alongthe axis of the structure. The impedance source on theDUT will scatter some field, i.e. exciting some higher or-der modes; such modes must not propagate otherwise thepropagating field will not be anymore similar to the theTEM beam field. In principle, then, simulating the beamfield with the TEM mode of a coaxial waveguide is possi-ble only at frequencies below the first higher mode cut-off,namely below the TM01 cut-off frequency. One can alsodemonstrate that the modes of the coaxial waveguide con-

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verges for vanishing wire radius to the analogous mode ofthe cylindrical waveguide, at least at the beam pipe bound-ary, where the impedance source is usually located.

To compare the excitation of a given DUT by a coax-ial wire and with the beam itself, we are going to dis-cuss some measurements done in the framework of the in-vestigations of the shielding properties of coated ceramicvacuum chambers [2]. The 500 MeV CERN EPA elec-tron beam was sent through two identical ceramic vacuumchamber sections; the first one was internally coated witha layer of 1.5 µm depth (DC resistance of 1Ω). Mag-netic field probes were placed to measure the beam fieldjust outside the two ceramic chambers (the coated and thereference one). In a first experiment, shielding propertiesof the resistive coating (thinner than the skin depth) weredemonstrated, confirming previous indirect measurementsand simulations [3]. In a following experiment, amongother results, it was proved that the screening properties ofthe coating can be spoiled by the addition of a second con-ducting layer placed outside the field probes and electri-cally connected to the metallic vacuum chamber sections.In this case, in fact, the magnetic field probe was measur-ing clearly the field of the 1ns (r.m.s.) bunched beam (seeFig. 1).

The same chamber in the same configuration (i.e. withthis additional external conductor) was then measured inthe bench set-up: a 0.8 mm diameter wire was stretchedon the axis of the structure. One end of the wire was con-nected to a 50Ω load while the other end was connectedto one port of a Vector Network Analyzer (VNA); match-ing resistors were used. The other port of the VNA wasconnected to the field probe. The network analyzer wasset to send through the wire a synthetic pulse (time do-main option) with 300 MHz bandwidth and measured thetransmission between the ports, i.e. the signal through theprobe.

This particular kind of set-up is not very often used, butit is very similar to the “time domain” measurement origi-nally proposed by Sands and Rees in the 70s [4]; nowadaystime domain measurements are often performed with syn-thetic pulse techniques in many microwaves applications.The measurement with the beam and with the wire shouldgive virtually the same result, apart from a scaling factordue to the difference of the power carried by the beam andby the VNA signal. The results are shown in Fig. 1 wherethe beam and the bench data have been normalized andtime shifted so that the traces coincides in their minimumpoint.

The external shield, having a DC resistance muchsmaller than the coating, carries the image currents, thefield penetrates the ceramic and the field probe can mea-sure a clear signal. This is only one of the configurationsmeasured both with the beam and in the bench set-up; theagreement with other measurements is similar to the one

of Fig. 1.The results of that comparison confirm the validity of the

coaxial wire approach to simulate the beam field effect on agiven DUT. Coaxial wire measurement are widely used toestimate impedances of many accelerator devices. Amongmany possible examples, we discuss issue of recent mea-surement on LHC collimators.

A. TCTP LHC collimator impedance measurementThe collimation system of the LHC is one of the largest

impedance contributors of the machine, in particular forits transverse imaginary part. In particular, a concernarose for the TCTP tertiary collimator: potentially harmfultrapped modes close to 100 and 200 MHz have been found.The effect of the trapped modes depends on the collima-tor tungsten jaws opening. Detailed simulation and benchmeasurements have been therefore performed. Eventuallyproper ferrite absorbers have been designed to try to dumpthem.

In the TCTP collimator, the main components of inter-est from a beam impedance reduction point of view are thelongitudinal RF fingers that cover the transition from thebeam pipe to the collimator structure, the transitions host-ing the BPM buttons and the RF system utilizing ferriteblocks and a screen structure as shown in Fig. 2.

In order to match the DUT (i.e. the collimator de-vice) with the VNA, a matching network needs to be de-signed. The standard procedure requires the knowledge ofthe DUT transmission line impedance Zc. In modern net-work analyzers it is possible to recover this informationby means of a time domain reflectometry measurement:the reflection coefficients Γ are measured from both theDUT ports and the corresponding input impedance calcu-lated from

Zc = Z01 + Γ

1− Γ, (3)

where Z0 is usually the 50 Ω cable impedance. Figure 3shows the characteristic impedance for 3 jaws openings inthe collimator: for large gaps, Zc appears flat, while, forsmaller gaps the reflections at the BPM transitions becomemore and more evident. For practical reasons, therefore,the stretched wire method can be only applied assumingan average value for Zc ' 230 Ω taken at the jaws locationfor intermediate jaws opening. It is moreover interesting tonotice how the wire profile could be inferred from the shortgap measurements: the flatness of the impedance curvecould be used as a wire-based jaws alignment method. Thecoaxial line characteristic impedance depends, indeed, onthe mutual position of the jaws and the wire and the dif-ference between Z1,1 and Z2,2 is due to difference on themutual position of the jaws and wire at the two sides of thecollimator. Such measurement technique could be used tobench measure the (hopefully small) jaws misalignmentswith a high level of precision, opening to metrological is-

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sues still to be investigated.The longitudinal impedance can be calculated from the

transmission parameters through the improved logarithmicformula [5] and provides an insight on the shunt impedancevalue in function of the collimator gap. Varying, then, thetransverse wire position we can get informations on theTCTP transverse impedance. Figure 4 shows the calcu-lated impedance value for the detected trapped mode at100 and 200 MHz. The absolute value might not be ac-curate depending on the field pattern perturbation of themode due to the wire, nevertheless it is useful for compar-isons once the mode damping ferrite will be installed in theTCTP collimator.

III. BEAD PULL TECHNIQUESAn important class of accelerator devices are cavities

which are now used both for accelerating and deflectingthe particle beam. Each cavity is characterized by its res-onant frequency f0, the quality factor of the resonance Qand its shunt impedanceR. One can think of measuring allthese quantities with the coaxial wire set-up, i.e. measur-ing strong notches in the transmission scattering coefficientbetween the ends of the wire. But the wire perturbs longi-tudinal cavity modes, e.g. lowers the Q and detunes thefrequency. Therefore the coaxial wire set-up is not usuallyrecommended for cavity measurements and it is advisableonly for special cases, mainly transverse modes [6].

The most used technique to characterize cavities is the“bead pull” measurement [7]. The field in the cavity can besampled by introducing a perturbing object and measuringthe change in resonant frequency: where the field is max-imum (minimum) the resonance frequency will be more(less) perturbed. It is a perturbation method, therefore theperturbing object must be so small that the field does notvary significantly over its largest linear dimension. Shapedbeads are used to enhance perturbation and give directionalselectivity among different field components.

Quantitatively, the change of the resonant frequency isrelated to the perturbed cavity field by the Slater theorem.The frequency variation can be measured by the variationof the phase at the unperturbed resonant frequency, ac-cording to Ref. [9]. Even if a very precise initial tuningis needed, this method allows easily measuring the fieldof many points (as many as the points of the instrumenttrace). The field shape can also be directly visualized onthe instrument screen, greatly facilitating the structure tun-ing procedure.

Novel accelerating devices RF structures foresee astanding wave part is tightly connected to a traveling waveone, thus the Slater resonant approach is not suitable.

Non resonant perturbation theory was first proposed bySteele [10] and allows the measurement of electromagneticfield in the perturbing bead position by measuring the com-plex variation of the reflection coefficient at a given fre-

quency ω, i.e.

∆S11 = S11,p (ω)−S11,u (ω) = −jωkSTE2/Pinc, (4)

where S11,p (S11,u) is the perturbed (unperturbed) reflec-tion coefficient, Pinc the average power entering the e.m.structure, kST a constant and E the electric field at thebead position and at frequency ω. Non resonant perturba-tion method (in the following referred to as Steele method)is the only way to measure e.m. field in non resonant RFstructures through a bead pull technique; it is used in res-onant structures when one is interested also in the phasebehavior of the field. Equation 4 is written only for electricfield, but a more general relation can be found in Ref. [10].

A. SPARC X-band cavityAs an example we can consider simulations and mea-

surements done on an 11.424 GHz standing wave multi-cell cavity, designed for the SPARC photo-injector [11].The cavity is supposed to work in the π-mode (all the cellsare filled with field) exhibiting a maximum field equal inevery cell (field flatness). A 9 cells prototype has been de-signed and built and all the details are reported in Ref. [12]while a picture is given in Fig. 5. We will present measureddata against numerical simulation results for the electricfield on axis.

Figure 6 compares measured data against numericalsimulation results for the electric field on axis. The fieldhas a maximum/minimum in the center of every cell andthe tuners have been set to have the required field flatness.The main measurement artifact was the non-negligible ef-fect of the glue used to fix the bead on a plastic wire to bemoved by the stepping motor; therefore the glue effect wasmeasured and calibrated away resulting in the data reportedin Fig. 6. Numerical codes gives very close results amongeach other and they all agree well with measurements.

B. Compact micro-acceleratorsX-band particle accelerators benefit from a reduced size

and an higher accelerating field with respect to the stan-dard S-band accelerators, nowadays used for high bright-ness electron beam production. High accelerating fieldin X-band, of 200 MV/m peak, allows the production ofhigh brightness beams. We have proposed a design a novelÒhybrid gunÓ from an electromagnetic and beam dynam-ics point of view together with the low power RF char-acterization of a preliminary copper prototype of such agun [13, 14].

The hybrid gun is a structure where the Standing Wave(SW) part hosting the cathode is tightly coupled to theTravelling Wave (TW) section through a coupling cell; aprototype is shown in Fig. 7. Such a device strongly mit-igates impedance mismatches, and therefore reflected RFpower, during and after the RF filling of the SW section.Therefore no circulator is needed to protect the klystron

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and this solves the problem of the absence of high powercirculator in X-band.

The hybrid gun avoids the bunch lengthening observedduring the drift in a split (conventional) photo-injector. Thebunch is indeed strongly focused longitudinally throughvelocity bunching, due to 90 phase shift between SWcell and input coupler. Numerical studies have shown thatthe emittance compensation dynamics remains manage-able even in the presence of strong compression.

We have studied the design of the hybrid gun from anelectromagnetic and beam dynamics point of view. Exten-sive numerical simulations have shown the control of beamsize and emittance and the possibility of tuning the work-ing point by changing the temperature of the SW part in thefew Celsius degree range. The electromagnetic design hasbeen finalized, according to the most recent design criteriaof high gradient accelerating RF structures.

Preliminary field measurement on a first prototype areshown in Fig. 8. According to Eq. 4, the reflection coeffi-cient as a function of the bead position is proportional tothe field seen by the particle. The non resonant methodallows to characterise both the SW and the TW part.

IV. CONCLUSIONSIn this paper we review the common bench methods to

measure coupling impedance for particle accelerator de-vice, both resonant and non resonant. Such methods arewidely used nowadays due to characterise most of the de-vices installed in modern accelerators. we have focusedour attention to devices used in state-of-the- art accelera-tors. Collimators are an open issue for the LHC impedancebudget and a careful estimation of their impedance is cur-rently ongoing. On the side of compact accelerators, theX-band technology is currently being investigated as wellas innovative RF designs; we have reviewed the measure-ment techniques needed to bench measure such devices.

V. ACKNOWLEDGEMENTSThis work has been partially funded by EU Commission

in the Seventh Framework Program, Contract n. 283745 -CRISP.

REFERENCES[1] L. Palumbo, V.G. Vaccaro and M. Zobov, in Fifth Ad-

vanced Accelerator Physics Course, CAS Cern Ac-celerator School, CERN 95-06 (1995), p.331. Seealso INFN LNF-94/041 (1994).

[2] L. Vos, F. Caspers, A. Mostacci et al., CERN AB-Note- 2003-02 MD EPA (2003).

[3] F. Caspers, E. Jensen, F. Ruggiero et al., RF Screen-ing by Thin Resistive Layers, PAC 99, New York(1999).

[4] M. Sands, J. Rees, SLAC report PEP-95 (1974).[5] E.Jensen, CERN-PS-RF-NOTE-2000-001, (2000).[6] F. Caspers in Handbook of Accelerator Physics and

Engineering, A. Chao and M. Tinger (editors), WorldScientific, Singapore (1998), p.570.

[7] R. Rimmer, M. Tinger in Handbook of AcceleratorPhysics and Engineering, A. Chao and M. Tinger (ed-itors), World Scientific, Singapore (1998), p.403.

[8] T.P.Wangler,Principles of RF Linear Accelerator,John-Wiley and Sons Inc., Canada (1998).

[9] F.Caspers, G.Dome, CERN SPS/85-46ARF (1984).[10] C.W. Steele, IEEE Trans. on Microwave Theory and

Techiniques, MTT-14, Vol. 2, February 1966.[11] Ferrario M. et al., Nucl. Instrum. Methods Phys. Res.

B, 309 (2013), p. 183.[12] A.Bacci, M.Migliorati, L.Palumbo, B.Spataro, INFN

LNF 03/008(R) (2003).[13] B. Spataro et al, Nucl. Instrum. Methods Phys.

Res., A 657, Issue 1, pp. 99-106, (2011);doi:10.1016/j.nima.2011.04.057.

[14] J.B. Rosenzweig et al, Nucl. Instrum. MethodsPhys. Res., A 657, Issue 1, pp. 107-113, (2011);doi:10.1016/j.nima.2011.05.046.

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Fig. 1. Signal from the field probe after normalizationand time shifting in the EPA experiment on coated chambershielding properties. The field probe is inserted betweenthe coated ceramic and an external conductor connectedto the beam pipe..

Beam

Jaws

RF fingers

BPM

Fig. 2. LHC TCTP collimator internal view: the RF fin-gers, BPM button and collimator jaws are visible. Thewire is stretched along the center of the collimator alongthe ideal beam trajectory.

−0.5 0 0.5 1 1.5 20

50

100

150

200

250

300

350

s [m]

Zc(s

) [Ω

]

Z

1,1

Z2,2

f.g. 20 mm

f.g. 5 mm

f.g. 60 mm

BPMtransition

BPMtransition

Jaws

Fig. 3. Transmission line characteristic impedance of theTCTP collimator as a function of length from time domainreflectometry measurement. For short full gaps (f.g.) theBPM transition regions become visible. For larger gapsthe impedance becomes flat. The symmetry of the curvesfrom the input ports reflect the DUT symmetry.

4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

full gap [mm]

Zt [

MΩ

/m]

Re(Zt) 100 MHz

Re(Zt) 200 MHz

Fig. 4. Peak of the TCTP transverse impedance versusfull gap obtained varying the single stretched wire hori-zontally. The impedance is critical for short gap values.

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Fig. 5. Nine cells copper prototype of the SPARC 11 GHzcavity.

Fig. 6. Longitudinal electric field on the SPARC cavityaxis: HFSS simulations (red line), SUPERFISH simula-tions (green line), MAFIA simulations (blue line) and beadpull measurements (black dashed line).

Fig. 7. Prototype of the hybrid gun, where the standingwave (SW ) part is tightly connected to the traveling wave(TW ) one. The RF power flows from port P1 to port P2,while port P3 is used to monitor the field in the SW cells.

Fig. 8. Longitudinal electric field on the hybrid gun axismeasured with the non resonant Steele method.

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