Particle Accelerators, 1994, Vol. 45, pp. 195-208

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A BROADBAND WAVEGUIDE TO COAXIALTRANSITION FOR HIGH ORDER MODE DAMPING

IN PARTICLE ACCELERATOR RF CAVITIES

R. BONI,l F. CASPERS,2 A. GALLO,l G. GEMME,3 andRe PARODI3

1 I.N.F.N., Laboratori Nazionali di Frascati, C.P. 13, 00044 Frascati, Italy

2 CERN, PS Division, CH-1211 Geneva 23, Switzerland

3 I.N.F.N., Sezione di Genova, Via Dodecaneso 33, 16146 Genoa, Italy

(Received 26 November 1993; infinalform 18 March 1994)

A novel !!roadband Waveguide to Coaxial !ransition for !!igh Order Mode Qamping in Particle Accelerator RFCavities (BTHD) has been studied and developed in the framework of the Frascati <t>-Factory project DA<t>NE.The cavity high order modes (HOM) are the primary source of coupled-bunch instabilities in multibunch storagerings. The energy delivered by the particle beam to the cavity HaMs and coupled out with waveguides is convertedby BTHD into the TEM coaxial mode and dissipated by a 50 n load connected via a ceramic feedthrough. Thisarticle deals with the design and the low power tests performed on a BTHD prototype and the considerations fora real application to an accelerator.

KEY WORDS: RF cavities, RF devices

1 INTRODUCTION

A broadband waveguide to coaxial transition (BTHD) has been designed for coupling outand thus damping the wake fields excited in the RF cavities by the DA<PNE bunched beams.The machine complex, which is presently under construction, is a double intersecting 500MeV ring for the accumulation of high current (up to 120 bunches, 46 rnA per bunch) elec­tron/positron beams. l In such a multibunch machine, like in similar storage ring projects inother Laboratories, coupled-bunch longitudinal instabilities can be excited by the interactionof the particle beams with the parasitic wake fields induced by the beam itself in the reso­nant accelerating cavities. The high quality factor Qof the HaMs (<?fthe order of 104 for anormal conducting undamped cavity) let the wake fields decay in a time sufficiently long tointeract with many bunch passages getting the beam unstable. A solution to this problem hasbeen proposed and is also being developed in other accelerator centers like LBL and Cornell(U.S.A.), Trieste (Italy) and KEK (Japan). It consists ofcoupling the HOMs out of the cavityover a wide frequency band by means of waveguides (WG) connected to the cavity surfaceand dissipating the associated energy in dummy loads. This method has been shown to

195

196 R. BONI etal.

TABLE 1: The DA<I>NE RF System Main Parameters

RF Frequency

Harmonic Number

Cavities per Ring

Cavity Impedance RlQ

Cavity Quality Factor

RF Peak Voltage

Cavity Wall Power

Current per Beam

368.25 MHz

120

61 Q

40000

260kV

13.8kW

1.4 Amps (30 bunches)

permit a reduction of the HOM Qs and shunt impedances by some orders of magnitude, thusreducing the intensity and the decay time of the cavity induced wake fields. For DA <I>NE,a reduction of the Q of some high impedance HaMs to a few hundreds is consideredsufficiently safe for an initial machine operation with 30 bunches. Table 1 shows the RFSystem main parameters. Tests have been carried out on a full scale cavity prototype2

equipped with three 305 x40 mm2 WGs with cut-off at 492 MHz and terminated with lossymaterials. Figure 1 shows a picture of the cavity prototype equipped with the WGs. TheHOM damping obtained with such a structure is satisfactory since the damped Qs are aslow as a few hundreds and even less over a wide frequency band (up to 2.6 GHz).

FIGURE 1: The DA<I>NE Cavity Prototype.

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION 197

Since the RF cavity in the ring must operate in ultra high vacuum (DRV) at 10-9 Torr,the lossy materials, based on ceramics or ferrites would be placed in DRV too and wouldrequire care for brazing to the internal WG surface and cooling when dissipating power.Although there is a good progress of the R&D in this field, to our knowledge, the capabilityof such materials to operate reliably for a long term in an accelerator DRV environmentat high power dissipation rate (in the kW range) has not been exhaustively proved. On theother hand, the use of alumina vacuum windows in the WGs is of some concern due to thelarge size required.

A simpler and, in our opinion, more reliable solution to convey the ROM power to adummy load is to use a transition from the rectangular WG to a coaxial 50 Q line. Thus,the power can be absorbed by an external 50 Q load via a vacuum feedthrough of standarddesign.

2 GENERAL CONSIDERATIONS

Ridged WGs are more suitable than rectangular WGs to convert, in a wide frequency band,the fundamental TElO WG mode to the coaxial TEM mode. For this reason the BTRDconsists, as shown in Figure 2, of two sections: a tapered transition from rectangular todouble-ridged WG followed by a transformer to 50 Q coaxial line.

Ridged WGs commonly used are single and double-ridged. The basic motivation forbuilding ridged WGs is to lower the cut-off frequency of the fundamental TElO modewithout increasing the external dimensions. This is done by introducing a metallic ridgeinto a normal rectangular WG. As an advantage of these WGs, the ratio of the cut-offfrequencies TE30/TElO may exceed a factor of 15 depending upon the aspect ratio of theWG and the ridges. These cut-off frequency ratios have been worked out by analytical aswell as numerical methods and can be found in the literatu~e for a wide variety of ridged andrectangular WG geometry. The TE20 mode is often not considered relevant in this context,as it may not be excited or transmitted via the coaxial to WG transition due to its symmetry.

As a very narrow gap between the ridges would lower the maximum permissiblevoltage, caution should be exercised for high power applications or under vacuum resonantdischarges (multipactoring). A method to reduce the maximum electrical field strength isto use semicircular ridges3 instead of rectangular ones, thus avoiding high peak values forthe electric field at the edges of a ridge.

Normalized ridged WG components (single and double ridge) are available from industryfor use in wideband applications. For special requirements, ridged WG horn antennas (e.g.1 to 12 GRz) for broadcasting are on the market. The basic ingredients of this subject havealready been discussed in 1947 and in 1955.4,5,6 Ridged WGs can be loaded with dielectricand/or magnetic material (non reciprocal devices).? As for standard WGs without partialdielectric or magnetic loading, the general dispersion relations for phase and group velocitystill hold.

Coaxial to WG transitions are basically transformers and mode transducers. A largevariety of structures are in use in order to obtain a good impedance matching overthe bandwidth required. For a rectangular WG this mode transducer is often sim­ply a probe with a small metallic ball attached to the end, protruding into the WG.

198 R. BONI eta/.

WAYEGJIIDEIO$OOCOAXI",

DANsmBMEB

TAPERED IR ANSITION

FIGURE 2: Sketch of the Broadband Transition.

However, the diameter, position and length of the probe have to be carefully evaluated.Other transitions have some sort of coupling loop, occasionally with dielectric loading.There exist no general synthesis methods for optimal coaxial line to WG transitions. ManydesignsS,g are based on experience and intuition, but nevertheless work surprisingly well.As for the analysis of a given structure, .a general analytical procedure would be a modematching technique, i.e. describing the field in the vicinity of the transition as the infinitesum of propagating and evanescent WG modes and working out the coupling coefficientfor each mode. This theoretically very elegant method meets many problems in its practicalsolution and thus, in the past, a design had often to go through many cut and try stages.With the availability of powerful computer codes, this tedious and time consuming cut-and­try work can be drastically reduced. Carefully done computer simulations usually lead toresults close to measured values.

3 BASIC BTHD SPECIFICATIONS

Coupling the cavity HOMs with WGs is favourable with respect to other techniques (suchas loop or antenna couplers) which do not provide wide frequency response and requirefiltering to reject the cavity fundamental mode (FM). The BTHD frequency response mustextend from the first HOM to the beam pipe cut-off (510 MHz to 2.6 GHz for the DA<I>NEcavity). A VSWR ~ 2 is required at the BTHD input in that frequency range, correspondingto more than 88% of power transmission to the coaxial output.

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION 199

The power handling capability is another relevant BTHD feature. The RF power, PROM,carried outside the cavity can be evaluatedlO from the beam and damped cavity spectraaccording to the following relation:

PROM =I: 2(R/Q)kQextIJ;

n=-oo 1+ Qk (nfr/fk - fk/ nfr)2k=all ROMs

(1)

where In is the amplitude of a beam spectrum line, (R/ Q)k is the ratio of the longitudinalHOM impedance at the resonance to its quality factor, Qextk and Qk are the external andloaded HOM quality factors respectively, fr is the beam revolution frequency (i.e. 3.07 MHzfor DA<I>NE) and fk is the HOM resonant frequency. The beam spectrum strongly dependsupon the distribution of the beam charge in the bunches, while the damped cavity spectrumcan be determined from computer code simulations and from prototype measurements.The estimated HOM power extracted in a 30 bunch machine operation, as reported in thereference, lOis around 150 W for three WGs. The power is mostly due to the interaction of thebeam spectrum with the first HOM monopole that has the highest impedance (R / Q = 16n).The BTHDs must handle this amount of power without discharges or multipactoring overthe complete frequency range.

4 THE BTHD DESIGN

The BTHD tapered transition and the mode transducer have been at first separately designedusing analytical approximations and then improved via a step-by-step refinement procedurebased on the use of the 3D electromagnetic (e.m.) computer code High Frequency StructureSimulator (HFSS HP trademark).ll The two sections mentioned above have been finallyjoined in a single model for the computer code simulation.

This transition has not been designed to couple to the TE20 mode that could in principlebe excited by the cavity HaMs. In our case, the cavity HaMs to be heavily damped aremonopoles and dipoles which can practically launch only the TElO WG mode due to theirazimuth symmetry. For those applications which also require transmission of TE20 mode,the transition design should be implemented with a different geometry of the ridges. Inaddition, a dedicated and more selective TE2o-TEM transducer must be foreseen.

4.1 Rectangular to Double-Ridged Waveguide Transition

The rectangular WG connected to the cavity surface smoothly adapts to a double-ridge toco~xial transformer through a 500 mm tapered section. This can be considered a double­ridged WG with a continuously variable cross-section (inhomogeneous WG) from 305 x40mm2rectangle at the cavity side to 140 x 40 mm2 with two 62 x 17 mm2ridges. The minimumridge distance is kept at 6 mm to reduce the risk ofdischarges; this conservative choice limitsthe maximum obtainable frequency bandwidth. The width of the structure varies linearlyfrom 305 to 140 mm while the height has a constant value of 40 mm.

Mechanical or electrical discontinuities in the WG taper can convert the TElO to theTE20 mode which cannot be transformed to the TEM coaxial mode. For this reason much

200 R. BONI etal.

care is required in avoiding any roughness of the internal surfaces. The electromagneticdiscontinuities can be avoided by shaping the ridge in order to keep the TEIO cut-offfrequency of any cross section at a constant value. In fact, electric and magnetic fieldvectors are orthogonal for TE and TM modes in the transverse plane regardless of the WGshape; for the TEIO mode (and generally speaking for any propagating mode) the ratio ofthe modules of the two vectors depends only upon the ratio between the mode cut-off andthe operating frequencies Ie /I as follows:

(2)

where 11 = J JL / c, often called characteristic wave impedance, is a constant of the fillingdielectric material (377 Q for vacuum) and ZTEIO is the "field impedance" which does notdepend on the WG shape. The field impedance must be distinguished from the characteristicWG impedance Zo that depends on the WG shape and is defined as:

y2Zo=­

2P(3)

where Y is the voltage across the WG gap and P is the transported power. For the TEIOmode of a rectangular WG the simple following relation holds:

bZo = 2 . - . ZTEIO

a(4)

where b and a are the WG height and width respectively. So, by keeping the cut-offfrequencyalong the tapered section constant, the ratio between the transverse components of theelectric and magnetic field vectors is a constant at any operating frequency. The ridgedprofile has been computed in order to keep the cut-off frequency at 490±1.5 MHz alongthe longitudinal axis of the tapered WG. The result of the BTHD tapered WG transitionsimulation is given in Figure 3 and shows that an input VSWR lower than 2 is achievablein the range 540 to 2800 MHz.

4.2 Double-ridged Waveguide to Coaxial Transducer

The transducer consists of the inner conductor of the coaxial line protruding into the double­ridged WG through the E plane. It is in contact with the opposite ridge and guides the e.m.field of the WG out in the TEM mode of the coaxial cable. A short section ofWG, terminatedwith a metallic plate (also called back-cavity) is situated beyond the transducer. It behaveslike a shorted line for matching the coaxial and the double-ridged WG impedances.

Dseful design criteria to initially define the main parameters of the transition wereobtained fromS,g and the first design of the transducer is shown in Figure 4. As a firstguess, a 7 mm (outer conductor diameter) coaxial line was chosen since this is a standardsize of commercially available DHV feedthroughs.

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION 201

1.0

0.54 FREQUENCY (GHz) 2.20 2.80 J.O

FIGURE 3: Code Simulation (HFSS) of the Tapered Waveguide Transition Response (S11 vs Frequency).

A I N type- I / Connector

SECTION A-A

-AI

FIGURE 4: Preliminary Design of the Mode Transducer.

The results of the HFSS simulation are shown in Figure 5 and could not be consideredas satisfactory. The SII parameter curve exhibits some narrow peaks in the upper bandof the spectrum corresponding to a VSWR as high as 7. Variations to the back-cavitydimensions did not significantly improve the response. By examining the HFSS field plotof the transducer at the frequency of the peaks, the regions hatched in Figure 4 were found toresonate as a )J4-like line producing sharp notches in the power transmission. This unwantedbehavior has been eliminated by rounding the profile of the ridge end and increasing thediameter of the inner conductor of the coaxial line. In this way, the length of the A/4-likelineis reduced and its resonant frequencies are shifted out of the BTHD bandwidth. Moreover,the ridged WG characteristic impedance of about 30 Q can better match to the coaxialline which is then tapered to fit with a 1-5/8" output flange. The actual geometry of thetransducer is shown in Figure 6 and the computed S parameters are depicted in Figure 7.

202 R. BONI etal.

1.0

VSWR =2.0

0.0 L- ...;........ ___

0.61..38

FREQUENCY CGHz) 3.0

FIGURE 5: Response of the Preliminary Mode Transducer simulated with HFSS. (S11 vs Frequency).

The S11 response of the complete BTHD, shown in Figure 8, has been consideredsatisfactory to proceed with the fabrication of a prototype.

5 EXPERIMENTAL RESULTS

Three full scale aluminum BTHD prototypes have been manufactured and RF tested atlow power. Figures. 9a,b and 10 show a picture of the prototype and a sketch of the RFtest bench respectively. The S11 parameter of one prototype at its coaxial input has beenmeasured with a network analyzer by connecting two BTHDs through the rectangular WGports and gating the total response to isolate the device under test. The result, presented inFigure 11, is better than that expected from simulations, the VSWR being lower than 2.1 inthe range 510 to 3000 MHz. Small tuning of the back-cavity length can optimize the BTHDbandwidth and VSWR ::s 1.6 is obtained in the 570 to 2600 MHz band.

The BTHD prototypes, loaded with 50 Q terminations, have been incorporated to theDA<I>NE cavity model through a waveguide straight section of 30 em. The quality factor Qofthe highest impedance HOMs has been compared with that obtained with the ferrite loadedWGs. The results, listed in Table 2, are almost the same in both cases. The obtained dampedHOM Qs are below the target values required by the DA<I>NE beam dynamics.12, 13, 14

The FM quality factor of the prototype is decreased by 12%; therefore an excess FMpower of about 500 W per waveguide is foreseen to be dissipated in the real cavity. Thispower will be mostly wasted in the 30 em waveguide straights that will require cooling.

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION

./

.LyI

FIGURE 6: Final Geometry of the Mode Transducer (HFSS Plot).

1. OOe+OO

Freqoorx:y(MHz) O. OOe+021div)

FIGURE 7: Response of the Final Mode Transducer simulated with HFSS. (SII vs Frequency).

203

204 R. BONI et ai.

1.00e+00

o. OOe+OO L- ~--__:::~_=

5. O0ei1>2 2500 3. 00e+03Frequ:rx:y(11fz)

FIGURE 8: Frequency Response Simulation of the Final BTHD (S 11 vs Frequency).

6 THE REAL APPLICATION

The experimental results are fully satisfactory with respect to the accelerator demands.The main troubles in a RF device operating under vacuum are the discharges due to fieldemission and multipactoring. All the discharges depend upon the local e.m. field strengthand distribution but some simple rules can give information about the discharge thresholds.

TABLE 2: Cavity Prototype HOM Quality Factors

MODE FREQ. RlQ (Q) UNDAMPEDQ FERRITE BTHD QTARGET

(MHz) DAMPEDQ DAMPEDQ

O-EM-l 357.2 61 25000 22000 22000

O-MM-l 745.7 16 24000 70 70 85

0-EM-2 796.8 0.5 ·40000 230 210 2500

0-MM-2 1023.6 0.9 28000 150 90 300

0-EM-3 1121.1 0.3 12000 300 300 3500

0-MM-3 1175.9 0.6 5000 100 90 1650

0-EM-4 1201.5 0.2 9000 130 180 4300

0-EM-5 1369.0 2.0 5000 300 170 450

0-MM-4 1431.7 1.0 4000 750 550 870

I-MM-1, a 490.0 5.1* 30500 350 650 9200

1-MM-l, b 491.3 5.1~ 28500 250 830 9200

l-EM-1, a 523.5 14.0* 31500 280 150 6200

l-EM-l, b 549.7 14.0* 32000 270 50 6200

(*): Normalized Impedance

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION

FIGURE 9a: Assembled

FIGURE 9b: Open

FIGURE 9: The BTHD Prototype.

205

206 R. BONI eta!.

Calibrated Cable

BTHD2BTHDI

Network Analyzer

D87~C

FIGURE 10: Scheme of the RF Test Bench.

CHi 511 5WR 200 m / REF 1 ~ 2.0006

COl"

Gat

Itil 2 790. ~o 3C ~ MHZ

MARt ER 12.79C 250 ~05 GHz

VSWR:2~:\ /

\ -)

\ V-~ /v- I'---

~~ //

"'-l--/

START 500.000 000 MHz STOP 3 000.000 000 MHZ

FIGURE 11: The Measured Frequency Response of the BTHD.

BROADBAND WAVEGUIDE TO COAXIAL TRANSITION 207

A largely accepted safety limit for vacuum discharge is a surface electric field of about3 MV/m. Since the WG characteristic impedance along the tapered section varies from50 Q to 30 Q at the coaxial insertion, a surface field of 3 MV1m in the ridge gap correspondsto 5.4 MW of transported power that is more than 3 orders of magnitude higher than inthe DA<PNE case. Therefore, by providing an accurate finishing of the internal surfaces,vacuum discharges due to field emission should be very unlikely.

Multipactoring can occur in RF devices under vacuum and it strongly depends on thefield distribution. Thus, due to the limited reliability of the simulation codes dealing withelectron discharges, only full power tests can give complete information. Nevertheless, frommultipactoring threshold evaluations15 it comes out that the propagating HOMs should notcause multipactoring in the BTHD. However titanium coating must be in any case foreseento prevent the multipactoring due to the penetration of the accelerating cavity mode in theregion near the WG openings.

The final transitions will be made, as the accelerating cavity, of oxygen free, highconductivity copper.

The BTHDs need a low VSWR, wideband 50 Q ceramic vacuum feedthrough. The useof a 1 kW standard N type device, available on the market, has been rejected since a biggersafety margin on the extracted power is advisable. Simulations carried out with the 3D codeshow that a 7/8" ceramic feedthrough with a low VSWR in the 0.5 to 3 GHz band is feasible.

The BTHD also allows the sampling of the HOM power by connecting a directionalcoupler at the 50 Q output.

7 CONCLUSIONS

A novel device (BTHD) for coupling the high order mode power out of the DA<PNE accel­erating cavities has been developed and three aluminum prototypes have been successfullytested on bench at atmospheric pressure and low power. The experimental results confirmthe code simulations. The BTHDs operate as mode transducers from the TEIO waveguidemode to the TEM coaxial mode; therefore the high order mode power can be dissipatedon standard 50 Q loads instead of on lossy materials brazed and operating in vacuum. Thehigh order mode damping 'obtained with the BTHD system meets the requirements of theDA<I>NE beam dynamics. 12, 13, 14

Power levels of hundreds of kilowatts can in principle be handled in ultra-vacuum by theBTHD, the operating limit depending only on the size of the output coaxial connector. Inour case, the 7/8" standard is sufficiently oversized to handle. the high order mode powertransmitted by each DA<PNE cavity waveguide. Multipactoring is unlikely to occur in ourBTHD; anyhow it can be inhibited with a titanium or other low secondary emission coatingof the internal surfaces. Power tests in vacuum are in program to check the reliability ofBTHD.

ACKNOWLEDGEMENTS

We wish to thank P. Baldini warmly for his invaluable collaboration in the RF tests andgratefully acknowledge the continuous technical support of S. Quaglia. We also very muchappreciated the collaboration of Dr. Siani of the E.S.O. Company, Rome, Italy.

208

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R. BaNI etal.

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8. K.L. Walton and V.C. Sundberg, "Broadband Ridged Hom Design", Microwave Journal, 7 (1964) pp.96-101.

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14. S. Bartalucci, M. Bassetti, R. Boni, S. De Santis, A. Drago, A. Gallo, A. Ghigo, M. Migliorati, L. Palumbo,R. Parodi, M. Serio, B. Spataro, G. Vignola and M. Zobov, "Analysis ofMethods for Controlling MultibunchInstabilities in DA<I>NE", LNF-93/067 (P) (1993).

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