The Compact Linear Collider (CLIC) PETS is required to produce about 0.5 GW RF power per metre in the 30 GHz CLIC decelerator when driven by the high current beam (~ 270 A). To avoid beam break-up in the decelerator it is necessary to provide strong damping of the transverse deflecting modes. A PETS geometry with a level of damping consistent with stable drive beam operation has been designed, using the frequency domain code HFSS. A verification of the overall performance of this structure has been made recently using the code GdfidL, which permits a very fine mesh analysis of a full-length structure in the time domain. This paper gives the results of this analysis

Bruns, W

Syratchev, I V

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TIME DOMAIN SIMULATIONS OF THE CLIC PETS (POWEREXTRACTION AND TRANSFER STRUCTURE) WITH GdfidLI. Syratchev, CERN, Geneva, SwitzerlandW. Bruns, TU-Berlin, GermanyAbstractThe Compact Linear Collider (CLIC) PETS [1] isrequired to produce about 0.5 GW RF power per metre inthe 30 GHz CLIC decelerator when driven by the highcurrent beam (~ 270 A). To avoid beam break-up in thedecelerator it is necessary to provide strong damping ofthe transverse deflecting modes. A PETS geometry with alevel of damping consistent with stable drive beamoperation has been designed, using the frequency domaincode HFSS. A verification of the overall performance ofthis structure has been made recently using the codeGdfidL, which permits a very fine mesh analysis of a full-length structure in the time domain. This paper gives theresults of this analysis.1 INTRODUCTIONTime domain simulations of RF fields in travellingwave structures give more precise information about thewakefield behaviour than the frequency domain approach.A time domain simulation of the CLIC PETS has beenmade using GdfidL [2]. This particular code was chosenbecause it has the ability to calculate dielectric losses andcan calculate very long structures (about 100 cells) in areasonable time. The ability to compute long structures isnecessary in order to differentiate the RF losses from thenatural decay associated with high group velocitystructures. The results of these simulations are given inthis paper.2 EM CODE GDFIDLGdfidL is a finite difference based code, which restrictscomputation to the field-carrying parts of thecomputational volume. In the case of the PETS, thismeans that GdfidL has to compute the fields in only 30 %of the total number of grid cells. Even though GdfidLcomputes efficiently, for a structure as large as the PETS,current single-processor systems are far too slow tocompute the electromagnetic fields in a reasonable timeand the use of multiprocessor systems becomesmandatory. The most powerful multiprocessor systemsare distributed memory systems, like the Cray T3E.GdfidL running on such systems partitions the totalcomputational domain in sub-domains. For every time-step, all processors simultaneously compute theelectromagnetic field in their local sub-domain andindicate to each other the tangential fields on their localouter boundaries. The measured performance of theparallel version of GdfidL on 100 processors of a T3E isabout 50 times the performance of a 1 GHz AMD-Athlon.3 SIX-WAVEGUIDE PETSA 6-waveguide version of PETS with large (30 mm)beam aperture has been designed (Fig. 1) to satisfy thelow-decelerating-impedance requirement for the CLICtwo-beam scheme. To avoid beam break-up in thedecelerator, strong damping of the transverse modes isneeded. The most dangerous mode is the first dipolemode, which has practically the same frequency as thedecelerating mode because in this particular PETSgeometry most of the energy is concentrated around thewaveguides. As a consequence, the usual dampingmethod for a classical accelerating structure, based on afrequency-selective interception of the longitudinal wallcurrent, could not be used. The damping scheme adoptedis shown in Fig. 1. Corrugated longitudinal slits interceptthe transverse image current of the TE-type hybrid mode[1]. Since the density of the dipole mode current in theslot area is rather weak, the coupling of the dipole modeto the damper was improved by making the slot and SiCdamper geometry resonant at 30 GHz. The structure wasoptimized using the frequency domain code HFSS. It wasshown that the Q-factor of unwanted transverse modearound 30 GHz was reduced to below 50 [3].To verify the presence of this strong damping,simulations of a 100–cell structure plus RF outputcouplers were done with GdfidL.waveguideSiC roddamping slotFigure 1. The quarter geometry of the 6-waveguide PETS.The damping observed with GdfidL was over 10 timesless than predicted with HFSS. The error was due to awrong interpretation in HFSS of the resonant character ofthe transverse mode coupling to the damper.The GdfidL simulation also showed the presence oflow-frequency trapped modes. These modes are simplythe cut-off modes of the PETS beam aperture and are not0-7803-7191-7/01/$10.00 ©2001 IEEE. 3780Proceedings of the 2001 Particle Accelerator Conference, Chicagodamped. Modes associated with the output coupler werealso found.Since the level of damping in the 6-waveguide structurewas found to be insufficient (~1000), an alternativedesign based on a structure with circular symmetry wasundertaken. This design is discussed in the next chapter.4 CIRCULARLY SYMMETRIC PETSEarlier attempts [4] to design a circularly symmetricPETS were abandoned because no satisfactory methodwas found to damp the high group velocity transversemodes. This was particularly problematic because theirfrequencies are very close to the frequency of the mainmode. However, as a result of a fairly even angulardistribution of the RF current on the surface of thecircular structure, it is clear that the damping does notneed to be resonant.A new concept of distributed damping of the transversemodes in a circularly symmetric structure has beendeveloped. It is best explained in terms of array antennas.The damping is provided by thin longitudinal slotsrunning all along the length of the structure. Every periodof the slot-loaded structure acts like a single source in anarray antenna, radiating through the slots to the outside.The radial component of the radiation (damping) is afunction of the phase advances between two cells. Thesmaller the phase advance, the stronger the damping.Broadband RF loads terminate the slots.4.1 HFSS resultsAs an example, a structure with a smooth, sinusoidalcorrugation of the 20 mm beam aperture, C-PETS(circular), was studied. The damping was provided by 12equally-spaced radial slots of 0.5 mm, as shown in Fig. 2.The 12 loads each consisted of a long SiC rod with atriangular cross-section which was matched to the slot.Figure 2. A quarter geometry of the C-PETS with 12damping slots and SiC loads.The slot depth and load geometry were chosen tominimize the external Q-factor of the first dipole modearound 30 GHz. The parameters for the optimisedgeometry are shown in Table 1 and Fig. 3. A very strongdamping of the dipole mode is seen, that increases as thephase advance is decreased, as expected.Table 1. The first dipole mode parameters with andwithout distributed damping.ϕO F(GHz)Q-factor βGROUP,(%c)Undamped 121 30.312 12315 83.4Damped 121 30.133 ~30 66.3Phase advance, degree0 30 60 90 120 150 180LoadedQ-factor101001000Figure 3. Damping of the dipole mode in C-PETS with 12damping slots for the different phase advances per cell.To make a qualitative study of the damping in the C-PETS, a constant beam current excitation was introducedin HFSS.Figure 4. Electric field pattern in C-PETS excited by thebeam.The radial propagation of the RF field towards the loadis clearly seen in Fig. 4 and indicates damping. Note thatthe same kind of simulations performed for the 6-waveguide PETS did not show much radial RF powerleak (damping).3781Proceedings of the 2001 Particle Accelerator Conference, Chicago4.2 GdfidL resultsThe same 100-cell C-PETS geometry (see Fig. 2) wasused to make simulations with GdfidL. A 1.5 cm longbeam pipe was added to both ends. The computation ofthe wake-potentials up to distances of 4 m was made for6×107 grid points. The computation time was 8 hours on100 CPUs of a Cray T3E, or 75 hours on eight AMD-Athlon-1000.The short-range transverse wakes for the undamped anddamped cases are shown in Fig. 5. The fast roll-off for theundamped case is caused by very fast evacuation of theRF power from the structure due to the high groupvelocity. This illustrates the importance of simulatinglong structures, especially with strong damping. For thedamped case, the even further decay of the wake is aresult of the strong damping. The loaded Q-factor in thiscase was calculated to be 35. This value is very close tothe one calculated with HFSS.s, m0.00 0.05 0.10 0.15Wt,V/pC/mm/m-2-1012Figure 5. The short-range wakes in the C-PETS,diamonds: undamped case, circles: with damping.The long-range transverse wakes and transverseimpedances are shown in Figs. 6 and 7. The second bigspike in the wake distribution for the undamped case(Fig. 6) is a result of partial (about 30 %) reflection fromthe ends of the structure. With damping the reflection isnot seen due to the strong attenuation of the reflectedwave.From a comparison of the transverse impedances (Fig.7) it is seen that low-frequency trapped modes are alsosignificantly suppressed with this distributed dampingtechnique.5 CONCLUSIONThe time-domain simulations of the full size6-waveguide PETS with GdfidL showed that the dampingof the transverse modes was strongly over-estimated withHFSS. A circularly symmetric version of the CLIC PETSstructure is in consequence being reconsidered. With thenovel concept of distributed damping, the strongsuppression of the transverse modes in a broad frequencyrange has been demonstrated both by HFSS and GdfidL.The design of the C-PETS prototype together with RFcouplers is now underway.GdfidL was found to be well adapted for the simulationof large, complicated RF structures, like PETS, in areasonable computing time.Figure 6. The long-range wakes in the C-PETS,grey: undamped case, dark: with damping.Frequency, GHz10 20 30 40 50 60Re(Zt),V/A/mm/m0.1110100Figure 7. The transverse impedance in the C-PETS,grey: undamped case, dark: with damping6 REFERENCES[1] G. Guignard, et al., “A 3 TeV e+e- Linear ColliderBased on CLIC Technology”, CERN 2000-008,Geneva 2000.[2] W. Bruns, "The GdfidL Electromagnetic Field Simu-lator", http://www.wbfb.de/.[3] M. Luong, I. Syratchev, “Simulations of the Dampingof the Power Extraction and Transfer Structure(PETS)”, CLIC-Note-442, 2000.[4] H. H. Braun, et al., “The CLIC RF Power Source”,CERN 99-06, Geneva, 1999.3782Proceedings of the 2001 Particle Accelerator Conference, Chicago

Time Domain Simulations of the CLIC PETS (Power Extraction and Transfer Structure) with GdfidL

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