Studies of waveguide damped 30 GHz accelerating structures for multibunching in CLIC are described. Frequency discriminated damping using waveguides with a lowest cutoff frequency above the fundamental but below the higher order modes was considered. The wakefield behavior was investigated using time domain MAFIA computations over up to 20 cells and for frequencies up to 150 GHz. A configuration consisting of four T-cross-sectioned waveguides per cell reduces the transverse wake below 1% at typical CLIC bunch spacings

Dehler, M

Wilson, Ian H

Wuensch, Walter

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CLIC WAVEGUIDE DAMPED ACCELERATING STRUCTURE STUDIESM. Dehler, I. Wilson, W. WuenschCERN, 1211 Geneva 23, SwitzerlandAbstractStudies of waveguide damped 30 GHz acceleratingstructures for multibunching in CLIC are described.Frequency discriminated damping using waveguides with alowest cutoff frequency above the fundamental but belowthe higher order modes was considered. The wakefieldbehavior was investigated using time domain MAFIAcomputations over up to 20 cells and for frequencies up to150 GHz. A configuration consisting of four T-cross-sectioned waveguides per cell reduces the transverse wakebelow 1% at typical CLIC bunch spacings.IntroductionExtension of the CLIC scheme to allow operation withtrains of 10-30 bunches (30 cm spacing and 8x109 particlepopulation) is being studied in an attempt to increase overallefficiency. Such an extension requires a new acceleratingstructure design that produces suppressed long rangewakefields. Preliminary tracking results indicate that theaccelerating structure must have a reduction of thetransverse wake by a factor of approximately 100 by thetime of arrival of a following bunch [1] - including thecumulative effects of all higher order modes. After the timeof the following bunch the wake should continue to decreasesuch that the wake from many bunches does not accumulate.Wakefield reduction based on detuning has been studied[2], however it does not appear that this scheme provides asufficient level of performance. The conclusion has persistedeven though proposed multibunching parameters havechanged significantly since the study was made.The scheme of wakefield reduction considered here isbased on frequency discriminated waveguide damping.Damping waveguides, connected to the outer cavity wall, arechosen to have a cut-off frequency above the fundamentalbut below all higher order modes - higher order mode energycan propagate out of the accelerating section but thefundamental mode energy cannot.A number of damping waveguide configurations havebeen studied using MAFIA. Time domain MAFIAcomputations were used to determine the transverse andlongitudinal wakefields because this direct calculationinvolves a minimum of assumptions and gives a more or lesscomplete wakefield in a single calculation. In all cases thesimplifying assumption of a constant impedance structurehas been made. The suitability of a structure design is to beconfirmed by beam dynamics simulations that use acomputed wakefield.Computation methodThe first step in the study of a candidate geometry was todetermine the dimensions needed for a correct fundamentalmode frequency by making frequency domain computations.This also gave the fundamental mode Q and R/Q.Initial time domain calculations over one or two cellsfollowed. If the results looked promising, more accuratecalculations of up to 20 cells followed, the number beinglimited by computer size and speed. The larger number cellsgives a more accurate wakefield because it more accuratelycaptures the correct R/Q and phase advance - the discrete setof modes given by a finite cell model does not in generalinclude the synchronous mode of the passband.The four lowest modes of the damping waveguides wereideally terminated. Thus the assumption that the dampingwaveguides are nearly perfectly terminated underlies all ofthe results  presented here. The beam pipes were terminatedwith electrical boundary conditions in order not to over-estimate the damping of the structures.Design considerationsThe transverse wakefield of the CLIC constantimpedance geometry is dominated by the lowest, TM110,transverse passband with a number of higher bandscontributing at the 5-10% level. The criterion for anacceptable design has been that modes in a wide frequencyband, up to about 150 GHz, must be damped.The basic design features that were used to produceadequate transverse wake damping include: the placement ofthe waveguides in the cells, the number of waveguides percell, the waveguide cutoff frequency, waveguide couplingstrength and the waveguide cross section.CLIC disk loaded waveguide is assembled from elementseach containing a full iris and a full cell. The waveguidesstudied here have been restricted to those which could inprinciple be milled into the top of the element on the cellside. This limitation was imposed to limit the mechanicalcomplexity of the design but it does restrict dampingwaveguides to being longitudinally off-center in the cellsand adjacent to the iris.A configuration with four waveguides per cell has theadvantage of coupling to both polarizations of transversemodes in each cell, and of maintaining a high order ofsymmetry in the fundamental mode. However the cellsbecome mechanically simpler if the number of waveguidesper cell can be reduced. Three waveguides spaced by 120°per cell [3] were considered. This solution damps bothpolarizations of the dipole mode and maintains anacceptable symmetry of the fundamental mode. However thesymmetry of the structure does not match that of thequadrupole modes and results in a shift of the center of thefield pattern (Fig. 1). Near the origin this gives thequadrupole modes a dipole mode characteristic thusincreasing the number of dipole modes contributing to thetransverse wake. Subsequently only two and fourwaveguides were considered - the choice being largelydetermined by the strength of coupling needed.Figure 1: Quadrupole mode in 3-fold symmetric cavity.The cutoff frequency of the damping waveguide isbounded by an excessive fundamental mode fieldpenetration into the waveguide and consequent loss of R/Qand Q the low side and by the persistent wake [4] on thehigh side. The persistent wake is a result of the resonanceassociated with the cutoff frequency of the waveguide - atthe cutoff frequency the group velocity goes to zero and thewaveguide acts like a resonator. The transverse wakefieldhas an initial exponential drop-off followed by a wakedecreasing with t-1.5 as the persistent wake becomesdominant. Lowering the cutoff frequency contributes tosuppressing the persistent wake.The coupling strength of the waveguide to the lowesttransverse mode of the accelerating structure also plays arole in the level of the persistent wake. An increasedcoupling can quicken the initial exponential drop-off but atthe expense of  increased coupling to the persistent wake andconsequently a higher value of the wake for longer times.The coupling can be adjusted by changes in the dampingwaveguide height (the cutoff frequency remains unchanged)or by adding an iris at the cell-waveguide connection.The waveguide resonance makes incorporating detuninginto the design more difficult as the waveguide cutofffrequency partially determines the frequency of thetransverse wake. In addition the varying frequency splitbetween the dipole mode and the fundamental mode alongthe length of a constant gradient or detuned structure impliesvarying damping characteristics.The waveguide (and iris) cross section at the connectionpoint to the cavity wall is the primary means to ensureadequate coupling to the forest of higher order transversemodes including the lowest hybrid TE mode (which itselfcontributes roughly 0.5 % to the amplitude of the undampedwake). For the class of waveguides considered here theprimary difficulty is that the TE01 cutoff frequency inrectangular waveguide is too high to couple to the TE11mode of the cavity. This has been resolved by using a ‘T’cross-sectioned waveguide (Fig. 2). This results in twowaveguide modes of relatively low cutoff frequency, one ofwhich couples to the TE11 cavity mode.Figure 2: Magnetic field patterns in a T cross-sectionedwaveguide.Design resultsThe application of the design considerations has lead totwo waveguide damped disk loaded waveguide designs. Onecell and iris of the disk loaded waveguide of each of thedesigns are shown in Figs. 3 and 4. Successive cells of thetwo waveguide geometry are rotated by 90° in order tocouple to both polarizations of the transverse modes. Thewakefield from the structure is shown in Fig. 5.Figure 3: Two waveguide damping.The primary defect of the design is a substantiallyreduced Q, 2800 rather than 4400 for the undampedgeometry. The Q is lost by the current density concentrationaround the edges of the top part of the ‘T’.  Closing of thispart of the ‘T’ off with an iris, as in the geometry shown infigure 4, reestablishes the Q. However four waveguides mustbe used in each cell in order to maintain an adequatecoupling. The wake from this geometry is shown in Fig. 6.Figure 4: Four waveguide damping with iris.Figure 5: Transverse wakefield from two waveguidegeometry computed over 20 cells.Figure 6: Transverse wakefield from four waveguidegeometry computed over 13 cells.Another perspective on the damping can be seen bycomparing the Fourier transforms of the wake from adamped and an undamped (CLIC constant impedance)structure geometry, Fig. 7.Figure 7: Fourier transform of the transverse wake of the 2waveguide damped (Fig. 5) geometry and correspondingwake of the undamped geometry.ConclusionsMAFIA computations have been used to design anaccelerating structure geometry with four dampingwaveguides per cell and to demonstrate that the geometrycan produce a reduction of the transverse wake by a factor100. Beam tracking simulations using the computed wakeare now being made to demonstrate that this damping isadequate.A number of further issues must now be addressed. Theeffects of imperfect waveguide terminations, the design of ahighly compact load effective near the waveguide cutofffrequency, the beneficial effects of adding detuning to thedamping and the complications of producing a constantgradient structure must all be considered.Finally, however, a number of mechanical andfabrication issues have lead to the conclusion that thedesigns presented here are probably not buildable. Anassessment, that includes consideration of mechanicalfeasibility, of the direction that the study will now take isbeing made.References[1] G. Guignard and J. Hagel, Multibunch EmittancePreservation in CLIC, proc. EPAC96, Sitges, 1996.[2] I. Wilson, W. Wuensch, Multibunch Studies for CLIC,proc. PAC93, Washington, 1993.[3] G. Conciauro and P. Arcioni, A New HOM-FreeAccelerating Resonator, proc. EPAC90, Nice,1990.[4] N. M. Lin and N. M. Kroll, Minimum WakefieldAchievable by Waveguide Damped Cavity, SLAC-PUB-95-6863.

CLIC Waveguide Damped Accelerating Structure Studies

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