Autin, Bruno

Corsini, R

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GENERATION OF A 30 GHZ TRAIN OF BUNCHES USING A MAGNETICSWITCH-YARDB. Autin, R. Corsini, CERN, CH 1211 Geneva 23, SwitzerlandA possible technique of generation of high-frequencydrive beam for a linear collider consists in creating electronbunches in a battery of guns and merging them in amagnetic circuit (switch-yard) at the end of which all thebunches are aligned on a common line with the rightspacing. Two types of scheme are discussed. The propertiesof the structure in terms of orbit dispersion, focusing andbunch lengthening due to finite momentum spread andemittance are analyzed.I. INTRODUCTIONThe CLIC project of a e+  e- linear collider is based onthe two-beam accelerator scheme [1]. The electron andpositron beams are accelerated in 30 GHz acceleratingstructures, the needed rf power being generated by theinteraction of a high power relativistic electron beam (theDrive Beam), running parallel to the main linac, withappropriate rf structures resonant at 30 GHz (transferstructures). Each drive beam (one for the positrons, and onefor the electrons) has an energy of 3 GeV and is composedof 2.5 m C, 12 ns long electron bursts, at the same ~ 2 kHzrepetition rate of the main beam. Each burst is composed oftypically four trains of 22 short ( s  ~ 1 mm) bunchlets. Thebunch charge is 30 nC, and the bunches are spaced by 1cm. This spacing corresponds to the 30 GHz frequency ofthe transfer structures. While it seems feasible to generateand accelerate single 30 nC bunchlets in an S-bandphotocathode rf gun + booster, with the desired bunchlength (possibly by using magnetic pulse compression), thecorrect spacing between bunchlets cannot be directlyachieved. Furthermore, the beam loading limits the numberof bunchlets that can be accelerated in such a systemduring the 12 ns duration of each burst. Therefore, oneneeds more of these sources to generate the full drivebeam, and a method of combining the pulses together atthe right spacing. The proposed technique consists of usingone array of 11 electron guns for each drive beam [2]. Eachgun delivers 2 bunchlets per train, and each operates at adifferent energy from 25 to 50 MeV. The bunchlets are thenmerged in a single trajectory using a dipole magnet andundergo further acceleration downstream. This bunchrecombination scheme could be tested in future (possiblywith only two lines) in the CLIC Test Facility (CTF) [3].The general shape of a switch-yard is shown in figure 1.The optical structure of the channels is presented for twotypes of scheme christened C and S. The C-scheme ispresently contemplated for the big machine and the S-scheme seems to be more appropriate for the test facility. Ithas also to be noted that such structures can be of interestall along the drive beam each time the beam has to be bentwhile satisfying the condition of isochronicity.Figure 1. Orbits in a switch-yardII C- and S-schemesTwo symmetric configurations of switch-yard channelsare compared in this paper. The C-scheme is symmetricalwith respect to an axis and the deflections of the twobending magnets add up. The S-scheme is symmetricalwith respect to a point and the two deflections are ofopposite sign so that the input and output trajectories areparallel. Their schematic structure is shown in figure 2. Thebending magnets are represented by white circles. Theshape is indeed circular for the magnet in which all thebunches are merged before exiting on a common straightsection.Figure 2. C-channel (a) and  S-channel (b).When few beams have to be combined, a static dipolemay advantageously be replaced by a radio frequencydipole. In this configuration, the bunches receive the samedeflections but with an alternating sign. The other dipole isactually a sector magnet proper to each channel. Thefocusing structure is idealized by thin lenses which permitalgebraic calculations and an analytical formulation of theproperties of the schemes. Detailed analysis using thicklenses is beyond the scope of this study. For reasons whichwill be discussed in the next chapter, the focusing isperformed with singlets in the C-case and doublets in the S-case.III. Optics of a switch-yard channelA magnetic switch-yard is easily analyzed when theparticles are traced backwards from the straight sectionwhere the bunches are merged to the photo-injectors. Thebunch motion is traditionally split into the motion of itscentre of gravity and the oscillations of the other particlesabout the centre of gravity.A. OrbitsThe orbits (see figure 1) are the trajectories of  thecenters of gravity of the bunches. They start with a commonstraight section and are then discriminated by aspectrometer whose magnetic field is constant and shape isa circle of radius R. The trajectories in the spectrometer arearcs of circles orthogonal to the contour circle; their radiusis proportional to the particle momentum. With respect to areference orbit of momentum p  and deflection f , aneighbour orbit of momentum p+ D p is radially displaced ata distance l from the end of the spectrometer by thequantity D D p/p where the orbit dispersion D is given by:D R l= +( ) sin fThis separation is needed for placing focusing elements. Inorder to keep the whole system compact, the separation isto be small and the space reserved to the quadrupoles iscomparable to the spectrometer radius and of the order of20 cm which is compatible with permanent magnettechnology. The second separation to be achieved concernsthe photo-injectors at the end of the channel. In asymmetric configuration, it is determined by the distance2d  between the two spectrometers. For the C- and S-scheme they are equal tos R d Rs R dCS= + + += +( ) sin ( cos )( ) sinf ff12The C-scheme is more practical than the S-schemebecause of its fan shape but, for a separation of 30 cm atthe location of the injectors, the distance between thespectrometers is of the order of 5 m in both cases.B. FocusingThe switch-yard channel is dispersive in its veryprinciple but it connects two straight sections where boththe orbit dispersion D  and its longitudinal derivative D ’must be zero. The dispersion increase in the spectrometersis always the same but keeps rising in the C-scheme up tothe F-lens where it is bent back towards the secondspectrometer whereas, in the S-scheme, it is immediatelyfocused to the center of symmetry. Such orbit dispersionpatterns impose the focal length of the F-lens:f R df R l d lR dCS=+=+ -+2( )( )In the S-case, l  is the distance from the end of thespectrometer to the F-lens. It turns out that the focusing ismuch stronger for the S- than for the C-scheme. Thevariation  of the orbit dispersion is shown in figures 3 and 4.Figure 3. Orbit dispersion in a half C-channel.Figure 4. Orbit dispersion in a half S-channel.The horizontal focusing being fixed, the verticalfocusing is provided by D-lenses located in zero dispersionregions, i.e. the input and ouput straight sections. Thestructure is made of alternating D- and F-lenses in the C-scheme and of two symmetric doublets in the S-scheme.The conditionsb ba ah vh v- =+ =00at the end of the channel are canonical to match a FODOcell directly or via a quarter wave-length transformer [4].The two unknowns of the problem are the focal length ofthe D-lens and the distance from the D-lens to the matchingpoint. With the help of a symbolic program, factorizationscan be performed and the physical solutions turn out to beuniquely determined though they are solutions of a fourthdegree equation. The b -functions are somewhat arbitrarysince the periodic lattice which surrounds the channel isnot a priori defined but rather fitted to the switch-yard. Theb -functions at the symmetry point which serve as inputvalues to the b -tracking have been chosen so as tominimize the a -function at the end point to facilitate thebetatron matching. The variations of the b -functions areshown in figures 5 and 6.Figure 5: b -functions in a half C-channel.Figure 6. b -functions in a half S-channel.In each bunch the particles have a finite momentum spreadand it is indispensable to superimpose on the quadrupolarcomponent of the lenses a sextupolar component¢ =f Dfwhere f’ is the radial derivative of the quadrupole focallength. This correction can only be performed in the Flenses where the orbit dispersion is non-zero and thechromatic aberrations, yet not fully compensated, remaintolerable.C. Path lengthIn the generation of the train of bunches the distancebetween bunches is determined by the trigger of theinjectors and by the path length of the various channels. Abunch lengthening due to the transverse emittance of thebeam and to its momentum spread must also be kept undercontrol.When two particles of same momentum andlongitudinal position enter a spectrometer, they leave it atdifferent longitudinal positions distant bydz x Rx= -( ' )sin fif their radial distance is x and their horizontal angles differby x’ at the input. From this stand point, an S-scheme isself compensated at least to first order. Position and angleare related by the Courant and Snyder invariant and it canbe shown that for a given emittance ellipse of area e , thebunch lengthening varies from zero to a maximum valuewhich depends on f , R, e  and the b -function at the end ofthe dipole.The change in path length is related to the relativemomentum error through the path length dispersion DlDDz D ppl=whose expression in a dipole isDl = -r f f( sin )In contrast to the case of the emittance dependence, thepath length always increases in a dipole because the radiusof curvature r  and the deflection f  have the same sign. Dlcan nevertheless be controlled by shifting the quadrupolesradially. A displacement D x produces a kickDfD=xfand a change in path length D  D f . The focal distance f ofthe F-lens has a new expression because the extra kickmodifies the orbit dispersionf R df R l d lR d d lCS=++=+ -+ + -( )sinsin( )( ) sin( )sin ( )ffff2 DfDfIV. CONCLUSIONThe characteristics of optical structures which can beinserted in zero dispersion regions with a controlledisochronicity have been described in the framework of alinear model which gives the basic parameters in ananalytical way. The simulation of higher order and spacecharge effects is not reported here but has been done andconfirms the feasibility of a magnetic switch-yard.V. REFERENCES[1] H. Braun et al., “CLIC - A Compact and Efficient HighEnergy Linear Collider”, This Conference.[2] W. Schnell, “The Drive Linac for a Two-Stage LinearCollider”, CERN-LEP-RF/88-89 and CLIC Note 85.[3] R. Bossart et al., “CLIC Test Facility Developmentsand Results”, This Conference.[4] K.L. Brown and R.V. Servranckx, AIP ConferenceProceedings, 127, pp 62-138 (1985)

Generation of a 30 GHz train of bunches using a magnetic switch-yard

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