We describe a base-line optics for a 3-TeV final-focus system of the Compact Linear Collider (CLIC). The proposed system consists of an initial beta-matching region, two chromatic correction sections, and a final transformer, and it provides a total demagnification by a factor 90 horizontally and 346 vertically. The length per side amounts to 3.3 km. The effect of synchrotron radiation and higher-order aberrations is minimised by an odd dispersion function in the chromatic correction section. For a total flat energy spread of 1%, the system promises a luminosity of about 80% of the ideal. The 20-30% spot-size dilutions in the two transverse planes reflect a trade-off between the Oide effect and higher-order chromo-geometric aberrations

Assmann, R W

Guignard, Gilbert

Napoly, O

Schulte, Daniel

Zimmermann, Frank

CERN Document Server

EUROPEAN  ORGANIZATION  FOR  NUCLEAR  RESEARCHCERN - SL DIVISIONCERN-SL-2000-057  APCLIC Note 446FINAL-FOCUS SYSTEM FOR CLIC AT 3 TEVF. Zimmermann, R. Assmann, G. Guignard,D. Schulte, O. Napoly*AbstractWe describe a base-line optics for a 3-TeV final-focus system of the Compact Linear Collider(CLIC). The proposed system consists of an initial beta-matching region, two chromatic correctionsections,  and a final transformer,  and it provides a total demagnification by a factor 90 horizontallyand 346 vertically. The length per side amounts to 3.3 km. The effect of synchrotron radiation andhigher-order aberrations is minimised by an odd dispersion function in the chromatic correctionsection. For a total flat energy spread of 1%, the system promises a luminosity of about 80% of theideal. The 20–30% spot-size dilutions in the two transverse planes reflect a trade-off between theOide effect and higher-order chromo-geometric aberrations.Paper presented at EPAC2000, 26-30 June 2000, Vienna, Austria*CEA SaclayGeneva, Switzerland08.08.00FINAL-FOCUS SYSTEM FOR CLIC AT 3 TEVF. Zimmermann, R. Assmann, G. Guignard, D. Schulte, CERN, Geneva, O. Napoly, CEA/SaclayAbstractWe describe a base-line optics for a 3-TeV final-focus sys-tem of the Compact Linear Collider (CLIC). The proposedsystem consists of an initial beta-matching region, twochromatic correction sections, and a final transformer, andit provides a total demagnification by a factor 90 horizon-tally and 346 vertically. The length per side amounts to 3.3km. The effect of synchrotron radiation and higher-orderaberrations is minimised by an odd dispersion function inthe chromatic correction section. For a total flat energyspread of 1%, the system promises a luminosity of about80% of the ideal. The 20–30% spot-size dilutions in thetwo transverse planes reflect a trade-off between the Oideeffect and higher-order chromo-geometric aberrations.1 INTRODUCTIONThe compact linear collider (CLIC) under study at CERN[1] will collide low-emittance electron and positron beamsat centre-of-mass energies extending up to 5 TeV. Table1 compares the design beam parameters at the interactionpoint (IP) for a 3-TeV CLIC with those actually demon-strated at the SLC and those envisioned for a 1-TeV NLC[2]. The NLC luminosity represents an increase by 4 or-ders of magnitude compared with the SLC, while the CLIC3 TeV parameters surpass this by about another factor often. The high luminosities are achieved by increasing thenumber of bunches per rf pulse and, mostly, by reducingthe IP spot size. For the latter, one can exploit the natu-ral reduction in geometric emittance at higher energies, butin addition reduced IP beta functions and a significant de-crease in the normalised emittances are required.The task of the final-focus system is to focus the twomain beams, after acceleration in the linac, to the trans-verse design spot sizes of 43 nm, horizontally, and 1 nm,vertically, at the interaction point (IP). The full momentumbandwidth of the final-focus system should be of the orderof 1%, in order to accommodate the beam energy spreadexpected from the linac. The final-focus optics describedin this paper nearly fulfills the requirements. The small IPspot size implies tight tolerances on magnet-position andfield stability. Both optics calculations and tolerance anal-yses [3] were performed using the computer codes FFADA[4] and MAD [5].2 OPTICSFigure 1 displays the base-line optics for a 3-TeV CLICfinal focus. The system consists of a beta-matching region,horizontal and vertical chromatic correction sections (CCXand CCY), and final transformer. The total length is about3.3 km per side.0.0 1000. 2000. 3000. 4000.s (m)δ E/ p 0c = 0 .Table name = TWISSCLIC 3-TeV Final Focus (90x346)HP/UX version 8.23/02 09/04/00  22.20.440.0.1.2.3.4.5.6.7.8.91.0β(m)[*10**(6)]0.0.01.02.03.04.05.06.07.08.09.10D(m)β x β y Dx DyFigure 1: Beta functions and dispersion for the entire final-focus system as a function of the longitudinal position. Theinteraction point is on the right.The final focus decreases the initial beam size 90 timesand 346 times in the two transverse planes. Most of thisTable 1: IP beam parameters for SLC, NLC and CLIC.parameter sym. SLC NLC CLICc.m. energy [TeV] E 0.1 1 3luminosity L 0.0002 1.3 10[1034 cm−2 s−1]repetition rate [Hz] frep 120 120 100bunch charge [1010] Nb 3.7 1 0.4bunches/rf pulse nb 1 95 154bunch spacing [ns] ∆b — 2.8/1.4 0.67beam power [MW] Pb 0.04 9 14.8hor. emittance [m] γx 50 4.5 0.68vert. emittance [m] γy 8 0.1 0.02hor. beta [mm] x 2.8 12 8vert. beta [mm] y 1.5 0.15 0.15hor. spot size [nm] x 1700y 235 43vert. spot size [nm] y 900y 4 1.0bunch length [mm] z 1 0.12 0.03y 1998 average valuedemagnification occurs in the final transformer, which ismade from two quadrupole doublets and which alone de-magnifies by a factor 15 horizontally and 50 vertically.A high gradient of the final quadrupole prior to the IPis necessary in order to confine the doublet chromaticity,which is closely related to the strength of higher-orderaberrations. For our base-line design, we have asssumeda quadrupole gradient of 450 T/m. To put this into per-spective, an NLC permanent magnet prototype has demon-strated a gradient of 500 T/m [6], and higher values, up to5000 T/m, are thought to be feasible [7]. For a large aper-ture s.c. quadrupole the assumed gradient would constitutea 30% increase from present designs [8]. A third possibilityis a pulsed quadrupole, which could also achieve gradientsof the order of 1000 T/m [9].We choose a free length from the exit face of the lastquadrupole to the IP of 2 m as in the NLC design [2]. Withthe assumed quadrupole gradients the chromaticity of thefinal doublet is 6900 in the horizontal and 27000 in thevertical plane. Here, chromaticity is defined in the linear-collider sense as the relative spot-size increase (added inquadrature) divided by the rms energy spread. The betafunctions at the entrance to the 5-m long final quadrupoleare 15 km horizontally and 88 km vertically, which corre-sponds to rms beam sizes of 59 m and 24 m. This trans-lates into a geometric acceptance of 50–140  for a perma-nent magnet with 3.3-mm bore radius and 450–1100  fora superconducting quadrupole with 2.7 cm radial aperture.The large chromaticity of the final doublet is compen-sated in the two chromatic correction sections, which fea-ture an odd dispersion function as proposed by Oide [10].Both chromatic correction sections comprise a pair of sex-tupoles, separated by a −I transformation and placed aninteger multiple of  in betatron phase away from the fi-nal doublet. The dispersion is nonzero only at the secondsextupole of each pair. This has two advantages: (1) it re-duces the number of bending magnets and the amount ofsynchrotron radiation by a factor of 2, and (2) it avoidsmany of the 5th-order chromo-geometric aberrations aris-ing from the chromatic breakdown of the −I between thesextupoles, which limit the momentum bandwidth. Thanksto the −I separation the individual sextupole pairs do notgenerate any 3rd-order geometric aberrations. The 2nd-order dispersion from the CCX is adjusted so as to cancelthe 2nd-order dispersion produced in the CCY. The ratioof dispersion values, or, alternatively, the ratio of bendingangles in CCX and CCY is thus constrained. In the presentdesign the net bending angles for the dipole regions in CCXand CCY are 63rad and 230rad, respectively. The peakbeta functions at the CCY sextupoles are about 1000 km,50 times larger than the peak beta function in the SLC finaltriplet, and the maximum value of the dispersion is 0.1 m.The initial beta functions of 65 m horizontally and 18 mvertically are chosen equal to the beta functions at the endof the main linac.In the final transformer the beta functions vary ratherdramatically with energy, as is illustrated in Fig. 2. Thiseffect must be taken into account when choosing magnetand beam-pipe apertures.3100. 3140. 3180. 3220. 3260. 3300.s (m)δ E/ p 0c = - .5 0 0 0 0 0 E- 0 2Table name = TWISSCLIC 3-TeV Final Focus (90x346)HP/UX version 8.23/02 09/04/00  22.54.480.010.20.30.40.50.60.70.80.90.100.β(m)[*10**(3)] β x β y3100. 3140. 3180. 3220. 3260. 3300.s (m)δ E/ p 0c = .5 0 0 0 0 0 E- 0 2Table name = TWISSCLIC 3-TeV Final Focus (90x346)HP/UX version 8.23/02 09/04/00  22.54.480.010.20.30.40.50.60.70.80.90.100.β(m)[*10**(3)] β x β yFigure 2: Beta functions in the final telescope for energyoffsets of −0:5% [left] and +0:5% [right].The system was optimised by varying the total length,the ratio of CCX and CCY lengths, the bending angles,and the strengths of the last two quadrupoles, in order tomaximise the luminosity for a 1% flat energy spread. Thefinal parameter choice is a trade-off [11] between Oide ef-fect [12,13] (vertical beam size increase due to synchrotronradiation in the last quadrupoles, favoring a weak second-to-last quadrupole Q2) and the momentum bandwidth inthe horizontal plane (demanding a small horizontal chro-maticity and, thus, a strong quadrupole Q2).3 PERFORMANCEThe geometric luminosity, without pinch, is calculatedusing FFADA by tracking two random sets of particlesthrough the entire system to the interaction point, and con-voluting them there on a grid. The luminosity so obtainedis displayed in Fig. 3 as a function of the full-width mo-mentum spread assuming a flat energy distribution. For theanticipated energy spread close to 1%, it is about 80% ofthe ideal value that would be attained for a perfectly linearand achromatic optics, without synchrotron radiation andaberrations.Figure 4 shows the dependence of the transverse rmsspot sizes on the full energy spread FW. The vertical spotsize is about 30% larger than the ideal value, only slightlyincreasing with energy spread. The 30% blow-up is dueto synchrotron radiation in the second-to-last quadrupolemagnet Q2. For small energy spread FW the horizontalspot size is close to the ideal value. However, the latter in-creases rapidly with increasing FW. As indicated above,the strength of Q2 as well as the bending angles in CCXand CCY have been adjusted such that for the nominal 1%energy spread the horizontal blow up is comparable to thevertical.4 TOLERANCESFigure 5 displays jitter and drift sensitivities (i.e., the in-verse tolerances) for the vertical magnet position. Jittersensitivities refer to both the induced orbit shift at the IP,which could be corrected over a few pulses, and the IP spotsize increase. Drift sensitivies are calculated only from theIP spot-size increase and, thus, they apply over a time in-terval of several minutes, at which the spot size can be re-tuned. All numbers in the table correspond to a 2% lu-minosity loss per magnet. The tightest jitter tolerance isFigure 3: Relative luminosity loss as a function of the full-width energy spread for a flat distribution. The luminos-ity was calculated by tracking two random distributions of5000 particles through the final focus to the IP and thereconvoluting them on a grid. The ideal reference luminositywithout pinch is L0 = 4:6 1034 cm−2s−1.Figure 4: Relative rms spot sizes as a function of the full-width energy spread for a flat distribution with and withoutsynchrotron radiation. The ideal linear spot sizes are x0 =43 nm and y0 = 1:0 nm.0.2 nm, for the last quadrupole. Various stabilising tech-niques as well as intra-pulse feedback can be employed tomeet this tolerance [14]. Drift tolerances are much looserand of the order of 100 nm. Finally, with sensitivitiesas shown in Fig. 6, typical field stability tolerances areabout 10−5, comparing favorably with the 10−6 precisionof LHC power converters [15].5 SUMMARYWe have presented a base-line final focus for 3 TeV. It is3.3 km long and promises satisfactory performance.6 REFERENCES[1] J.P. Delahaye and I. Wilson, “CLIC a multi-TeV e+e- LinearCollider”, CERN/PS 99-062 (LP); G. Guignard (ed.), “Gen-eral Description of a 3 TeV Linear Collider based on theCLIC Technology”, in preparation.[2] C. Adolphsen at el., “NLC Zeroth Order Design Report forthe Next Linear Collider”, SLAC Report 474 (1996).Tolerances to magnet VERTICAL displacements  δyQS1/δyQS [µm-1 ]Figure 5: Vertical displacement sensitivity correspondingto a 2% luminosity loss for the various magnets [3, 4]. Thefull bars represent pulse-to-pulse ‘jitter’ tolerances, due toboth the induced IP orbit motion and IP spot-size increase.The open bars are ‘drift’ tolerances referring only to in-creases in the IP beam size.Tolerances to magnet field errors  (δkBQ/kBQ)1/(δκBQ/κBQ)Figure 6: Sensitivities to a relative change in field strengthfor all final-focus magnets. Again, the full and open barsrepresent jitter and drift tolerances, respectively.[3] S. Fartoukh, O. Napoly, EPAC98, Stockholm (2000); S. Far-toukh, Ph.D. thesis, DAPNIA/SEA-97-02T (1997).[4] O. Napoly and B. Dunham, Proc. EPAC94, London, vol. 1, p.698 (1994).[5] H. Grote, F. C. Iselin, CERN-SL-90-13-AP-REV.2 (1990).[6] J. Spencer, in section 118 of Ref. [2].[7] K. Egawa and T.M. Taylor, CERN LEP-MA/89-08 and PAC1989 Chicago (1989).[8] S. Caspi et al., 15th Int. Conf. Magnet Techn., Bejing (1997).[9] M. Modena and P. Sievers, CERN/AT-MA/91-24, and Proc.12th Int. Conf. Magnet Techn., Leningrad (1991).[10] K. Oide, HEACC’92, Hamburg, p. 2993 (1992).[11] O. Napoly, CERN-SL-99-054, CLIC Note 414 (1999).[12] K. Oide, Phys. Rev. Lett. 61, p. 1713 (1988).[13] K. Hirata, K. Oide, B. Zotter, Phys. Lett. B224, p. 437(1989).[14] R. Assmann et al., this conference.[15] I. Barnett, et al., LHC Project Report 293, PAC 1999.

Final-Focus System for CLIC at 3 TeV

We describe a base-line optics for a 3-TeV final-focus sys-tem of the Compact Linear Collider (CLIC). The proposed system consists of an initial beta-matching region, two chromatic correction sections, and a final transformer, and it provides a total demagnification by a factor 90 horizon-tally and 346 vertically. The length per side amounts to 3.3 km. The effect of synchrotron radiation and higher-order aberrations is minimised by an odd dispersion function in the chromatic correction section. For a total flat energy spread of 1%, the system promises a luminosity of about 80 % of the ideal. The 20–30 % spot-size dilutions in the two transverse planes reflect a trade-off between the Oide effect and higher-order chromo-geometric aberrations. 

Final-Focus System for CLIC at 3 TeV

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