The bunch spacing in the main-beam train imposes an RF acceleration frequency of 1.5 GHz. The RF guns and all the linacs are L-band except the Booster Linac which is S-band. The particle production is 61.6 ¥ 1012 e/s, with the present parameters. A total incoherent energy spread of DE/E = 1%, for the L-band pre-injector, corresponds to a maximum r.m.s. bunch length of sz = 3 mm. The same bunch length is assumed from the RF gun up to the first bunch compressor located downstream from the damping ring. Two stages of bunch compressors are foreseen (Section 2.2.5 ). The first, at the damping ring exit, works at 3 GHz while the second, at the entrance of the main linac, works at 30 GHz.
The normalized transverse beam emittances at the IP are imposed by the luminosity, and their expected growths are given in Table 2.3 . The damping rings have to be designed to cope with the emittances consequently requested at the ring extraction, given the maximum emittances provided by the lepton sources. The maximum single-bunch charge is 5% higher than the charge at the IP in order to allow for beam losses in the injector complex and collimation at the entrance of the main linac. Table 2.3 summarizes the CLIC injector basic parameters.
The general layout of the main-beam injection complex is given in Fig.2.2 . This complex is composed of two systems.
The laser system and the photocathode RF electron gun generate a 10 MeV, low-charge beam. The pre-injector linac provides an energy gain of 190 MeV and an e - beam energy at the exit of 200 MeV. The injector linac accelerates the beam by 1.78 GeV, giving a final energy of 1.98 GeV. This linac accelerates alternately the train of electrons and the train of positrons. A DC dipole magnet separates the e- beam from the e+ beam. It also allows the beam to be sent towards a dump where some beam instrumentation will be implemented. Then, there are, successively, the damping ring for e - , the first stage of the bunch compressor working at 3 GHz and 1.98 GeV, the booster linac accelerating alternately e- and e+ beams up to 9 GeV, the transfer line, and finally the second stage of the bunch compressor working at 30 GHz and 9 GeV at the entrance of the e- Main Linac.
The laser system and the photocathode RF electron gun generate a 10 MeV, high-charge beam. The e- Primary Beam Linac sends a 2 GeV beam onto the e+ target. Following the conventional positron source, which receives the high-intensity primary e- beam, the e+ Pre-injector Linac accelerates e+ (and secondary e- ) up to 200 MeV. The injector linac (common to e- and e+ ) provides a 1.78 GeV energy gain. Then, follow the pre-damping ring and the damping ring for e+ . The rest of the system consists of the same kind of compressors and transfer lines as in the electron system and includes the common booster linac.
Fig. 2.2 : Sketch of the injection complex
The RF gun should produce 1nC/bunch. The charge of 6.25¥ 10 9 e-/bunch takes into account the transfer efficiency between the RF gun, at 10 MeV, and the damping ring exit, at 1.98 GeV. A total charge of 154nC is not an issue for an RF gun based on a Cs2 Te photocathode if one uses non-polarized electrons, but it should be studied for polarized electrons. The emittances scale approximately linearly with the charge for a given RF wavelength. At 1.5 GHz, the RF gun should work with an electric field of 50 MV/m. The expected normalized emittance [2.1] is between 4 and 7¥ 10-6 rad m (cylindrical symmetry).
The use of a second RF photo-injector, for the e- beam, is envisaged. It will allow beam profile studies and could be used as a spare RF gun or as a polarized e- source. The severe requirement on the vertical emittance of the electron damping ring could indeed be relaxed if the beam profile was shaped in order to get an asymmetric electron beam coming out from the photocathode.
Since CLIC also requires polarized electrons, they can be generated by using GaAs photocathodes and the SLC source is the reference, which is based on a DC gun with a GaAs photocathode. However, it has to be demonstrated that the electron beam characteristics required for CLIC are obtainable with the same technology. A review has been made of the polarized RF guns [2.2] , but more work remains to be carried out in order to establish the feasibility of a polarized RF gun with the CLIC parameters.
Based on the assumptions developed in Ref. [2.1] , the RF gun should deliver 2 ¥ 10 10 e-/bunch. A linear scaling with the charge provides an emittance of 13¥ 10-6 rad.m (both planes) for the 2.2 nC/bunch needed to create the train for positron production. The positron source for the CLIC is a conventional one based on an electromagnetic shower created by electrons impinging on a high-Z material target. The design takes into account the experience gained from the SLC source. The source and its associated 2 GeV linac meet the specifications for the 1 TeV option. The strategy developed for CLIC is explained in Ref. [2.1] . The radius of the incident electron beam is 1.6 mm (factor 2 compared to SLC) and the e+ beam is accelerated at 1.5 GHz in a structure twice as large as that of the SLC with a uniform magnetic field in the solenoid. The normalized yield is 0.30 e+/e- ¥ GeV at the exit of the e+ pre-injector linac. The charge per bunch for the primary electron beam is 1.35 ¥ 10 10 e-/bunch. The incoming e+ emittances (edges) into the pre-damping ring are 0.06 rad.m in both planes. This value is based on ETRANS simulations [2.3]
A possibility to produce positrons by a channelling process is under development. However, the thermal and radiation effects due to the high-intensity incident electrons should not affect the crystal structure. Preliminary and encouraging results have been obtained with the SLC 30 GeV beam [2.4].
The maximum charge required for the positron production described above is 493 nC in 154 bunches. A quantum efficiency of 1.5% (at l = 262 nm) on the photocathode implies a laser energy of 156 mJ at the same wavelength. The maximum charge required for the electron production (for the collisions) is a factor 3 smaller. The maximum charge produced, today, by a Cs 2 Te photocathode, in CLIC Test Facility 2 (CTF2), is 750 nC in 48 bunches. Therefore for both photo-injectors of the CLIC injection complex the charge is not an issue.
The train-to-train and bunch-to-bunch charge jitters required must remain below 0.5% and 1% r.m.s., respectively. The transverse laser spot size on the photocathode should have a diameter variation smaller than 1%.
Based on the NLC studies for the positron capture and beam loading compensation, the e+ pre-injector linac (~20 m long) accelerates the particles up to 200 MeV with a loaded gradient of 24 MV/m and the energy at the end of the e- pre-injector linac is the same. The energy gain in the e- primary-beam linac is a free parameter that will be adjusted for a good trade-off between cost and efficiency. The injector linac (1.5 GHz) is based on a loaded gradient of 17 MV/m and is approximately 110 m long in order to accelerate both beams to 1.98 GeV. The Booster linac (3 GHz) has a loaded gradient of 21 MV/m and is approximately 350 m long in order to boost both beams up to 9 GeV. The RF pulse is 10 ms long and accommodates two consecutive SLED (compression system) pulses. The first is for e+ acceleration and the second is for e- acceleration.
The yield at the exit of the e+ pre-injector (200 MeV) is 0.59 e+ per drive electron which is two times the maximum bunch intensity desired at the IP. The normalized yield, at 200 MeV, is 0.30 e+/e- ¥ GeV. The e+ target is 15.4 mm long. For W 75 Re 25 material, it corresponds to 4.5 c 0 (radiation length). The beam power on the target is 67 kW and the deposited energy 220 J. The 22 kW power deposited in the target corresponds to 33% of the beam power. The density in the CLIC target of ª 0.5¥ 1012 GeV/mm 2 is a factor 4 below the failure threshold due to single pulse heating, which is 2¥ 1012 GeV/mm 2 for a W 75 Re25 target. However, according to the recent experience of SLC e+ target failure, careful attention will be necessary in the design of the e+ target. Two L-band sections are foreseen for the beam loading compensation. The positron collection system is based on the Adiabatic Matching Device (flux concentrator). For reasons of reliability and high level of radiations, a second e+ source could be implemented near the first one, but with an independent access. Table 2.4 presents the CLIC parameters for the positron source and compares them to those of SLC and NLC.
The CLIC damping ring complex provides positron and electron bunch trains at a repetition period of 10 ms with a normalized emittance of 430 nm rad in the horizontal and 3 nm rad in the vertical plane (Table 2.5). For the positron beam, with a pre-accelerator normalized emittance of 42 ¥ 106 nm rad in both planes, the vertical emittance reduction will be a factor close to 107 which requires 10 damping times in order to have the beam emittances close to the equilibrium emittances of the ring, while the horizontal emittance will be reduced by a factor 105 . To decouple the wide aperture requirements for the incoming positron beam from the final emittance requirements of the main linac, a collector ring with a large dynamic acceptance and relatively large equilibrium emittances is used to pre-damp the incoming beam. Then after six damping times the beam is injected into a final damping ring with very small equilibrium emittances adapted to the main linac injection. In the case of electron production, taking into account the incoming normalized emittances of 7000 nm rad provided by the high brilliance injector linac, a single ring similar to the final positron damping ring will be sufficient.
At each repetition period a train of damped bunches is extracted from these damping rings, and at the same time a new train coming from the injector linac or from the positron source is injected. For a damping ring of circumference C accommodating a bunch train of length l s (including space for the injection and ejection fast kicker rise and fall times), transferring the beam at a repetition frequency fr , we define the reduced damping time tr = tx,y / C which has to satisfy in both planes t r < 1/( nt l s fr ), nt being the number of damping times necessary to damp the incoming emittance to the acceptable level e target .
The optimum beam energy must not be determined from optical considerations, but rather be based on Intra-Beam Scattering (IBS) and polarization. The polarized lepton option requires an energy of (n +0.5)¥ 0.44 GeV to avoid depolarizing resonances. The g 3 dependence of the normalized equilibrium emittance of a lattice prevents energies larger than 2 GeV. In order to avoid strong IBS, an energy of 1.98 GeV has been chosen.
The total radiation loss in the presence of wigglers with a given field, for a fixed value of t r , is independent of the ring structure and of the value specified for the target emittance e target [2.5] the required wiggler length for a well-defined reduced damping time is shown for different combinations of arc and wiggler field. The quantity R ra will be used in the following to denote the ratio of the total losses around the ring to the losses in the arcs.
Even though they are installed in a dispersion-free straight section, the wigglers will create local dispersion and thereby generate additional emittance. The aim of a very low ring equilibrium emittance, and thus a small wiggler contribution to the emittance, requires a short wiggler period. Furthermore, increasing the wiggler length or field will not reduce indefinitely the ring equilibrium emittance as it will become dominated by the wiggler contribution to the emittance (Fig. 2.4 ).
As proposed in Ref.[2.6] the arcs are made of detuned Theoretical Minimum Emittance (TME) cells. The dispersion and b x functions in the bending magnets are chosen larger than those required for the minimum emittance, in order to increase the dispersion both in the bending magnets (and consequently the momentum compaction a ) and at the potential sextupole locations.
A given detuning ratio er of the actual equilibrium emittance to the minimum possible emittance may be achieved by different combinations of Dx and bx at the centre of the bending magnets. It is important to select the combination yielding the largest possible D x value for a given e r , as a large momentum compaction a is required to maximize the impedance threshold. In this case the lattice parameters in the centre of the bending magnet are entirely determined [2.6] , and given by
where q and l bend are the deflection angle and the length of the bending magnet.
Using the above expressions the momentum compaction factor of a ring containing exclusively regular TME cells depends only on the cell length l cell , the bending magnet parameters and the detuning ratio er .
The horizontal cell phase advance depends only on the emittance detuning ratio. A value of e r = 3.9 is proposed for the three rings of the 3.0 TeV option (Table 2.5). This yields sufficiently large D x values.
The ring used in the analytical calculations has a race-track shape. It consists of two 180° arcs, made of bending magnets of length l bend in regular arc cells of length l cell ~ 2 l bend and a constant space required for the focusing part of the cell. Two long straight sections house the injection/ejection system and the RF cavity, with a total length assumed to be the sum of a fixed part of ~18 m and a variable part of 1.8 times the wiggler length. The wigglers are distributed among the two straight sections in order to minimize the ring dimensions. Using this geometry the expression for the momentum compaction shown above may be corrected for the presence of the two long straight sections.
The number of regular arc cells required to produce the target emittance and the reduced damping time, taking into account the wiggler effects, can now be evaluated. It is a function of the wiggler characteristics (field, period), of the emittance detuning ratio chosen and, obviously, of the target emittance and the beam momentum.
As se has a weak dependence on the ratio Rra , the turbulence impedance threshold, calculated with the usual formula (Z/n)thr = a(2p )3/2 E se2 ss /(Nb e2c ), will show approximately the same behaviour as a . Large Rra ratios yield large (Z/n)thr and a values, and small arc bend fields (Fig. 2.5 ). This allows an increase of lbend and larger values for Dx and bx , easing the chromaticity correction.
Fig. 2.4 : Wiggler contribution to the normalized emittance, vs. R ra , for B wig = 1.73 T, <b x > = 2.5 m at 1.98 GeV and t r = 35 m s/m for wiggler wavelengths 0.35 m and 0.20 m.
Fig. 2.5 : (Z/n) thr and arc field vs. R ra , for B wig = 1.73 T, <b x > = 2.5 m at 1.98 GeV and t r = 35 m s/m, a normalized emittance of 1.9 ¥ 10 -6 m assuming s s = 3 mm and 4.2 ¥ 10 9 particles per bunch.
The proposed Electron (EDR) and Positron (PDR) Damping Rings are assumed to have the same ring, cell and wiggler geometry. The ring has a racetrack shape with two long straight sections, the lengths of which are included in the circumference equal to 485 m. These sections contain in common the RF cavities, the wiggler magnets, and the injection and extraction insertions. The chosen emittance detuning ratio e r of 3.9 yields reasonable values for the momentum compaction and the strength of the chromaticity correction. Further optimization of the damping ring parameters requires detailed modelling of the effects of the wigglers, intra-beam scattering, errors and misalignments.
The Positron Collector Ring (PCR) is assumed to operate at the same beam energy as the damping rings. Although the damping time parameters are similar to those of the damping rings, the large target emittance requires a much smaller number of arc cells. With a circumference of only 155 m, the collector ring could be installed inside the damping rings (Table 2.5 ).
The damping ring is designed to deliver a beam at the energy of 1.98 GeV, bunched at the RF frequency of 3 GHz, of relative r.m.s. energy spread 0.082% and of r.m.s. bunch length of 3 mm. The required bunch length in the main linac should be 30 m m in order to reduce the dilution effect of transverse wakefields on the vertical emittance. The corresponding compression rate is 100 which cannot be obtained by a single compression stage because at the energy of 1.98 GeV the r.m.s. energy spread will rise to 8.2%, too large to transport the beam through the injector complex, and at the energy of 9 GeV the R 56 becomes -0.166 m implying either a short and strongly radiating chicane or a long one with too high values of the maximum b optical function.
Thus two stages of compression are proposed: one at 1.98 GeV and one at 9 GeV, the latter in order to benefit from a higher gradient and a larger RF frequency [2.7] . A compromise has to be found between an acceptable r.m.s. energy spread at the exit of the first stage and the R 56 required by the second stage. The compression factor of 12 of the bunch compression first stage has been chosen because the r.m.s. energy spread at the exit is an acceptable value of about 1% and the resulting R 56 of the second stage is relatively small (-0.014 m). The first pseudorotation in the longitudinal phase-space is obtained through RF systems working at a phase equal to kp , which linearly correlate the momentum with the position of the particles in the bunch. This rotation requires integrated RF voltages of 103 MV at 3 GHz and of 1026 MV at 30 GHz for each compressor stage, respectively. The second pseudorotation in the longitudinal phase space is achieved by a magnetic chicane consisting of two parts, one being the mirror image of the other. Each part is composed of two rectangular dipoles, of length L m and bending angle q, separated by a drift space of length L . The chicanes have been optimized to reduce the maximum values of the bTwiss function. Their optical functions are shown in Fig. 2.6 and Fig. 2.7 .
The parameters of the two bunch compressors [2.8] obtained to first order have been inserted into a longitudinal tracking program to investigate how the beam will behave when the higher-order magnetic effects (of the chicane) and the strong wakefields are taken in account. Figure 2.8 and Fig. 2.9 show the longitudinal phase space before the compressor (horizontal scatter plot), after the RF pseudo-rotation (oblique scatter plot) and at the exit of the chicane (vertical scatter plot) for the first and second stage, respectively. The high-order effects are small, only slightly lengthening the bunch by one micron.
The effect of the coherent radiation has not been investigated but a rough estimate suggests that it should be negligible. Numerical tracking has to be carried out to confirm this. The present design might be slightly modified to reduce its consequences.
Since the injection complex is foreseen to be in a central position (Fig. 2.2 ) each beam (e- and e+ ) has to be transported at 9 GeV to the entrance of the second bunch compressor, before injection in the main linac. These two transfer lines consist of regular FODO cells, with sufficiently low vacuum (~ 10-10 Torr) in order to prevent ion-trapping instability. Removal of the beam halo generated in the injector complex is foreseen in these transfer lines, either by conventional spoilers and collimators or by resonant drift in nonlinear fields; both techniques remaining to be studied and compared.
The 360° turn-round consists of 48 isochronous modules [2.9] , each one made of three identical dipoles (1 m long) and of four quadrupoles. Symmetric triplets match the modules between them. The overall diameter of the turn-round is 430 m approximately, in order to limit to 60 nm rad the horizontal emittance growth due to the synchrotron radiation. All the other major bends can be built on the same basis.
Fig. 2.6 : Optical functions in the first chicane
Fig. 2.7 :Optical functions in the second chicane
Fig. 2.8 : Longitudinal phase space in the first stage
Fig. 2.9 : Longitudinal phase space in the second stage