The main issue in the compression system (delay line plus combiner rings) is the preservation of the bunch quality during the combination process. In particular, the bunch length and longitudinal phase-space distribution must be preserved and the fluctuations in phase and transverse position between trains and between bunches minimized. The rings, the delay line and the transfer lines must therefore be isochronous. The final bunch length must be short in order to maximize the 30 GHz RF power production efficiency in the drive-beam decelerator. The aim is an r.m.s. bunch length of sz = 0.4 mm, for a 16 nC bunch-charge. High-charge, short bunches can radiate a considerable amount of Coherent Synchrotron Radiation (CSR), leading to both a significant average energy-loss and energy-spread within the bunch [3.15]. The emission is concentrated at low frequencies [n £ 1/(2 s )], and can be partly suppressed if at least a fraction of the emitted spectrum is below the cut-off of the beam pipe (shielding effect), though a lower limit in the beam pipe dimensions is imposed by the necessary beam clearance. Both the energy loss and spread must be kept small, in particular because the bunches belonging to different trains make a different number of turns in the rings (from 1/2 to 7/2) and will develop different energy distributions. This will cause relative phase errors between bunches and some bunch lengthening. These intense and short bunches will also interact with any small discontinuity of the beam chamber (e.g., bellows and septa), possibly being subject to longitudinal and transverse wakefields. It is therefore highly desirable to have relatively long bunches to manipulate in the compression system, and to compress them just before the injection into the drive-beam decelerator sections. An upper limit to the bunch length is given by the non-uniform kick experienced by the bunches at injection in the RF deflectors, due to their phase extension, causing growth of the single-bunch emittance. The bunch length has been fixed at the exit of the accelerator to be 2 mm r.m.s. approximately. The emittance growth in this case is approximately 2% (for an initial r.m.s. normalized emittance of 200 µ m rad), arising mainly in the deflectors (3.75 GHz) of the second combiner ring, where their effect is large. A correlated energy spread (~1% r.m.s.), suitable for the final bunch compression, is obtained in the accelerator by the combined effect of the RF curvature and longitudinal wakefields. The need to preserve the correlation all along the compression system means that all the distortions of the longitudinal phase space must be kept small. In particular, attention must be given to the higher orders of the momentum compaction. A numerical analysis has shown that second-order effects would be unacceptable and must be corrected by using sextupoles [3.2].
Another concern is the beam loading in the RF deflectors, particularly just before the extraction from the second combiner ring, where the average current in the train and the deflector's frequency (3.75 GHz) are the highest. In order to overcome this problem, a travelling-wave iris-loaded structure with a short filling time with respect to the train duration has been chosen. A steady-state condition is then reached with minimum transient effects, although at the expense of a loss in the deflection efficiency. The extraction system for both rings is also a critical item, the two main issues being the high repetition rate (particularly in the first ring -250 kHz) and the interaction with the high-current beam (particularly in the second ring -262 A). A possible solution is based on the use of pairs of travelling TEM wave transmission-lines [3.16].
A preliminary design of the lattices for the delay line and the combiner rings was made in 1999 [3.2]. Since then, the CLIC RF pulse length has been reduced from 143 ns to 130 ns. Such a parameter change implies a reduction of the delay introduced in the delay-line and of the circumference of the combiner rings. The existing lattice design could in principle be modified to fit the new parameters. Another possibility would be to use an alternative design for the isochronous cells [3.17], presently under investigation for CTF3. Such a design is based on the use of three bending magnets per module or cell instead of four. Being more compact, it would be better adapted to shorter rings and transfer lines. In the following, only the first-order design with the old parameters will be described in some detail. Tables 3.7 and 3.8 present the main parameters of the subsystems with the delay length and ring circumferences selected at the time of the study. The delay-line geometry has been chosen to minimize both CSR emission and overall dimensions. One 3-bend magnetic chicane is located in the delay line and two in each ring. They are used for fine path-length tuning ( 0.5 mm tuning range), in order to adjust the relative phase of the bunches and compensate for orbit variations. Each chicane is 3.5 m long and works around an average bending angle of q 0 ~150 mrad. The tuning range is obtained with a bending angle variation of Dq = 1.5 mrad; such a small value of Dq/q 0 does not perturb the optics. Each chicane has a linear transfer matrix element R 56 = 0.065. Both the delay line and the ring arcs are based on the same type of isochronous lattice cell (see Fig. 3.17), a modified four-cell FODO structure with `missing magnets' [3.18]. The small finite R 56 generated by the chicane is compensated in the two adjacent cells with R56 = 0.065/2, slightly detuned away from their isochronous point. In order to avoid distortions in the longitudinal phase space, all the arcs are made isochronous up to second order by the use of sextupoles placed in the high-dispersion regions where there are no dipoles. The use of different families of sextupoles makes it possible to correct the third order as well. These designs will have to be re-adjusted to the new nominal delay length of 39 m and ring circumferences of 78 m and 312 m (Fig. A.1).
Fig. 3.17 : Lattices of the basic isochronous cell (left),
and of the first ring arc (2 cells + 1 chicane), globally
isochronous to 1st order (right).
The b -functions and the dispersion curve are
shown.
The ring injection is similar to a conventional fast injection scheme based on a septum and a fast kicker, where the kicker is, however, replaced by an RF deflector. Another deflector is placed upstream of the septum (at -p phase advance), and provides the pre-compensation of the kick given by the injection deflector to the circulating bunches. A p/ 2 phase advance FODO lattice is used in the injection straight section, with the septum and deflectors close to the focusing quadrupoles, such that the angular kick from the deflector corresponds to a maximum displacement in the septum (see Fig. 3.18 ).
Fig. 3.18 : Injection-insertion layout with the RF deflector
(left) and first-ring lattice (right). Circulating bunches will travel on the
central or inner orbit,
while the injected bunches are kicked by the 2nd deflector onto the equilibrium
orbit. The train of combined bunches is ejected before the next pulse
reaches the deflecting phase represented by the dotted line trajectory (intercepting
the septum).
All the RF deflectors are short travelling-wave iris-loaded structures, in which the resonant mode is a deflecting hybrid mode with a 2p /3 phase advance per cell and a negative group velocity [3.19]. The design is basically the same for all the deflectors, with the cell dimensions linearly scaled with frequency. They are made of 4 cells at 937 MHz and 10 cells at 3.75 GHz, and provide the 2 mrad deflection needed in both rings, with a 50 MW and 15 MW power consumption, respectively.
The extraction kickers consist of pairs of TEM travelling-wave transmission-lines (Fig. 3.19 ) [3.16], powered in anti-phase, with the wave moving against the beam; the kicker length is chosen to be 2 m, with a half-aperture of 1.5 cm. A deflection of 3 mrad requires a voltage of 11.3 kV, corresponding to 2.6 MW into each 50 W line. The kicker filling time of 6 ns remains small compared with the 130 ns available rise time. Because of the length of the extraction kicker, a different design is used for the extraction region lattice, based on a triplet placed between the kicker and the extraction septum. The phase advance between the kicker and the septum remains ~ p/ 2. The use of a triplet allows a rather constant b -amplitude along the kicker.
Fig. 3.19 : Extraction-insertion layout (left) and lattice (first-ring case, right).
As mentioned earlier, the preservation of the longitudinal phase-space of the bunches is important in order to be able to compress them before injection in the drive-beam decelerator. The main sources of phase-space distortion in the pulse compression chain are the coherent synchrotron radiation (CSR) emission and the higher-order momentum compaction. The evaluation of the longitudinal bunch-dynamics in both rings takes into account the CSR effect with shielding and the isochronicity curves in the arcs after sextupole correction up to second order [3.2]. The results are promising; the final bunch-length after compression is smaller than the target value, with small bunch-to-bunch variation (from 340 to 360 m m r.m.s., depending on the number of turns in the rings). The contribution of the delay-line arcs, as well as the non-linear contributions from the return loops and the final bunch-compressor, have been neglected for the moment. Nevertheless, these contributions are smaller, and further improvement can be obtained, e.g., either by using different sextupole families, or by adding pulse stretchers and compressors in front of each ring and optimizing the bunch length in each component.
The drive-beam accelerator and the combiner rings are planned to be in a central position with respect to the two main linacs of the collider. This means that all the drive beams have to be first transported in a direction opposite to that of the main beams, before being turned around over 360° and injected in the different decelerating units where they travel parallel to the main beams.
The transport line for the beam going upstream is of course located in the same tunnel as the decelerators, near the tunnel roof in order to minimize the loss of space (cf. Fig. 1.2 ). This position offers the advantage of preventing interference with the main linac and the decelerator by keeping the turn-around loops at a different level both in the tunnel and in the individual alcoves which will house these loops.
The different beam-transport elements of the turn-around area [3.2]are schematically shown in the plan view of Fig. 3.20 (bottom part). The up-going drive beam arrives from the left through a simple FODO transfer line. After a small vertical deflection [see the solid line branching above the dashed line at the top of the drawing (Fig. 3.20), (side view)], the selected drive-beam pulse enters the 360° loop, consisting of a 90° right-turn followed by three 90° left-turns. Drifts between these 90° turns are added to adjust the geometry and separate the axis of the down-going beam from the up-going one. These modules are designed to be isochronous ( R56 = 0) in order to preserve the bunch length and are based on the design concept elaborated for such applications with compact lattice and acceptable synchrotron radiation effects [2.9]. Table 3.9 summarizes the main parameters.
Table 3.9 : Isochronous module parameters
Fig. 3.20 : Layout of the turn-around area.
After the loop, the beam traverses a sort of bending chicane that serves to adjust the path length and at the same time to compress the bunch length. The present proposal is a generalized chicane consisting of a series of four double-bends with two dipoles deflecting the beam in the same direction, i.e., with a bending radius r and a bending angle q of the same sign. In this case, the integral of D / r over the two dipoles is positive by definition. The dispersion D, assumed to be zero, together with D ¢ , at both the entrance and the exit of the double-bend, is simply controlled by putting a focusing quadrupole at the mid-point between the two dipoles. The quadrupole inverts the sign of D ¢ and the function D is mirror-symmetric with respect to this point. The correlation between the energy spread and the position z within the bunch requires a positive R 56 for bunch compression. The total compression corresponds to a reduction of the bunch length from 2 mm to 290-170 m m with a correlated r.m.s. momentum-spread of approximately 1.5-1.2%. This gives a total R56 of ~0.15 m. On the other hand, the R 56 coefficient must be sufficiently large for an adjustment D l between 2 mm and 5 mm at most (i.e., half the RF period at 30 GHz). The proposed path-length module has an R56 equal to 0.13 m, the remaining compression being provided by the following vertical-bend (see side view of Fig. 3.20 ). In order to reach such a high value of R56 without increasing too much the angle or the dipole length, it is necessary to have a succession of four double-bends arranged in a geometry that looks like a chicane (Fig. 3.21). The total contribution to R56 is simply equal to the sum of the individual contributions. These do not depend on the sign of the deflection, since the double bends are separated by dispersion-free drifts. It is important to note that a triplet of quadrupoles must be inserted in the middle of these drifts. This matching triplet has no influence on R56 but is necessary to focus the beam and match the optics of the two adjacent double-bends. The following parameters of the generalized chicane were selected to give R56 = 0.13 m and Dl = 0.5 mm/mrad:
A path-length adjustment of 2 mm implies a change in the bending angle by 4 mrad, which induces in the mid-point of the snake a still tolerable lateral shift by approximately 4.8 cm.
Fig. 3.21 : Layout of the path length module.
The vertical translation which adds some bunch compression can be obtained by using the same double-bend concept. The coefficient R 56 should be equal to 0.03 m in order to give a total of 0.16 m together with the path length module. Using the exact geometry, the following set of parameters for the elements of the two double-bends is proposed:
The drift in the middle of the module, containing a matching quadrupole triplet, has a total length equal to 1.0 m, adjusted such as to satisfy the translation amplitude required.
Another promising design consists in using the tunable achromats developed for the CTF3 project [3.20]. Its main advantages are its geometrical flexibility, its capability of easily adjusting the coefficient R56 , and its much smaller number of magnetic elements.