The drive-beam accelerator consists of 50 FODO cells with a constant phase advance of 117 degrees. The spacing between quadrupoles is 3.8 m and one accelerating structure with a length of 3.1 m is placed between each pair. The beam is accelerated from 50 MeV to about 1.2 GeV. Every second bucket of the beam is filled with a charge of about 16 nC, switching from odd to even buckets or vice versa every 60 bunches.
For the simulation the single-bunch wakefields were derived from the ones calculated for SBLC [3.6] by scaling with the frequency and iris radius. The longitudinal multibunch wakefields were ignored, their effect should be small due to the beam loading compensation scheme. The transverse wakefields were calculated for a constant impedance structure for four different iris radii [3.7]. For each cell the loss factor and the frequency of the two most important dipole modes were derived by interpolation. An analysis that includes the coupling between cells and the damping remains to be done. Conservatively, a damping with Q = 100 was assumed for the first dipole mode and with Q = 400 for the second.
The initial bunch length in the accelerator is sz = 4 mm while in the decelerator it should be smaller than 0.4 mm. Therefore, bunch compression is needed. On the other hand, the bunch length has to be larger than 2 mm in the combiner rings and the following bends in order to suppress coherent synchrotron radiation. Thus a final compression is needed at the point where the beam is bent into the decelerator. To evaluate the final bunch length a simple calculation was performed [3.8]. The compression stages are assumed to be linear. The longitudinal single-bunch wakefield was scaled from the one from SBLC assuming W 1/ a 2 . Two different strategies of compression exist. One can compress the beam to sz= 2 mm at about E = 100 MeV and then just accelerate it. The final compression after the final bends then yields a bunch length of sz = 290 mm. It is also possible to compress the beam as much as possible at three stages in the linac. Before the rings the beam is uncompressed to sz = 2 mm. After the final bend it is compressed as much as possible yielding sz = 170mm. The phase space for this case is shown in Fig. 3.11.
Coherent jitter of the beam is one of the possible sources of instability. Fig. 3.11 shows the final offset of the different bunch slices at the exit of the accelerator for an initial offset of D = s . Large amplitudes occur periodically. At these positions one switches from one train to the next. The offsets reach a steady state before the next train. It is therefore not important to simulate the exact pattern of the switching with the precise length of the trains. However, the time necessary for switching is important, as can be seen in Fig. 3.12. Here, the amplification of an initial offset is shown for a fast switch without any ramp and one with a ramp of 20 bunches. The points represent different slices of the beam. Initial and final offset are normalized to the beam size. Without a ramp the maximum amplification is significantly larger than with a ramp. Even a short ramp results in a significant reduction of the amplification.
The initial misalignment of the accelerator components needs to be corrected with beam-based alignment. Only a simple one-to-one correction is used in the simulation, since this machine needs to be very simple to operate in order to minimize down-time. All components are assumed to be scattered around a straight line with a normal distribution with a sigma of 100 mm. For the quadrupoles larger errors are assumed, but they have no influence on the results.
Fig. 3.12 shows the result of the correction in one case. The simple correction technique seems to be sufficient. This was verified by simulating 20 other cases [3.9] in which similar results were found.
Fig. 3.12 : Left: The amplification of an initial jitter. Initial and
final position are normalized to the beam size at the corresponding energy.
Right: The final bunch positions for a corrected machine.
The group velocities and the R ¢ /Q values must be such as to enable the beam to use up properly the electromagnetic energy before it reaches the structure end. Two possible designs of the accelerator cavities are being investigated. A new concept based on a slotted iris and constant aperture is proposed (E. Jensen et al., LINAC 2000). The model based on a classical geometry in order to avoid excessive surface gradients is described below.
First beam transport simulations with 937 MHz structures of 29 cells having an average iris radius a equal to 48.5 mm, an average outer radius b = 144 mm and a disc thickness d = 19 mm demonstrated that both detuning and damping were necessary to preserve a sufficiently low transverse beam emittance. The design is based on the same principles proposed for the CLIC main accelerating structures [2.23]. Good beam transmission was obtained with a dipole frequency spread of about 10% and a Q -value of 100 for the first mode and 400 for the second one (see Section 3.3.1 on beam dynamics). Since some scaled model work was planned at 3 GHz, the investigations with the code ABCI were all done for structures with this fundamental frequency (the average iris radius a scales to 15 mm at 3 GHz). A 29-cell structure having for the first cell a = 17 mm and for the last one a = 13.3 mm was used.
Table 3.4 lists the relevant parameters of the two extreme cells for zero bunch length and the 937 MHz operating frequency of the CLIC drive beam.
A 32-cell damped, detuned scale-model has been realized for 3 GHz (Fig. 3.13). Damping was confirmed by computations on a single cell using the HFSS code yielding Q -values of 11 and 100 for the first and second transverse modes, respectively [3.10] . The model work and the HFSS calculations have demonstrated that sufficient damping for beam survival is obtainable.
Fig. 3.13 : Front end of a 3 GHz scaled CLIC drive-beam acceleration
structure with transverse damping waveguides
against bipolar and quadrupolar high-order modes. Each such waveguide contains
a SiC absorber.
The short-range wakefields of the structures are derived by scaling from those for the S-Band Linear Collider (SBLC). For the SBLC frequency of 2.998 GHz the longitudinal delta-wakefield can be expressed as follows [3.6] :
For fixed ratio a /l , the scaling of the wakefield amplitudes with frequency goes with the frequency ratio to the square, i.e. ( f 1 / f 0 ) 2 . For a change of a /l , the scaling law is not straightforward, but goes with the square of the inverse of the radius-ratio, i.e. ( a 0 / a 1 ) 2 . The long-range longitudinal wakefields are neglected in the simulations reported in Section 3.3.1. Their effect on the mean bunch energy should be taken out by the beam loading compensation, so that only the distribution might slightly change.
The transverse delta-wakefield for 2.998 GHz can be approximated by the following relation [3.6] :
.Provided that a /l remains constant, the scaling with the frequency is proportional to the cube of the frequency-ratio, i.e. ( f 1 / f 0 ) 3 as shown in Ref.[3.11]. For a variation of a /l , the scaling of the amplitudes is approximately given by the following law ( a 0 / a 1 ) 2.2 .
The ratio a /l selected for the accelerator is larger than that for SBLC by a factor 1.25. The long-range transverse wakefield is calculated by assigning specific modes to the individual cells. It is assumed that the modes are trapped and do not propagate longitudinally. For each cell the two modes with the highest loss factors are used and the transverse field of the cell is given by the summation of these sinusoidal modes, exponentially decreasing with the distance z behind the particles driving the wakefield.
In order to obtain a realistic model at 937 MHz, the loss factors and frequencies for all the 29 cells are estimated by interpolating between the four cells simulated with the code ABCI at 3 GHz [3.12], [3.10]. The radii are equally spaced in the range 42.6-54.4 mm, corresponding to 13-17 mm at 3 GHz. Once the frequencies and amplitudes of the two most important modes in the four simulated cells have been calculated, the results are fitted by interpolation with a continuous function. These fits give closed expressions for the amplitudes and frequencies of the first two modes of the transverse wakefield which can then be used in beam tracking simulations (Section 3.3.1).
The damping was measured on a model indicating an upper limit for the damping of the first transverse mode of Q < 100 and a value of Q ª 400 for the second mode. In what follows, a quality factor for the main mode Q = 100 is used but more precise measurements are expected to show significantly smaller values. Calculations predict Q ª 11 for perfect loads [3.10].
The CLIC drive-beam RF power system provides 100 MW, 100 ms long pulses for each single accelerating structure of the 1.2 GeV, fully loaded and conventional 937 MHz, L-band linac [3.2]. A modular drive power system approach has been chosen, where the RF outputs from two 50 MW klystrons are connected to this single 3.4 m long, travelling wave structure, via 3 dB power combiners. Each of the 50 MW klystrons is driven by high-power modulators as shown below in Fig. 3.14 . The CLIC scheme will contain in total about 90 of these RF power modules in each of the drive-beam linacs.
CLIC requires a high conversion efficiency of AC power into klystron RF output power in order to reduce overall power consumption. Multibeam klystrons (MBKs) are being designed for this task in the above drive scheme (Table 3.5). These can be likened to a number of separate klystrons that share common cavities, a common collector structure, and the axial magnetic focusing field. For a given peak output power (Po) and efficiency (hMBK) the MBK beam voltage reduces with an increasing number of beams (nb) within the structure. This lower voltage reduces the probability of gun breakdowns with long pulse lengths and reduces any X-ray emission. It also permits the overall tube length to be reduced by up to 25%, leading to a smaller total volume for the installation. The MBK efficiency is expressed empirically as a function of the single-beam microperveance (mP ) by:
Fig. 3.14 : The 50 MW MBK RF network module.
This low, single-beam microperveance,
with low space-charge forces, enables stronger beam-bunching and so a higher electron
efficiency compared to the standard monobeam, higher microperveance tube. An efficiency
of 65-70% is calculated for the CLIC MBK. For high efficiency, as much of the
kinetic energy as possible in the bunched beams must be converted into electrical
energy at the RF output. This is achieved by decelerating the electron beam in
the output gap. On account of the potential drop at the collector entrance, some
electrons are accelerated in the reverse direction, particularly from the central,
seventh beam, giving rise to oscillations and unwanted sidebands. An alternative
six-beam MBK is also being investigated in case this difficulty has an impact
on the use of the central beam and restricts the present design (Table
3.5). Each of the parallel beams is the MBK transport part of the total output
power 
so that the effective tube
microperveance is nb (mP
). The peak output power is then given by:
The simulated power transfer curves [3.13] for a seven-beam MBK are shown in Fig. 3.15.
Fig. 3.15 : Simulated MBK power transfer curves.
The present MBK design parameters are given in Table 3.5.
Table 3.5 : Six- and seven-beam MBK design parameters
The choice of six beams is a minimum to meet initial design parameters and stay within current experience limits. An MBK with a seventh beam should enable a device to be developed that is close to the required RF power output specification. A further increase in the number of beams in the tube envelope will again reduce the beam voltage requirements and enable a higher peak output power to be obtained, but will not increase the efficiency, and increases the complexity of the gun and beam focusing systems.
For a greater number of beams ( n b > 7) a larger-diameter cavity would probably be needed, and could be operated as a higher-order mode multibeam klystron (HOM-MBK). However, larger cavities have multiple resonances that may bring difficulties in selecting the right operating mode for the klystron and cause a reduction in gain or efficiency. A larger-diameter cavity could make the internal geometry simpler with a beam convergence ratio closer to unity reducing the focusing power needed for the electromagnet and improving overall klystron-modulator system efficiency. All of the multibeam klystron scenarios discussed above require development to ensure that the operational parameters can be obtained.
The conventional line-type modulator baseline design, shown in Fig. 3.16, has been studied [3.14]. for powering a single 50 MW multibeam klystron and can also be used with two parallel, lower-power (25 MW) klystrons in an initial development phase. A key consideration is the conversion efficiency of AC wallplug power to pulsed RF power from the klystron. This requires that each major functional part be optimized for efficiency as well as for high-voltage performance and reliability. In this baseline design a high-efficiency switched-mode power unit is proposed for the high-voltage charging system. This is connected to a Rayleigh multicell (~33 cells) pulse-forming network (PFN), and discharged by two thyratron switches into the MBK load via a step-up pulse transformer. Auxiliary power systems provide the thyratron and klystron tube heating and focal power to an electromagnet for a magnetic field of around 2.5 times the Brillouin level. An overall AC-to-RF power efficiency of about 52% for a klystron modulator should be obtainable. The parameters for a 50 MW baseline modulator are shown below (Table 3.6).
Fig. 3.16 : Block diagram of a basic modulator
Different modulator designs using Insulated Gate Bipolar Transistors (IGBTs) for high-voltage switching are also being investigated as a possible future replacement for the thyratron in the baseline design. Large IGBT arrays can be used to handle the switched voltage and current requirements, and these need adequate protection to ensure correct load sharing. Alternatively, a high-frequency 3-phase switching supply, with low leakage inductance mains transformers, that is gated on and off by its primary circuit IGBTs will produce a high-voltage pulse directly for the klystron, or via a step-up pulse transformer. In the CLIC klystron-modulator application the requirements of high conversion efficiency, with high reliability and the handling of high-average switched power are important issues that need to be resolved.
