Accelerator Physics Considerations

A number of beam dynamics issues were considered in the design and specifications of the RTML.

Incoherent (ISR) and Coherent (CSR) Synchrotron Radiation: Current esti-mates indicate that the horizontal emittance growth from ISR will be around 90 nm (1.1%) in the Arc, 380 nm (4.8%) in the Turnaround, and 430 nm (5.4%) in the Bunch Compressor in its nominal configuration. Vertical emittance growth from ISR in the Escalator is negligible.

Studies of the ILC Bunch Compressor indicate that there are no important effects of coherent synchrotron radiation, primarily because the longitudinal emittance of the beam extracted from the damping ring is so large [42].

Stray Fields: Studies have found that fields at the level of 2.0 nTesla will lead to beam jitter at the level of 0.2 σ_y [43]. This is considered acceptable since the orbit feed-forward will correct most of this beam motion. Measurements at existing laboratories [44] indicate that 2 nTesla is a reasonable estimate for the stray field magnitude in the ILC. Emittance growth considerations also place limits on the acceptable stray fields, but these are significantly higher.

Beam-Ion Instabilities: Because of its length and its weak focusing, the electron Return line will have potential issues with ion instabilities. To limit these to acceptable levels, the base pressure in the Return line must be limited to 20 nTorr [45].

Static Misalignments: The main issues for emittance growth are: betatron coupling introduced by the Spin Rotator or by rotated quads; dispersion introduced by rotated bends, rotated quads in dispersive regions, or misaligned components; wakefields from misaligned RF cavities; and time-varying transverse kicks from pitched RF cavities.

Studies of emittance growth and control in the region from the start of the Turnaround to the end of the second emittance region have shown that a combination of beam steering, global dispersion correction, and global decoupling can reduce emittance growth from magnetostatic sources to negligible levels, subject to the resolution limits of the measurements performed by the laser wires [46, 47]. Although the upstream RTML is much longer than the downstream RTML, its focusing is relatively weak and as a result its alignment tolerances are actually looser. Studies have shown that the same tuning techniques can be used in the upstream RTML with the desired effectiveness [48]. The tolerances for RF cavity misalignment in the RTML are large (0.5 mm RMS would be acceptable) because the number of cavities is small and the wakefields are relatively weak [49]. Although in principle the RF pitch effect is difficult to manage, in practice it leads to a position-energy correlation which can be addressed by the Bunch Compressor global dispersion correction [50]. A full and complete set of tuning simulations have not yet been performed, but it is expected that the baseline design for the RTML can satisfy the emittance preservation requirements.

Phase Jitter: Phase and amplitude errors in the bunch compressor RF will lead to energy and timing jitter at the IP, the latter directly resulting in a loss of luminosity. Table 2.5-3 shows the RMS tolerances required to limit the integrated luminosity loss to 2%, and to limit growth in IP energy spread to 10% of the nominal energy spread [51]. The tightest tolerance which influences the arrival time is the relative phase of the RF systems on the two sides: in the nominal configuration, a phase jitter of the electron and positron RF systems of 0.24^◦ RMS, relative to a common master oscillator, results in 2% luminosity loss. The tight tolerances will be met through a three-level system:

• Over short time scales, such as 1 second, the low-level RF system will be required to

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TABLE 2.5-3

Key tolerances for the two-stage bunch compressor.

Parameter Arrival Time Tolerance Energy Spread Tolerance

Correlated BC phase errors 0.24^◦ 0.35^◦

Uncorrelated BC phase errors 0.48^◦ 0.59^◦

Correlated BC amplitude errors 0.5% 1.8%

Uncorrelated BC amplitude errors 1.6% 2.8%

keep the two RF systems phase-locked to the level of 0.24 degrees of 1.3 GHz. See Section 3.9 for a fuller description of the low-level RF system.

• Over longer time periods, the arrival times of the two beams will be directly measured at the IP and a feedback loop will adjust the low-level RF system to synchronize the beams. This system is required to compensate for drifts in the low-level RF phase-locking system which occur over time scales long compared to a second.

• Over a period of many minutes to a few hours, the arrival time of one beam will be

“dithered” with respect to the arrival time of the other beam, and the relative offset which maximizes the luminosity will be determined. This offset will be used as a new set-point for the IP arrival-time feedback loop, and serve to eliminate drifts which arise over time scales long compared to a minute.

Halo Formation from Scattering: Halo formation is dominated by Coulomb scattering from the nuclei of residual gas atoms, and it is estimated that 100 nTorr base pressure in the downstream RTML will cause approximately 9 × 10⁻⁷ of the beam population to enter the halo [52]. A similar calculation was performed for the upstream RTML, which indicates that 20 nTorr base pressure will cause approximately 2 × 10⁻⁶ of the beam population to enter the halo. This is well below the budget of 10⁻⁵ which has been set for all beamlines between the damping ring and the BDS collimators (see 2.7.3.2.2).

Space Charge: In the long, low-energy, low-emittance transfer line from the damping ring to the bunch compressor, the incoherent space-charge tune shift will be on the order of 0.15 in the vertical. The implications of such large values in a single-pass beamline have not been studied.

Collimator Wakefields: Assuming collimation of the beam extracted from the damping ring at 10σx, 60σy, and ±1.5% (10σ_δ) in momentum, the worst-case jitter amplification for untapered, “razor-blade” spoilers is expected to be around 10% in x, around 75% in y, and the contribution to x jitter from energy jitter is expected to be negligible [53, 54]. The vertical jitter amplification figure is marginal, but can be substantially improved through use of spoilers with modest longitudinal tapers. The other collimator wakefield “figures of merit”

are acceptable even assuming untapered spoilers.

2.5.5 Accelerator Components

Table 2.5-4 shows the total number of components of each type in each RTML. The number of quadrupoles, dipole correctors, and BPMs is larger in the electron RTML than in the positron RTML due to the longer electron Return line; for these 3 component classes, the different totals for each side are shown in Table 2.5-4. Each quadrupole and dipole has its own power supply, while other magnets are generally powered in series with one power supply supporting many magnets. The cost estimate for the S-band dipole-mode structures

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was developed by the RTML Area Systems group based on recent experience with accelerator structure construction at IHEP; all other component cost estimates were developed by the ILC Technical and Global Systems groups.

TABLE 2.5-4

Total number of components in each RTML. Where 2 totals are shown, the larger number refers to the longer electron-side RTML, the smaller number refers to the shorter positron-side RTML.

Magnets Instrumentation RF

Bends 362 BPMs 772/740 1.3 GHz cavities 414

Quads 789/752 Wires 12 1.3 GHz cryomodules 48

Dipoles 1185/1137 BLMs 2 1.3 GHz sources 16 + 1

Kickers 17 OTRs 5 S-band structures 2

Septa 7 Phase monitors 3 S-band sources 2

Rasters 6 Xray SLMs 2

Solenoids 4

Table 2.5-5 shows the system lengths for the RTML beamlines.

TABLE 2.5-5

System lengths for each RTML beamline. Where 2 values are shown, the larger number refers to the longer electron-side RTML, the smaller number refers to the shorter positron-side RTML.

Upstream RTML Turn Spin Emit BC Dumplines

15,447 m / 14,247 m 275 m 82 m 47 m 1,105 m 180 m

Total 17,136 m / 15,936 m

Total, excluding extraction lines 16,956 m / 15,756 m

Footprint length 1,301 m

2.5.5.1 Vacuum Systems

The base pressure requirement for the downstream RTML is set by limiting the generation of beam halo to tolerable levels, while in the upstream RTML it is set by the necessity of avoiding beam-ion instabilities. As described in 2.5.4, the base pressure requirement for the downstream RTML is 100 nTorr, while in the upstream RTML it is 20 nTorr. Both upstream and downstream RTML vacuum systems will be stainless steel with 2 cm OD; the upstream RTML vacuum system will be installed with heaters to allow in situ baking, while the downstream RTML vacuum system will not. The bending sections of the turnaround and bunch compressors are not expected to need photon stops or other sophisticated vacuum systems, as the average beam current is low, and the fractional power loss of the beam in the bending regions is already small to limit emittance growth from ISR.

2.5.5.2 Service Tunnel

There is a service tunnel that runs parallel to the beam tunnel for the full length of the RTML and is shared with other systems. All of the power supplies, RF sources, and

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mounted instrumentation and controls equipment and computers are installed in the service tunnel This configuration allows repairs and maintenance to be performed while minimizing disruption to the accelerator itself.

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2.6 MAIN LINACS