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We use Bane's approximation to the Bjorken-Mtingwa theory of intrabeam scattering to calculate the emittance growth as a function of bunch charge in the KEK ATF. We find that our results are consistent with the experimental data. We then calculate the emittance growth in the NLC Main Damping Rings using the same formulae; we allow for some uncertainty in the ATF data by using two different values for the Coulomb log factor in the formulae for the emittance growth rates. We find that despite the IBS emittance growth, it should still be possible to achieve the specified transverse and longitudinal emittances in the NLC Main Damping Rings at the specified bunch charge.

We describe the results of studies comparing differentoptions for the baseline configuration of the ILC damping rings. Theprincipal configuration decisions apply to the circumference, beamenergy, lattice type, and technology options for key components,including the injection/extraction kickers and the damping wigglers. Toarrive at our recommended configuration, we performed detailed studies ofa range of lattices representing a variety of different configurationoptions; these lattices are described in Chapter 2. The results of thevarious studies are reported in chapters covering issues of beamdynamics, technical subsystems, costs, and commissioning, reliability andupgradeability. Our detailed recommendations for the baselineconfiguration are given in Chapter 7, where we also outline furtherresearch and development that is needed before a machine using ourrecommended configuration can be built and operated successfully. In thesame chapter, we suggest possible alternatives to the baselineconfiguration.

Author(s): Wolski, Andrzej; Ross, Marc C.; Woodley, Mark D.; Nelson, Janice; Honda, Yosuke | Abstract: Orbit Response Matrix (ORM) analysis is a technique used to diagnose and correct optics errors in storage rings. We report the results obtained from the use of ORM analysis at the KEK-ATF to reduce the equilibrium vertical emittance. Measurements of the vertical beam size using a laser wire indicate that the vertical emittance was successfully reduced from 12 pm to around 6 pm (at a bunch charge of 7e9 particles) using ORM analysis.

Author(s): Wolski, Andrzej | Abstract: The ILC damping rings will need a large acceptance to ensure good injection efficiency for the high-emittance, high-power beam from the positron source. The damping rings also need to have very low natural emittance for the collider to reach good luminosity. Meeting the simultaneous requirements for large dynamic aperture and low natural emittance presents a challenge for the lattice design. Previous designs have been based on theoretical minimumum emittance cells in the arcs; here, we present two lattice designs using simple FODO cells. The first design is for a 5 GeV ring with 16 km circumference and a layout similar to the TESLA "dogbone" damping ring. The second design is based on the same optics, but the circumference is reduced to 6.3 km by eliminating part of the long straight sections; this results in a small improvement in the dynamic aperture. The shorter ring also operates at the lower energy of 3.74 GeV. A drawback with both designs is that the high dispersion in the arcs leads to a large momentum compaction, which in turn leads to a requirement for a very high RF voltage, and a large value for the synchrotron tune. As well as presenting the designs and an analysis of the dynamic aperture in each lattice, we briefly consider the collective effects and, for the 16 km lattice, discuss the coupling bumps needed to reduce the space-charge tune shift.

We describe a simple lattice that meets the specifications for the damping times and horizontal and longitudinal emittances for the International Linear Collider (ILC) damping rings. The circumference of a little over 3 km leads to a bunch spacing of around 3 ns, which will require advances in kicker technology for injection and extraction. We present the lattice design, and initial results of studies of the acceptance and collective effects. With the high bunch charge and close spacing, the ion and electron cloud effects are expected to be severe; however, the simple structure of the lattice allows for easy variation of the circumference and bunch spacing, which may make it useful for future investigations.

To avoid radiation damage, the acceptance of linear collider damping rings must be large enough that injection efficiency close to 100 percent can be achieved. Survival plots based on tracking particles in the NLC Main Damping Ring lattice suggest a dynamic aperture with some margin over the specified injected beam size and energy spread. Here, we apply Frequency Map Analysis to give a more detailed picture of the dynamical stability of particle trajectories in the presence of lattice nonlinearities arising from the sextupoles and the damping wiggler. The techniques that we use are of general applicability to nonlinear elements in beamlines, and in particular will be used for analysis of wiggler effects in future damping ring designs.

The damping rings of a future linear collider will have demanding alignment and stability requirements in order to achieve the low vertical emittance necessary for high luminosity. The Accelerator Test Facility (ATF) at KEK has successfully demonstrated the vertical emittance below 5 pm that is specified for the GLC/NLC Main Damping Rings. One contribution to this accomplishment has been the use of Beam Based Alignment (BBA) techniques. The mode of operation of the ATF presents particular challenges for BBA, and we describe here how we have deduced the offsets of the BPMs with respect to the quadrupoles. We also discuss a technique that allows for direct measurements of the beam-to-quad offsets.

The techniques of normal form analysis, well known in the literature, can be used to provide a straightforward characterization of linear betatron dynamics in a coupled lattice. Here, we consider both the beam distribution and the betatron oscillations in a storage ring. We find that the beta functions for uncoupled motion generalize in a simple way to the coupled case. Defined in the way that we propose, the beta functions remain well behaved (positive and finite) under all circumstances, and have essentially the same physical significance for the beam size and betatron oscillation amplitude as in the uncoupled case. Application of this analysis to the online modeling of the PEP-II rings is also discussed.

We report results from studies of spin dynamics in the NLC Main Damping. Our studies have been based on spin tracking particles through the lattice under a range of conditions. We find that there are a number of spin resonances close to the nominal operating energy of 1.98 GeV; however, the effects of the resonances are weak, and the widths are narrow. We do not expect that any significant depolarization of the beam will occur during the store time.

We study transverse coupled-bunch instabilities driven by the resistive-wall impedance in the NLC Main Damping Rings. We compare the growth rates of the different modes predicted by a simple theory using a simplified lattice model with the results of a detailed simulation that includes variation of the beta functions and the actual fill structure of the machine. We find that the results of the analytical calculations are in reasonable agreement with the simulations. We include a simple model of a bunch-by-bunch feedback system in the simulation to show that the instabilities can be damped by a feedback system having parameters that are realistic, and possibly conservative. The noise level on the feedback system pick-up must be low, to avoid driving random bunch-to-bunch jitter above the specified limit of 10 percent of the vertical beam size.

The techniques of normal form analysis, well known in the literature, can be used to provide a straightforward characterization of linear betatron dynamics in a coupled lattice. Here, we consider both the beam distribution and the betatron oscillations in a storage ring, assuming that the beam emittances and betatron actions respectively are provided as parameters. We find that the beta functions for uncoupled motion generalize in a simple way to the coupled case. Defined in the way that we propose, the beta functions remain well behaved (positive and finite) under all circumstances, and have essentially the same physical significance for the beam size and betatron oscillations as in the uncoupled case. We discuss a technique for making direct measurements of the ratio of the coupled lattice functions at different points in the lattice.

We derive two formulae relating the variation in closed orbit in a storage ring to variations in quadrupole strength, neglecting nonlinear and dispersive effects. These formulae correct results previously reported [1,2,3]. We compare the results of the formulae applied to the ATF with simulations using MAD, and consider their application to beam-based alignment.

LOCO is a computer code for analysis of the linear optics in a storage ring based on the closed orbit response to steering magnets. The analysis provides information on focusing errors, BPM gain and rotation errors, and local coupling. Here, we discuss the details of the LOCO implementation at the KEK-ATF Damping Ring, and report the initial results. Some of the information obtained, for example on the BPM gain and coupling errors, has not previously been determined. We discuss the possibility of using the data provided by the LOCO analysis to reduce the vertical emittance of the ATF beam.

The consequences of beam conditioning in four example cases (VISA, a Soft X-Ray FEL, LCLS and a ''Greenfield'' FEL) are examined. It is shown that in emittance limited cases, proper conditioning reduces sensitivity to the transverse emittance, and allows stronger focusing in the undulator. Simulations show higher saturation power, with gain lengths reduced up to a factor of two. The beam dynamics in a general conditioning system are studied, with ''matching conditions'' derived for achieving conditioning without growth in effective emittance. Various conditioners are considered, and expressions derived for the amount of conditioning provided in each case when the matching conditions are satisfied. We discuss the prospects for conditioners based on laser and plasma systems.

The KEK Accelerator Test Facility (ATF) damping ring is a prototype low emittance source for the NLC/JLC linear collider. To achieve the goal normalized vertical emittance {gamma}{var_epsilon}{sub y} = 20 nm-rad, magnet placement accuracy better than 30 mm must be achieved. Accurate beam-based alignment (BBA) is required. The ATF arc optics uses a FOBO cell with two horizontally focusing quadrupoles, two sextupoles and a horizontally defocusing gradient dipole, all of which must be aligned with BBA. BBA at ATF uses the quadrupole and sextupole trim windings to find the trajectory through the center of each magnet. The results can be interpreted to assess the accuracy of the mechanical alignment and the beam position monitor offsets.