A high-precision intra-bunch-train beam orbit feedback correction system has been developed and tested in the ATF2 beamline of the Accelerator Test Facility at the High Energy Accelerator Research Organization in Japan. The system uses the vertical position of the bunch measured at two beam position monitors (BPMs) to calculate a pair of kicks which are applied to the next bunch using two upstream kickers, thereby correcting both the vertical position and trajectory angle. Using trains of two electron bunches separated in time by 187.6~ns, the system was optimised so as to stabilize the beam offset at the feedback BPMs to better than 350~nm, yielding a local trajectory angle correction to within 250~nrad. The quality of the correction was verified using three downstream witness BPMs and the results were found to be in agreement with the predictions of a linear lattice model used to propagate the beam trajectory from the feedback region. This same model predicts a corrected beam jitter of c.~1~nm at the focal point of the accelerator. Measurements with a beam size monitor at this location demonstrate that reducing the trajectory jitter of the beam by a factor of 4 also reduces the increase in the measured beam size as a function of beam charge by a factor of c.~1.6.

A sub-micron resolution, bunch-by-bunch beam trajectory feedback system and its application to reducing wakefield effects in single-pass beamlines

The accelerator and particle physics communities are considering a lepton Linear Collider LC as the most appropriate machine to carry out high precision particle physics research in the TeV energy regime. The Compact Linear Collider CLIC and the International Linear Collider ILC are the two proposals for the future e+e- LC. Both designs achieve a luminosity L above 10^(34) cm-2 s-1 at the interaction point IP, satisfying the particle physics requirements.
The LC consists of different systems, being the Final Focus System FFS the last one before colliding the beam at the IP. It is responsible to focus the beams at sizes in the range of nanometres by means of the Final Doublet FD. The FFS designs of the CLIC and ILC projects are based on a new local chromaticity correction scheme which has never been experimentally tested before.
The Accelerator Test Facility ATF2 at KEK (Japan) aims to experimentally verify the feasibility of the FFS based on this novel scheme.
The present thesis is devoted to the design and higher order optimisation of FFS for linear colliders based on the local chromaticity correction scheme. 
The CLIC design luminosity L0 is 5.9·10^(34) cm-2 s-1 assuming head-on collisions. However the beams cross each other at the IP forming an angle of 20 mrad. Due to this crossing scheme the luminosity would be reduced by 90%. Crab cavities are dedicated to tilt the bunches in order to provide head-on like collisions preserving the design L0. In this thesis different solutions that recover the design luminosity for the CLIC FFS are proposed.
The designs of a new ATF2 Nominal and Ultra-low beta* lattices, to test the feasibility of the ILC and CLIC FFS respectively, are presented in this thesis. The expected IP vertical beam sizes sy* for these lattices are 38 and 23 nm respectively, at this beam size regime the magnetic field quality of the FFS magnets is a concern. Indeed, the evaluated sy* with the measured multipole components is 100% for the Nominal lattice and 400% for the Ultra-low beta* lattice. The study of the higher order aberrations performed in this thesis is crucial for identifying possible cures that minimise the observed beam size growth. Different solutions have been studied: (i) replacing the FD by better field quality magnets, (ii) swapping the ATF2 quadrupole magnets according to their skew sextupole component and (iii) modifying the lattice optics. 
The new lattice designs ATF2 Bx2.5By1.0 and ATF2 Ultra-low betay* are based on the prosposed solutions. The impact of the multipoles components is effectively minimsed for both new designs, achieving a sy* equal to 38 and 27 nm ,respectively.
The tuning study of the FFS determines its feasibility under realistic error conditions. 100 machines with different initial error configurations are used to address this problem. 
The tuning simulation study for the alternative CLIC FFS design takes into account BPM resolution, the effect of synchrotron radiation and the misalignment errors of the magnets, being the later a critical parameter on the tuning performance of the system. The motion of the magnetic centre when shunting the quadrupole magnet might represent a limiting factor for further improvement of its alignment. Dedicated measurements at ATF2 have shown a motion of the magnetic centre below 1 micrometre for a shunting variation of 20%. Under this alignment condition the tuning study of the CLIC FFS shows that 80% of the machines reach a L equal or above than L0.
The errors included in the tuning study of the ATF2 lattices are misalignments, tilts and miss-powering of the ATF2 FFS magnets. The simulated tuning results show that 80% of the machines reach a final sy* that does not exceed in more than 11% and 35% the design sy* for the ATF2 Bx2.5By1.0 and Ultra-low beta_y* lattices respectively.
These results demonstrate the theoretical feasebility of FFS based on the novel chromaticity correction scheme.

/pdf/design-and-higher-order-optimisation-of-final-focus-systems-47shbmt1c6.pdf

Design and higher order optimisation of final focus systems for linear colliders

Ultra-low latency beam-based digital feedbacks have been developed by the Feedback On Nanosecond Timescales (FONT) Group and tested at the Accelerator Test Facility (ATF2) at KEK in a programme aimed at beam stabilisation at the nanometre level at the ATF2 final focus. Three prototypes were tested: 1) A feedback system based on high-resolution stripline BPMs was used to stabilise the beam orbit in the beamline region c. 50m upstream of the final focus. 2) Information from this system was used in a feed-forward mode to stabilise the beam locally at the final focus. 3) A final-focus local feedback system utilising cavity BPMs was deployed. In all three cases the degree of beam stabilisation was observed in high-precision cavity BPMs at the ATF2 interaction point. Latest results are reported on stabilising the beam position to approximately 50nm.

Progress Towards Electron-Beam Feedback at the Nanometre Level at the Accelerator Test Facility (ATF2) at KEK

In this brief overview we will reflect on the process of the design of the linear collider (LC) final focus (FF) optics, and will also describe the theoretical and experimental efforts on design and practical realisation of a prototype of the LC FF optics implemented in the ATF2 facility at KEK, Japan, presently being commissioned and operated.

Experimental and theoretical progress of linear collider final focus design and ATF2 facility

https://iopscience.iop.org/article/10.1088/1748-0221/16/01/P01005/pdf

The two major goals for this facility, called ATF2, are : (A) Achievement of a 37 nm beam size, and (B) control of beam position down to 2 nm level. The scientific justification for the ATF2 project and its technical design have been described in Volume 1 of the ATF2 Proposal. We present here Volume 2 of the ATF2 Proposal, in which we present specifics of the construction plans and the group organization to execute the research programs at ATF2.

ATF2 Proposal. Vol. 2

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ATF2 Proposal. Vol. 2