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**Accelerator Science and Technology**

Gabriele Bassi University of Liverpool / Cockcroft Institute I.R. Bailey, G. Bassi, J.B. Dainton, L.J. Jenner, K.M. Hock, M. Korostelev, L.I. Malysheva, K. Panagiotidis, D.J. Scott, A. Wolski, L. Zang Group Members

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Group Activities Development of high-intensity sources for polarized positron beams Spin dynamics Low-emittance storage ring beam dynamics Computational methods to model collective effects in future accelerators

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**HeLiCal Collaboration: ILC Undulator-based positron source**

I.R. Bailey, P. Cooke, J.B. Dainton, K. Hock (University of Liverpool / Cockcroft Institute) L.J. Jenner, L.I. Malysheva, L. Zang (University of Liverpool / Cockcroft Institute) D.P. Barber (DESY / Cockcroft Institute) A. Hartin (Oxford University / JAI) G.A. Moortgat-Pick (IPPP, University of Durham / Cockcroft Institute) J.A. Clarke, O.B. Malyshev, N. Ryder, D.J. Scott (CCLRC ASTeC Daresbury Laboratory / Cockcroft Institute) E. Baynham, T. Bradshaw, A. Brummit, S. Carr, Y. Ivanyushenkov, A. Lintern, J. Rochford (CCLRC Rutherford Appleton Laboratory) I EUROTeV: WP4 I. Bailey, J. Dainton, L. Zang (Cockcroft Institute / University of Liverpool) D. Clarke, N. Krumpa, J. Strachan (CCLRC Daresbury Laboratory) C. Densham, M. Woodward, B. Smith, (CCLRC Rutherford Appleton Laboratory) J.L. Fernandez-Hernando, D.J. Scott (CCLRC ASTeC Daresbury Laboratory / Cockcroft Institute) P. Cooke, P. Sutcliffe (University of Liverpool) In collaboration with Jeff Gronberg, David Mayhall, Tom Piggott, Werner Stein (LLNL) Vinod Bharadwaj, John Sheppard (SLAC)

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**Latest ILC Layout… Centre of mass energy 500 GeV Luminosity**

2×1034 cm-2s-1 Machine repetition rate, frep 5 Hz Bunches per pulse, nb 2610 Particles per bunch, N (max) 2×1010 Horizontal beam size at IP, sx 650 nm Vertical beam size at IP, sy 5 nm

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**Undulator-Based Polarised Positron Source for ILC**

The ILC requires of order 1014 positrons / s to meet its luminosity requirements. A factor ~60 greater than the ‘conventional’ SLC positron source. Undulator based source lower stresses in the production target(s) and less activation of the target station(s). Collimating the circularly-polarised SR from the undulator leads to production of longitudinally-polarised positrons. Conversion Target (0.4X0 Ti) Polarised Positrons (≈ 5 MeV) Helical Undulator (≈ 100 m) Photon Collimator Photons(≈ 10 MeV ) Electrons (150 GeV)

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**ILC Photon Collimator Work**

In the current baseline design, photons (10 MeV) are emitted from an undulator insertion device, and are then collimated by a photon collimator before striking into a rotating titanium alloy target. Simulating a realistic photon beam with the correct energy spectrum, angular distribution and polarisation is very important for understanding the effect of the collimator. Initial simulation (thermal condition of photon collimator) has been carried out in FLUKA. Currently modifying photon beam simulation to include polarisation effects.

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**Preliminary Design of Photon Collimator**

There are two purposes for the photon collimator: Scrape the photon beam to limit the extraneous halo (to protect the target). Adjust the polarisation by varying the collimator aperture. The left hand side shows an EGS4 simulation of the DESY design. The right hand side shows the model built in SIMPLEGEO and used for the FLUKA simulations. Design of Photon Collimator Length=90cm, Radius=6cm Inner spoiler: Inner radius 0.44cm, outer radius maximum 1.56cm, material is titanium. Outer absorber: Inner radius 2 cm, outer radius 6 cm, material is copper. Special feature: Spoilers are separated into different cylindrical fragments with inner diameter of ~4mm.

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**Photon Energy Spectrum Photon Angular Distribution**

The plot shows the energy distribution of photons generated by electrons (150 GeV) passing through 100 meters of undulator (period of undulator is 1 cm). Angular distribution of power (integrated over all frequencies) from the ILC baseline helical undulator. The horizontal axis is the polar angle.

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**Target Systems Working in collaboration with SLAC and LLNL.**

The CI plays a key role in the EUROTeV-funded task to carry out design studies of the conversion target and photon collimator for the polarised positron source. Capture Optics Positron beam pipe/ NC rf cavity Target wheel Photon beam pipe Motor Vacuum feedthrough LLNL - draft design Working in collaboration with SLAC and LLNL. Developing water-cooled rotating wheel design. 0.4 radiation length titanium alloy rim. Radius approximately 0.5 m. Rotates at approximately 2000 rpm.

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**Target Wheel Design & Assembly**

Iterative design evolution between LLNL and DL Constraints: Wheel rim speed fixed by thermal load and cooling rate Wheel diameter fixed by radiation damage and capture optics Materials fixed by thermal and mechanical properties and pair-production cross-section (Ti6%Al4%V) Wheel geometry constrained by eddy currents. LLNL - draft design DL - draft design

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Robust Spin Transport Developing reliable software tools that allow the machine to be optimised for spin polarisation as well as luminosity. Aiming to carry out full cradle-to-grave simulations. Currently carrying out simulations of depolarisation effects in damping rings, beam delivery system and during bunch-bunch interactions. Developing simulations of spin transport through the positron source. Will soon extend simulations to main linac, etc. Energy spectrum and circular polarisation of photons from helical undulator. Trajectories of electrons through helical undulator. Example of SLICKTRACK simulation showing depolariation of electrons in a ring. Collaborating with T. Hartin (Oxford) P. Bambade, C. Rimbault (LAL) J. Smith (Cornell) S. Riemann, A. Ushakov (DESY)

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**Depolarisation Processes**

Both stochastic spin diffusion through photon emission and classical spin precession in inhomogeneous magnetic fields can lead to depolarisation. 1 mrad orbital deflection 30° spin precession at 250GeV. Largest depolarisation effects are expected at the Interaction Points. Photon emission Spin precession

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**SLICKTRACK Simulations**

Damping Rings OCS, OCS6 and TESLA lattices analysed for ILC DR group. Depolarisation shown to be negligible. Ongoing rolling study. Beam Delivery System with and without misalignment For 2 designs:2mrad and 14 mrad crossing angles Linac study (acceleration mode)

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**Future Spin Transport Activities**

Future work motivated by Growing HEP community support for polarised beams to offset any reduction in ILC design luminosity Precision physics requires uncertainty ≤0.1% on luminosity-weighted polarisation. We’ve shown depolarising effects also of order 0.1%. ILC compatability with upgrade to a 60% polarised positron beam has been identified as a critical R&D topic by the Global R&D board (see April 2007 report) Spin transport is already incorporated in plans for 2 of the 7 accelerator systems EDR groups, with more anticipated. Goals Inclusion of non-linear transport maps in SLICKTRACK Development of positron source simulation including electron beam jitter, photon collimation effects, etc Use MAP2 and other computing resources. Continued theoretical work on beam-beam interactions including second-order coherent pair-production processes, etc. A continued rolling study of the whole machine to optimise use of polarisation as a tool for the ILC.

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**Preliminary Estimates of Impedance**

for the ILC Damping Rings Maxim Korostelev Andy Wolski

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**EM Field in Cylindrical Beam Pipe and Coax Waveguide**

- Particles travelling through an accelerator excite electromagnetic fields in the vacuum chamber. - The electromagnetic fields excited by "leading" particles affect the motion of "trailing" particles. - If the fields are very strong, the beam can become unstable. - Modelling the generation of the fields helps us to understand how to design the chamber to keep them small.

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**Transmission Line Model**

The field of a relativistic point charge q in a perfectly conducting beam pipe is a Transverse Electric Magnetic (TEM) wave where electric (radial) and magnetic (azimuthal) field components are transverse to the direction of propagation (z-axis) Log formula (Walling et al, 1989) Improved log formula (Vaccaro, 1994)

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**The Effect of Beta Function Variation on Wakefield Coupled Bunches**

Kai Hock Andy Wolski

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**The ILC Damping Rings Baseline Configuration**

RF shaft & cavern wiggler wiggler 6 ns - 3 ns Bunch spacing (max - min) 25.7 ms Transverse damping times 0.13% Natural energy spread 9 mm Natural bunch length 5.2 μm Normalized natural emittance 2× ×1010 Bunch population (max - min) Number of bunches (min - max) 405 mA Average current 5 GeV Beam energy 6476 m Circumference injection extraction wiggler shaft & cavern wiggler RF

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**Coupled Bunch Instabilities**

Long-range wake fields in the damping rings are of concern for two reasons: Initial estimates based on resistive-wall wake fields indicate coupled-bunch instability growth rates that could be challenging to deal with. The large jitter of injected bunches could couple through the wake fields to damped bunches awaiting extraction, leading to bunch-to-bunch jitter in the extracted beam that exceeds specifications. The stability of the beam extracted from the damping rings is critical for the performance of the ILC, so we are therefore taking a careful look at the effects of long-range wake fields. Generally, time-domain simulations confirm the growth rates expected from analytical estimates… Initial growth rates from simulation using real beta function.

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**Simple Lattice – 10 FODO Cells**

Variation in beta function causes coupling of multi-bunch modes. As a result … Max. growth rate is larger than analytic result for constant beta. Decay modes can grow. (a) (b) Figure 24. Amplitudes of (a) mode 2 and (b) mode 3 in the simple lattice with 4 bunches. The points are sampled for 1 turn at every 10 turns. (Hock, Wolski, Phys. Rev. ST Accel. Beams 10, (2007))

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**Low Emittance Tuning for the ILC Damping Rings**

Kosmas Panagiotidis Andy Wolski

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Achieving the luminosity goal of 21034 cm-2s-1 in the ILC will depend on producing a 5 nm beam size at the interaction point… …which requires a beam emittance a factor of 2 smaller than achieved in any operating accelerator. Understanding and being able to correct errors in the damping rings that could increase the emittance will be critical for effective operation of ILC. I've edited this slide… Effect of vertical sextupole misalignments on the vertical emittance. The error bars indicate the 5th and 95th percentiles over many sets of misalignments with given rms. Dependence of the emittance on quadrupole tilts. The error bars indicate the 5th and 95th percentiles over many sets of tilts with given rms.

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**Orbit Correction Simulations for the ILC DR**

Orbit correction is essential for successful operation of the machine Recent work has been focused on simulating an Orbit Correction Algorithm. Next figures illustrate initial BPM measurements of the vertical position of the beam before and after correction Reduction in orbit error after successive iterations of orbit correction Scales on the plots are rather small. You might just omit the left-hand graphic, and explain that the right hand plot shows the reduction in orbit error after successive iterations of orbit correction: that makes the main point. Perhaps add a couple of lines to explain the goals of future work: - include correction of vertical dispersion as well as the vertical orbit (dispersion is a source of emittance growth); - include a wider range of errors (including magnet alignment and field errors, and diagnostics errors) in simulations; - develop and optimise algorithms for minimising the vertical emittance (correcting dispersion and coupling); - optimise the correction system (i.e. numbers and locations of diagnostics and correctors), and specify initial alignment tolerances. Goals of future work: - include correction of vertical dispersion as well as the vertical orbit (dispersion is a source of emittance growth); - include a wider range of errors (including magnet alignment and field errors, and diagnostics errors) in simulations; - develop and optimise algorithms for minimising the vertical emittance (correcting dispersion and coupling); - optimise the correction system (i.e. numbers and locations of diagnostics and correctors), and specify initial alignment tolerances

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**A Vlasov-Maxwell Approach to Study Coherent Synchrotron Radiation Effects**

Gabriele Bassi

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**CSR Effects in Accelerators**

• Motivation: Coherent Synchrotron Radiation (CSR) from arbitrary orbits important. For example, for Bunch Compressors and Wigglers CSR may cause: a) transverse emittance growth in a bunch compressor b) microbunch instabilities • Coupled Vlasov-Maxwell (VM) System: a) less numerical noise then Macroparticle simulations b) allow study of emittance growth and microbunching .

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**Self Consistent Vlasov-Maxwell Treatment**

2D wave equation in lab frame: . Vlasov equation in beam frame:

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**Field Calculation (Lab Frame)**

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Numerical Results See PAC2005, EPAC2006, PAC2007

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**FERMI@ELETTRA First Bunch Compressor**

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**Conclusion Liverpool has a well established accelerator physics group**

The activities of the group cover many topics Many collaborations within the Cockcroft Institute and at international level Merry Christmas and Happy new Year !!!!

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