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

Gabriele Bassi

University of Liverpool / Cockcroft Institute

Accelerator Science and Technology

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

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)

IHeLiCal Collaboration:

ILC Undulator-based positron source

IEUROTeV: 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)

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, x 650 nm

Vertical beam size at IP, y 5 nm

•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 Undulat

or(≈ 100

m)

Photon Collimator

Photons(≈ 10 MeV )

Electrons(150 GeV)

Undulator-Based Polarised Positron Source for ILC

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.

Preliminary Design of Photon Collimator

• 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.

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.

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 plot shows the energy distribution of photons generated by electrons (150 GeV) passing through 100 meters of undulator (period of undulator is 1 cm).

0 2 . 10 7 4 . 10 7 6 . 10 7 8 . 10 7 1 . 10 80

2 . 10 38

4 . 10 38

6 . 10 38

8 . 10 38

1 . 10 37

P ho ton E nergyeV

Powe

rSp

ectru

mwa

ttseVofB

andw

idth

mAofele

ctron

beam

T he P hoton Energy Sp ect rum

Photon Angular Distribution

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .00

1 . 10 11

2 . 10 11

3 . 10 11

4 . 10 11

dW dwattse

Vof

band

widt

h

1m

A

1m

rad

2 T he A ngular D is t ribut ion of R adiat ed P ow er

Angular distribution of power (integrated over all frequencies) from the ILC baseline helical undulator. The horizontal axis is the polar angle.

Photon Energy Spectrum

Capture Optics

Positron beam pipe/NC rf cavity

Target wheel

Vacuum feedthrough

MotorPhotonbeam pipe

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.

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.

Target Systems

LLNL - draft design

Target Wheel Design & Assembly

LLNL - draft design

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.

DL - draft design

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.

0E+00

5E+13

1E+14

2E+14

2E+14

3E+14

3E+14

0.0 20.0 40.0 60.0 80.0 100.0

Photon Energy (MeV)

Flu

x (p

ho

ton

s/s/

mA

/0.1

%)

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Cir

cula

r P

ola

risa

tio

n R

ate

20 x 20 urad flux2 x 2 urad flux20 x 20 urad polarisation2 x 2 urad polarisation

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)

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.

Depolarisation Processes

Photon emission

Spin precession

( 2)

2spin orbit

g

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)

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.

Preliminary Estimates of Impedance for the ILC Damping Rings

Maxim Korostelev

Andy Wolski

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.

Transmission Line Model

Log formula (Walling et al, 1989)

Improved log formula (Vaccaro, 1994)

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)

Kai Hock

Andy Wolski

The Effect of Beta Function Variation on Wakefield Coupled Bunches

The ILC Damping Rings Baseline Configuration

injection extraction

wiggler wiggler

wigglerwigglerRF

RFshaft &cavern

shaft &cavern

6 ns - 3 nsBunch spacing (max - min)

25.7 msTransverse damping times

0.13%Natural energy spread

9 mmNatural bunch length

5.2 μmNormalized natural emittance

2×1010 - 1×1010Bunch population (max - min)

2610 - 5265Number of bunches (min - max)

405 mAAverage current

5 GeVBeam energy

6476 mCircumference

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.

(Hock, Wolski, Phys. Rev. ST Accel. Beams 10, 084401 (2007))

(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.

Simple Lattice – 10 FODO CellsVariation in beta function causes coupling of multi-bunch modes. As a result …

Decay modes can grow.Max. growth rate is larger than analytic result for constant beta.

Low Emittance Tuning for the ILC Damping Rings

Kosmas Panagiotidis

Andy Wolski

0 0.2 0.4 0.6 0.8 1 1.2

x 10-4

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6x 10

-11

Sextupole Misalignment (m)

Ve

rtic

al E

mitt

an

ce (

m)

simulation data

theoretical prediction

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.

0 0.2 0.4 0.6 0.8 1 1.2

x 10-4

0

0.2

0.4

0.6

0.8

1

1.2

1.4x 10

-11

Rotation Angle (rad)

Ve

rtic

al E

mitta

nce

(m)

simulation data

theoretical prediction

Dependence of the emittance on quadrupole tilts. The error bars indicate the 5th and 95th percentiles over many sets of tilts with given rms.

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.

Orbit Correction Simulations for the ILC DR

Orbit correction is essential for successful operation of the machine

Reduction in orbit error after successive iterations of orbit correction

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

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

Gabriele Bassi

A Vlasov-Maxwell Approach to Study Coherent Synchrotron Radiation Effects

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

Self Consistent Vlasov-Maxwell Treatment2D wave equation in lab frame:

.Vlasov equation in beam frame:

Field Calculation (Lab Frame)

Numerical Results

See PAC2005, EPAC2006, PAC2007

FERMI@ELETTRA First Bunch Compressor

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 !!!!