ILC Positrons

1
ILC Positrons
Positron Production for the ILC

• J. C. Sheppard
• SLAC
• July 26, 2007

2
Positron Production for the ILC
What is the ILC e System How to make
e Something about polarization Who works on
this stuff What are the design issues What next
3
THE INTERNATIONAL LINEAR COLLIDER (ILC)

• Parameter  Reference Upgrade
• Beam Energy (GeV) 250  500 
• RF gradient (MV/m) 28  35 
• Two-Linac length (km) 27.00  42.54 
• Bunches/pulse  2625  2625 
• Particles/bunch (1010) 2  2 
• Beam pulse length (µs ) 968  968 
• Pulse/s (Hz) 5  5 
• ?x(IP) (nm) 543  489 
• ?y(IP) (nm) 5.7  4.0 
• ?z(IP) (mm) 0.3  0.3 
• dE  () 3.0  5.9 
• Luminosity (1033cm-2s-1) 25.6 38.1
• Average beam power (MW)  22.6  45.2 
• Total number of klystrons  603  1211 
• Total number of cavities  18096  29064 
• AC to beam efficiency () 20.8  17.5 

• WORLD Collaboration
• Multi-billion dollar project
• Proposed ee linear collider
• 0.5-1.0 TeV center-of-mass energies
• Major elements
• Electron injector
• Electron damping ring
• Main electron linac
• Electron beam delivery to IR
• Positron Source
• Positron damping ring(s)
• Main positron linac
• Positron beam delivery to IR
• IR
• Detectors at IR

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ILC Positron Source Parameters
Parameter Symbol Value Units
Bunch Population Nb 2x1010
Bunches per pulse nb 2625
Bunch spacing tb 369 ns
Pulse repetition rate frep 5 Hz
Injection Energy (DR) E0 5 GeV
Beam Power (x1.5) Po 300 kW
Polarization e-(e) P 80(30)
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POSITRON SOURCE DESIGN ISSUES

• Drive beam
• Electrons or photons
• Photons allow for the possibility of polarized
  positrons
• How are the photons made
• Multi-hundred GeV electron beam through an
  undulator
• Compton back-scattering laser beam on a multi-GeV
  electron beam
• Drive beam phase space
• Target
• Choice of material
• Target heat/shock/stress
• Positron capture
• Beam heating
• Capture RF
• Capture magnetic field
• Damping ring acceptance
• Target vault

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ILC Layout

• e e- Damping Rings centrally located
• positron source uses 150 GeV electron beam
• L-band superconducting RF for acceleration

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(No Transcript)
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POSITRON PRODUCTION SCHEMES DRIVE BEAMS
6 GeV e-
W-Re Target
Undulator-based (from USLCTOS)
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COMPTON-BASED POSITRON SOURCE LASERS
GLC laser power 9.8 MW peak power per laser
bunch 400 kW average power (40kW with use
of mirrors) 73 GW peak power ILC bunch
structure 2820 5 95 150 but 2820 bunch
pulse trains may be able to use mirrors to
relax laser parameters
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Snowmass 2005 Ring based Compton
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ERL based Compton scheme requirements to lasers
Tsunehiko OMORI (KEK)
my talk is inspired by Variola-san's talk at KEK
Nov/2006 and Rainer-san's suggestion at SLAC
Apr/2004
PosiPol2007_at_LAL 23/May/2007
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UNDULATOR BASED POSITRON SOURCE
Need to use ILC electron beam possible
reliability, machine development and
commissioning issues Can use electron source for
commissioning Long helical undulator, small
aperture permanent magnet warm
pulsed superconducting
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Positron Source Layout
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Polarized Positrons from Polarized gs
Circular polarization of photon transfers to the
longitudinal polarization of the positron.
Positron polarization varies with the energy
transferred to the positron.
(Olsen Maximon, 1959)
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Photon Intensity, Angular Dist., Number,
Polarization
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Polarized Positron Production in the FFTB
Polarized photons pair produce polarized
positrons in a 0.5 r.l. thick target of Ti-alloy
with a yield of about 0.5. Longitudinal
polarization of the positrons is 54, averaged
over the full spectrum Note for 0.5 r.l. W
converter, the yield is about 1 and the average
polarization is 51.
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Photon Number Spectrum
Number of photons per e- per 1m undulator Old
BCD 2.578 UK1 1.946 UK2 1.556 UK3
1.107 Cornell1 0.521 Cornell2 1.2 Cornell3
0.386
Gai and Liu, ANL
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Photon Spectrum and Polarization of ILC baseline
undulator
Results of photon number spectrum and
polarization characteristic of ILC undulator are
given here as examples. The parameter of ILC
undulator is K1, lu1cm and the energy of
electron beam is 150GeV.
Figure1. Photon Number spectrum and polarization
characteristics of ILC undulator up to the 9th
harmonic. Only those have energy closed to
critical energy of its corresponding harmonics
have higher polarization
Gai and Liu, ANL
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Initial Polarization of Positron beam at Target
exit(K0.92 lu1.15)
Gai and Liu, ANL
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ILC Positron Polarization,captured 30 Pol
Gai and Liu, ANL
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ILC Positron Polarization
In the case of the ILC baseline, the composite
polarization of the captured positrons is about
30. Spin rotation to preserve the polarization
in the damping ring(s) is included To upgrade to
higher polarization, the incident photon beam is
collimated to remove the low energy, reversely
polarized component of the spectrum (gq 1.414).
The length of the undulator needs to be increased
to compensate for the loss in absolute flux.
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US Institutions

• Institutions doing substantial work on ILC e
  development
• SLAC
• overall coordination leadership for the RDR
• define parameters
• target hall, remote handling, activation
• beamline optics and tracking
• NC L-Band accelerator structures and RF systems
• Experiments E166, FLUKA validation experiment
• LLNL
• target simulations (thermal hydraulics and
  stress, rotordynamics, materials)
• target design (testing and prototyping)
• pulsed OMD design
• ANL
• optics
• tracking
• OMD studies
• eddy current calculations
• Cornell
• undulator design, alternative target concepts

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European Institutions

• Institutions doing substantial work on ILC e
  development
• Daresbury Laboratory
• EDR leadership
• undulator design and prototyping
• beam degradation calculations
• Rutherford-Appleton Laboratory
• remote handling
• eddy current calculations
• target hall activation
• Cockcroft and Liverpool University
• target design and prototyping
• DESY-Berlin
• target hall activation
• spin preservation
• photon collimation
• E166

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ILC e Collaboration Meeting
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ILC Polarized Positron System Technical Issues

• 1. Demonstrate undulator parameters
• 2. Demonstrate NC SW structure hi power rf
  performance
• 3. Spinning target pre-prototype demonstration
• 3. Eddy current measurements on spinning target
• 4. Selection and Technical design of Optical
  Matching Device
• 5. System engineering for e source remote
  handling
• 6. System engineering for photon dump
• 7. System design compatibility with ILC upgrade
  scenarios polarization and energy

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ILC Positron EDR Milestones

• Sep 07 Full layout with l/4 XMFR OMD
• Dec 07 EDR Scope definition design depth and
  breadth, cost, schedule, staff
• Jun 08 Full upgrade scenario polarization and
  ILC energy
• Sep 08 OMD selection (dc immersed, pulsed FC,
  l/4 XMFR), Und parameter selection
• Dec 08 Freeze layout, full component and civil
  specifications (yield, overhead, remote handling,
  upgrades)
• Jan 09 EDR detailed component inventory
• May 09 First cost review
• Dec 09 Deliver EDR and preconstruction work plan

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ILC Positron Design Issues, Undulator

• Ne ecYgLungNe-
• ec (Adr,DEdr,Ac,ee) 15-25
• Yg(Eg, X0,Z) 1-5
• ng(K,lu) 2
• Lu 100 m

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ILC Positron Design Issues, Target

• FOM aE/2(1-n)/Cv/r/UTS(fatigued)
• Thermoelastic stress wrt material strength
• Targets break rather than melt
• DE/mass lt 100 J/g
• High strength Ti-alloy (Ti6Al4V)

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ILC Positron Design Issues, Target

• Need to spread out the energy deposition
• This is done by spinning the target at 100 m/s
• Same problem with windows but do not know how to
  spin
• Can imagine an entrance window
• Exit window will not survive

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• RDR Parameters
• Centre of undulator to target 500m
• Active (K0.92, period1.21mm) undulator 147m
• Photon beam power 131kW
• Beam spot gt1.7 mm rms

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Baseline Target Design

• Wheel rim speed (100m/s) fixed by thermal load
  (8 of photon beam power)
• Rotation reduces pulse energy density from
  900J/g to 24J/g
• Cooled by internal water-cooling channel
• Wheel diameter (1m) fixed by radiation damage
  and capture optics
• Materials fixed by thermal and mechanical
  properties and pair-production cross-section
  (Ti6Al4V)
• Wheel geometry (30mm radial width) constrained
  by eddy currents.
• 20cm between target and rf cavity.

T. Piggott, LLNL
Drive motor and water union are mounted on
opposite ends of through-shaft.
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Target Progress

• Baseline target/capture
• RAL, ANL and Cornell have done Eddy current
  simulation which produce consistent results with
  multiple codes. Estimates for power dissipation
  in the target are gt100kW for a constant field and
  are considered excessive.
• Evaluation of ceramic target material is
  on-going. No conclusions.
• Radiation damage of the superconducting coil is
  still TBD but may not be worthwhile unless a
  solution can be found for the eddy currents.
• ANL simulation of beam heating in windows shows
  that an upstream window is feasible but a
  downstream window is not.
• Alternative target/capture
• Capture efficiency for the lithium lens focusing
  and ¼ wave solenoid is still TBD
• Thermal heating and stress for the lithium lens
  is still on-going.
• Thermal stress calculation for the liquid metal
  target is still on-going

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Capture versus Optical Matching Device Type
0.4
0.3
Positron Capture (arb. units)
0.2
0.1
0
No OMD
¼ l xfrm
Pulsed FC
Immersed
From F. Zhou, W. Liu
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Optical Matching Device (OMD)

• Optical Matching Device
• factor of 2 in positron yield (3 if immersed
  target)
• DC solenoid before target or pulsed flux
  concentrator after target
• Pulsed device is the baseline design
• Target spins in the magnetic field of the OMD
• Eddy currents in the target need to calculate
  power
• Magnetic field is modified by the eddy currents
  effect on yield??
• Eddy current mitigation
• Reduce amount of spinning metal
• Do experiment to validate eddy current
  calculations
• Look for low electrical / high thermal
  conductivity Ti-alloys
• Other materials such as ceramics
• No OMD
• Use focusing solenoidal lens (1/4 wave) lower
  fields
• OMD is upgrade to polarization(??)

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Eddy Current Experiment
Proposed experiment Layout at Cockcroft Institute/
Daresbury (this summer)
Eddy current calculation mesh - S. Antipov, W.
Liu, W. Gai - ANL
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Calculated Eddy Current Power
Nominal RPMs
sTiAlV 6e5
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Pulsed Flux Concentrator 7T, 1 ms, 5 Hz
Pulsed Flux Concentrator, circa 1965 Brechna et
al.
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OMD Progress

• Plans and Actions (baseline target/capture)
• ANL will simulate eddy currents in the pulsed
  magnet configuration.
• UK will evaluate suitability of non-conducting
  materials for the target
• Daresbury/Cockroft/RAL will spin a one meter
  target wheel in a constant magnetic field and
  will measure the forces.
• Eddy simulations will be calculated and
  benchmarked against this configuration
• Plans and Actions (alternative targets/capture)
• ANL will determine the capture efficiency for ¼
  wave focusing optics and lithium lens.
• LLNL will evaluate the survivability of lithium
  lens to beam stress
• Cornell will specify an initial design of a
  liquid metal target. LLNL will calculate the
  Stress-strain behavior of the outgoing beam
  window.

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Undulator Challenges

• High fields
• Pushing the limits of technology
• Short Periods
• Shorter periods imply higher fields
• Narrow apertures
• Very tight tolerances - Alignment critical
• Cold bore (4K surface)
• Cannot tolerate more than few W of heating per
  module
• Minimising impact on electron beam
• Must not degrade electron beam properties but
  have to remove energy from electrons
• Creating a vacuum
• Impossible to use conventional pumps, need other
  solution
• Minimising cost
• Minimise total length, value engineering

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UK Undulator Recent Highlights

• Two 12mm period SC undulator prototypes built and
  tested
• Period reduced to 12mm from 14mm
• Better, more reproducible, fabrication technique
• Full inclusion of iron for the first time
• One 11.5mm period SC undulator built and tested
• Period further reduced to RDR value of 11.5mm
• New SC wire used (more SC and less Cu)
• Field strength measured greater than expected,
  possibly due to increase in SC content of wire
• Best ever field quality results (well within
  spec)
• Full length prototype will use these parameters
• Full length prototype construction started
• 4m prototype design complete
• Fabrication has commenced
• Undulator impact studies ongoing
• Emittance growth due to misalignments
  wakefields shown to be lt2
• Paper on undulator technology choice published by
  Phys. Rev. ST-AB
• Paper on vacuum issues submitted to JVSTA

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UK Prototypes
I II III IV V
Former material Al Al Al Iron Iron
Period, mm 14 14 12 12 11.5
Groove shape rectangular trapezoidal trapezoidal trapezoidal rectangular
Winding bore, mm 6 6 6.35 6.35 6.35
Vac bore, mm 4 4 4 4.5 (St Steel tube) 5.23 (Cu tube)
Winding 8-wire ribbon, 8 layers 9-wire ribbon, 8 layers 7-wire ribbon, 8 layers 7-wire ribbon, 8 layers 7-wire ribbon, 8 layers
Sc wire CuSc 1.351 CuSc 1.351 CuSc 1.351 CuSc 1.351 CuSc 0.91
Status Completed and tested Completed, tested and sectioned Completed and tested Completed and tested Completed and tested
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Prototype 5

• Same parameters as RDR Baseline undulator
• 11.5 mm period
• 6.35 mm winding diameter
• Peak on-axis field spec of 0.86T (10 MeV photons)
• Winding directly onto copper tube with iron pole
  and yoke
• New wire with more aggressive CuSC ratio of
  0.91.0

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1st results from prototype 5 at RAL
Measurements for Prototype 5
Quench current 316A Equates to a field of 1.1 T
in bore RDR value is 0.86 T 80 of critical
current (proposed operating point) would be 0.95 T
Measured field at 200A 0.822 T /- 0.7 (spec
is /- 1)
Prototype 5 details Period 11.5
mm Magnetic bore 6.35 mm Configuration Iron
poles and yoke
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Summary of Prototype Results
Fe former yoke
Fe former
Prototype 5 _at_ 250A _at_ 200A
Aluminium former
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Specification for 4m Undulator Module
On axis field 0.86 T
Peak to peak variation lt1
Period 11.5 mm
Nominal Current 250 A
Nom current as of Short Sample 80
SC wire NbTi 0.4mm dia., SCCu ratio 0.91
Winding Cross Section 7 wires wide x 8 high
Number of magnets per module 2 (powered separately for tests)
Length of magnetic field 2 x 1.74 m
No Beam Collimators or Beam Pipe Vacuum pumping
ports in the magnet beam pipe
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4m Prototype Module
Construction has started, will be complete by
Autumn 07
50K Al Alloy Thermal shield. Supported from He
bath
U beam Support rod

• Stainless steel vacuum vessel with Central turret

Stainless Steel He bath filled with liquid
Helium.
Magnet support provided by a stiff U Beam
Beam Tube
Superconducting Magnet cooled to 4.2K
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Magnet Design Concept
Steel Yoke. Provides 10 increase in field and
mechanical support for former
Winding pins
PC board for S/C ribbon connections

• 2 start helical groove machined in steel former

Steel yoke
Cu beam pipe, withconductor wound on to tube OD
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STATUS OF CORNELL UNDULATOR PROTOTYPING

• Alexander Mikhailichenko, Maury Tigner
• Cornell University, LEPP, Ithaca, NY 14853

A superconducting, helical undulator based source
has been selected as the baseline design for the
ILC. This report outlines progress towards
design, modeling and testing elements of the
needed undulator. A magnetic length of
approximately 150 m is needed to produce the
desired positron beam. This could be composed of
about 50 modules of 4 m overall length each. This
project is dedicated to the design and eventual
fabrication of one full scale, 4 m long undulator
module. The concept builds on a copper vacuum
chamber of 8 mm internal bore
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Fig.1Extensible prototype concept for ILC
positron undulator . Diameter of cryostat 102mm
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Several 40 cm long undulator models with 10 and
12 mm period, Ø 8 mm clear bore have been made
and measured. See Table OFC vacuum chamber,
RF smoothness
SC wire 54 filaments 56 filaments 56 filaments
layers 5 6 9 (12) sectioning
?10 mm K0.36 tested K0.42 tested K0.5 (calculated)
?12 mm K0.72 tested K0.83 tested K1 (calculated)
) Wire Ø0.6 mm bare ) Wire Ø0.4 mm
bare ) Wire Ø0.3 mm bare
Fig.3 Field profile conical ends. 6 layer, 12
mm period orthogonal hall probes. 1Tesla full
scale
For aperture diameter 5.75 mm we expect for
period 8mm K0.4 for period 10mm -K0.9
51

• Progress to Date
• An overall concept design for the module as shown
  in Fig. 1 has been developed. The design is very
  compact, having an outside cryostat diameter of
  100 mm. Standard size plumbing components are
  used throughout. Figure 1 shows the cross
  section design for tapered end coils.
• We have made optimization studies for undulators
  having 10 and 12 mm period with 8 mm clear bore
  and wound with various commercially available
  wires.
• Technology for fabrication of the undulator has
  been reduced to practice including winding of the
  wire and the helical iron yoke as well as
  procedures and apparatus for measuring the field
  distribution at the operating temperature.
• Several 40 cm long undulator models with 10 and
  12 mm period, 8 mm clear bore have been made and
  measured.

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Capture versus initial rf gradient
Positron Capture (arb. units)
Initial rf gradient (MV/m)
Batygin slac-pub-11238
53
Prototype Positron Capture Section
54
Preliminary Microwave Checking
Measurement Setup for the Stacked Structure
before Brazing without Tuning
Field Plots for Bead Pulling Two Different
Frequencies Showing the Correct Cell Frequency
and Tuning Property.
1300.175 MHz at 20C, N2
1300.125 MHz at 20C, N2
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Brazed Coupler and Body Subassemblies - Ready for
Final Brazing
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Summary Page for the Capture RF

• Vacuum Leak Check
• Recheck the RF Properties
• Installation
• Support
• Cooling system
• Waveguide system
• Window
• Vacuum system
• Solenoid
• Monitoring System.
• High Power Test (5MW, 1.2 ms,5 Hz)
• Beam Acceleration Test

Juwen Wang
57
Optics

• Source optics laid out. Need to look at details
• Beam loss and collimation
• Component interferences (target halls, DR
  injection)
• Refine and document optics and beam physics

58
E-166 Experiment
E-166 is a demonstration of undulator-based
polarized positron production for linear colliders
- E-166 uses the 50 GeV SLAC beam in conjunction
with 1 m-long, helical undulator to make
polarized photons in the FFTB. - These photons
are converted in a 0.5 rad. len. thick target
into polarized positrons (and electrons). - The
polarization of the positrons and photons will be
measured.
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Undulator-Based Production of Polarized Positrons
E-166 Collaboration
(45 Collaborators)
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Undulator-Based Production of Polarized Positrons
E-166 Collaborating Institutions
(15 Institutions)
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FLUKA Validation Experiment
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FLUKA Validation Experiment

• SLAC/CERN Collaboration (RP groups)
• Validation of FLUKA activation calculations
• 100 W
• 30 GeV electron beam in ESA at SLAC
• Cylindrical copper dump
• Samples around the dump (including a Ti-4V-6Al)
• Look mr/hour and gamma spectrum from irradiated
  samples
• Run at the beginning of April

65
Experiment Setup
66
Preliminary Data Ti and Ti-alloy
67
Target Hall / Remote Handling

• Projected ILC running mode
• 9 month run 3 month shutdowns
• Target stations designed with 2 year lifetime
• Replace target station every shutdown
• If target fails then
• EITHER a hot spare
• OR fast replacement
• Radiation levels 100 rem/hour immediately after
  beam shutoff
• Remote handling needed
• Target hall deep underground
• Vertical target extraction/replacement
• Vinod used to work in the FNAL antiproton source!!

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ILC Target Hall Cartoon (single target)
69
Target Remote Handling
Estimated 53 hour replacement time
70
Remote-Handling Module and Plug
Cryocooler (if required) vacuum pump water
pump
M. Woodward, RAL
Module contains target, capture optics and first
accelerating cavity.
Details of vertical drive for target wheel not
yet considered.
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TRIUMF ISAC FACILITY
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Visit to ORNL
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Visit to ORNL
74
Visit to ORNL
75
Visit to ORNL

• The remote handling systems for the SNS target is
  estimated to have cost about 100M
• Off the cuff estimate to work up ILC e Remote
  Handling Systems for the EDR would be about 4-5
  FTE spread out over 3 years

76
ILC Status

• Reference Design Report (RDR) completed
• Design feasibility
• Alternative technologies (cost saving, risk
  reduction ..)
• RD priorities
• 4-volume report, Executive Summary, Physics Case,
  Accelerator, Detectors 700 pages produced
• Printed version in August
• Now setting up Engineering Design Phase (EDR)
• Define EDR, (nn design complete?)
• Choose final design technologies
• Setup structure to get it done (regional balance
  to optimize use of resources)
• Three year timescale

77
What do we want

• RDR to EDR phase
• ILC management is trying to match ILC tasks to
  world wide ILC resources
• ILC positron source EDR leadership may well
  migrate to Europe
• Strong US input is still needed to finish EDR
• Design of all aspects of the ILC e Sub-systems
  needs help
• Need people to consult with
• Need collaborators to help with design
• Need collaborators to take the lead in the design
• Need collaborators to do the design

78
Polarized Electron Source (A. Brachmann, SLAC)
79
Select Positron References, 1

• ILC RDR Positron Chapter
• http//media.linearcollider.org/report-apr03-part1
  .pdf sec. 2.3, pg. 45 ff
• ILC Positron Source Collaboration Meetings
• 1st meeting at RAL September, 2006
  http//www.te.rl.ac.uk/ILC_Positron_Source_Meeting
  /ILCMeeting.html
• 2nd meeting at IHEP, Beijing January, 2007
  http//hirune.kek.jp/mk/ilc/positron/IHEP/
• ILC Notes
• 1. ILC Target Prototype Simulation by Means of
  FEM Antipov, S Liu, W Gai, W
• ILC-NOTE-2007-011 http//ilcdoc.linearcollider
  .org/record/6949
• 2. On the Effect of Eddy Current Induced Field ,
  Liu, W Antipov, S Gai, W
• ILC-NOTE-2007-010 http//ilcdoc.linearcollider
  .org/record/6948
• 3. The Undulator Based ILC Positron Source
  Production and Capturing Simulation Study
  Update,
• Liu, W Gai, W ILC-NOTE-2007-009
  http//ilcdoc.linearcollider.org/record/6947
• Other Notes
• 1. F.Zhou,Y.Batygin,Y.Nosochkov,J.C.Sheppard,and
  M.D.Woodley,"Start-to-end beam optics development
  and multi-particle tracking for the ILC
  undulator-based positron source", slac-pub-12239,
  Jan 2007. http//www.slac.stanford.edu/cgi-wrap/ge
  tdoc/slac-pub-12239.pdf
• 2. F.Zhou,Y.Batygin,A.Brachmann,J.Clendenin,R.H.Mi
  ller,J.C.Sheppard,and M.D.Woodley,"Start-to-end
  transport design and multi-particle tracking for
  the ILC electron source", slac-pub-12240, Jan
  2007. http//www.slac.stanford.edu/cgi-wrap/getdo
  c/slac-pub-12240.pdf

80
Select Positron References, 2

• Other Notes, contd
• 4. A.A. Mikhailichenko lthttp//www-spires.slac.sta
  nford.edu/spires/find/wwwhepau/wwwscan?rawcmdfin
  22Mikhailichenko2C20A2EA2E22gt, "Test of SC
  undulator for ILC.",Jun 2006. 3pp. Prepared for
  European Particle Accelerator Conference (EPAC
  06), Edinburgh, Scotland, 26-30 Jun 2006.
• Published in Edinburgh 2006, EPAC 813-815.
• 5. A.Mikhailichenko, "Issues for the rotating
  target", CBN-07-02, 2007, http//www.lns.cornell.e
  du/public/CBN/2007/CBN07-2/CBN07-2.pdf
• 6. A.Mikhailichenko, "Positron Source for ILCA
  perspective", CBN-06-06, 2006, http//www.lns.corn
  ell.edu/public/CBN/2006/CBN06-1/CBN06-1.pdf
• 7. Preliminary Investigations of Eddy Current
  Effects on a Spinning Disk, W.T.
• Piggott, S. Walston, and D. Mayhall.
  UCRL-TR-224467, Sep. 8, 2006
• 8. Positron Source Target Update, W.T. Piggott,
  UCRL-PRES-227298, Jan. 16, 2007.
• 9. Computer Calculations of Eddy-Current Power
  Loss in Rotating Titanium Wheels and Rims in
  Localized Axial Magnetic Fields. D.J. Mayhall,
  W. Stein, and J. Gronberg, UCRL-TR-221440, May
  17, 2006
• 10. A Preliminary Low-Frequency Electromagnetic
  Analysis of a Flux Concentrator, D.J. Mayhall,
  UCRL-TR-221994, June 13, 2006
• Also see Posipol 2007 and Posipol 2006
• http//events.lal.in2p3.fr/conferences/Posipol07/
• http//posipol2006.web.cern.ch/Posipol2006/