1. The Design and Effects on the Electron Beam of the International Linear Collider Positron Source Helical Undulator Duncan Scott Magnetics and Radiation Sources group ASTeC STFC Daresbury Laboratory

2. Duncan Scott: Liverpool University Dec 2007 Introduction Positron Source Overview E166 Derivation of Synchrotron Radiation from an Undulator Selection of the Optimum Undulator Magnet Design Resistive Wall Wakefields of the Vacuum Vessel Geometric Wakefields of the Vacuum Vessel Other Effects on the Undulator and Electron Beam Vessel Heating Achieving the Required Vacuum

3. Duncan Scott: Liverpool University Dec 2007 ILC Positron Source Schematic Undulator is a periodic magnetic field 100s m

4. Duncan Scott: Liverpool University Dec 2007 Proof of Principal E-166 Polarised positrons created and detected @ SLAC

5. Duncan Scott: Liverpool University Dec 2007 Derivation of Synchrotron Radiation from an Undulator Go from Maxwell equations: To the energy radiated per electron, per unit solid angle per unit circular frequency through a perfectly helical field:

6. Duncan Scott: Liverpool University Dec 2007 Optimum Magnet Design Planar Permanent Magnet Designs (used in light sources)

7. Duncan Scott: Liverpool University Dec 2007 Optimum Magnet Design – Ring Undulator

8. Duncan Scott: Liverpool University Dec 2007 Optimum Magnet Design Super-Conducting Magnet Two wires wound in double helix, current is passed in opposite directions Longitudinal magnetic field cancels leaving rotating transverse magnetic field

9. Duncan Scott: Liverpool University Dec 2007 Optimum Magnet Design SC Measurements Field Quality as expected PPM Measurements Field Quality not as expected Relaxed Block Quality Demagnetisation during assembly

10. Duncan Scott: Liverpool University Dec 2007 Wakefields A beam of charged particles traveling through an accelerator will interact with its surroundings through self generated, co-propagating electromagnetic fields. These fields are known as wakefields They are the Fourier transform of the impedance of the environment They can have harmful effects on the beam properties, Energy change, emittance growth, drive instabilities Two main types considered – Resistive Wall and Geometric

11. Duncan Scott: Liverpool University Dec 2007 Resistive Wall Wakefields Depends on vessel conductivity, dc, ac and ASE conductivity models at 273K and 77K considered

12. Duncan Scott: Liverpool University Dec 2007 Resistive Wall Wakefields Induced energy spread for different materials, charge distributions and temperatures

13. Duncan Scott: Liverpool University Dec 2007 Geometric Wakefields Geometry also induces wakefields Undulator room temperature to cryogenic transitions

14. Duncan Scott: Liverpool University Dec 2007 Geometric Wakefield Emittance Growth Wakes can give a transverse momentum kick to the beam and cause emittance growth Emittance increase due to mis-alignment of tapered elements

15. Duncan Scott: Liverpool University Dec 2007 Heating due to Synchrotron Radiation

16. Duncan Scott: Liverpool University Dec 2007 Vacuum – Incident number of photons Achieving the required vacuum depends on the number of incident photons and their energy Undulator spectrum High and low energy dipole radiation spectrum

17. Duncan Scott: Liverpool University Dec 2007 Conclusions The helical undulator magnet design for the ILC positron source is selected Main affects on the electron beam considered Wakefields Main affect of the electron beam on the undulator considered Wakefields Vacuum E-m theory deriving radiation from moving charges First draft written up and hopefully will submit soon (before redundancy?)

18. Duncan Scott: Liverpool University Dec 2007