1. Photon Collimation For The ILC Positron Target Lei Zang The University of Liverpool Cockcroft Institute 24 th March 2007

2. Contents Introduction of International Linear Collider (ILC) ILC positron source Photon Collimator Photon collimator design and Simulation tools FLUKA benchmarking test FLUKA simulation results Conclusion Plan for future work

3. International Linear Collider (ILC) ILC is a proposed high-energy electron-positron linear collider with a baseline design of 500 GeV (CoM), supporting a later upgrade to 1 TeV and baseline luminosity of 2×10 34 cm -2 s -1. In order to achieve this luminosity we need order 10 14 positrons s -1. 60% polarised positron beam produced by the baseline source The ILC is important for future precision physics measurements.

4. Positron Source 150 GeV Electrons Helical Undulator Photon Collimator Target Optical Matching Device (OMD) Capture RF NC Linac SC Booster Damping Ring

5. Simulation Tools FLUKA: is Monte Carlo code (written in the FORTRAN 77 programming language) for simulating and calculating the particle transport and interaction with matter with high accuracy. The code can model 60 different type of particles and handle complex geometries. For more applications, there are a number of user interface routine available for special requirements. SIMPLEGEO: allows the user to build geometries interactively, in which we build up a logical tree to define the regions and bodies. After procedural modelling the geometries, it can be easily exported to FLUKA for simulation FLUKAGUI: it is a graphical user interface for FLUKA. It is used to view standard FLUKA output and to inspect the implemented geometries following the traditional FLUKA 2D concept. This project is developed within the ROOT framework

6. Design of Photon Collimator There are two purposes for photon collimator: Scrape the photon beam to limit the extraneous halo Adjust the polarisation.

7. FLUKA Simulations 1×10 6 Events The plot is energy distributions of photons generated by electrons (150 GeV) passing through 100 meters undulator (period of undulator of 1 cm and K=1). A modified FLUKA user routine was used to generate the photon beam energies. The angular dependence was approximated by a Gaussian distribution of standard deviation 1/.

8. FLUKA Benchmarking Test Shape of Cascade shower where a=0.5 for photon, E is the energy of incident particle and εis the critical energy of the material The shower depth for 95% of longitudinal containment is given approximately by And the transverse shower dimension with 95% of containment

9. FLUKA Simulation- Energy Deposition plot is energy deposition in 15 sections of spoilers. Each of the horizontal line stands for 15 spoilers with length from 1mm to 15mm (so 15 lines). The horizontal axis gives the spoilers number (from the 1 located at the entrance of collimator, to the 15 the last one). Vertical axis gives the energy deposited in the spoilers per machine pulse. 1×10 6 Events

10. FLUKA Simulation- Energy Deposition 1×10 6 Events Simulation of FLUKAGUI, Energy Deposition in Photon Collimator.

11. FLUKA Simulation- Peak Temperature Rise In order to approximate the temperature rise in the photon collimator, I use the specific heat capacity. The formula is T is instantaneous peak temperature change after absorbing energy Q in mass m, C s is the specific heat capacity. 1×10 6 Events

12. FLUKA Simulation- Radiative cooling The total power radiated for a surface area is proportional to the 4 th power of the Temperature, and is given by the Stefan Boltzmann law Assume the emissivity for Titanium is 0.5. The spoiler sections equilibrium temperature obtained for pure radiative cooling is 1×10 6 Events

13. FLUKA Simulation- Convective cooling We can calculate the convection heat transfer between a moving fluid and a solid in thermodynamics where Q is the power input or heat lost, h is overall heat transfer coefficient, A is the outside solid-fluid contact surface area, and T is the difference in temperature between the solid surface and surrounding fluid area. For now I will use the heat transfer coefficient equals to 100 W/K/m 2 which is approximate value taken for forced convective cooling of the system. 1×10 6 Events

14. Conclusion An initial study of a previous design for the ILC positron source photon collimator have been carried out. With help of FLUKA, undulator photon energy spectrum is generated using an analytical expression for an ideal undulator. Benchmarking test show reasonable agreement with FLUKA. Instantaneous heating of the spoilers could be very large. Spoilers could be damaged from thermal shock. I will do a further investigation. Radiative cooling and convective cooling appear to be both possible. Further analysis will take place.

15. Plan for future work Another version of DESY designed collimator with tilted spoiler sections need to investigate Simulate Cornell designed collimator Neutron production rate in the photon collimator need to be considered. Additional software would be needed to understand radiation damage. Remote handling system