Photon Collimation For The ILC Positron Target

Lei ZangThe University of LiverpoolCockcroft Institute24th March 2007

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

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 2×1034 cm-2s-1. In order to achieve this luminosity we need order 1014 positrons s-1.

60% polarised positron beam produced by the baseline source The ILC is important for future precision physics measurements.

Positron Source

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

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

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

FLUKA Simulations

Undul ator Photon Energy Spectrum

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0 3 7 10 13 17 20 23 26

Energy (MeV)

Flue

nce

of P

hoto

ns[c

m-2]

1×106 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/.

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

FLUKA Simulation-Energy Deposition

Energy deposi t i on(per pul se)

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

spoi l er secti ons

E(jo

ule)

sp 1mmsp 2mmsp 3mmsp 4mmsp 5mmsp 6mmsp 7mmsp 8mmsp 9mmsp 10mmsp 11mmsp 12mmsp 13mmsp 14mmsp 15mm

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.

1×106 Events

FLUKA Simulation-Energy Deposition

1×106 Events

Simulation of FLUKAGUI, Energy Deposition in Photon Collimator.

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, Cs is the specific heat capacity.

s

QT

m C

Temperature ri se per pul se i n 1ms

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spoi l er secti ons

ΔT(K)

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1×106 Events

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

Equi l i bri um Temperature

800900

10001100

120013001400

15001600

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Spoi l er sect i ons

Temperature

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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/m2 which is approximate value taken for forced convective cooling of the system.

Q h A T

Equi l i bri um Temperature

050

100150200250300350400450500

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spoi l er secti ons

Temp

erat

ure

(K)

1mm2mm3mm4mm5mm6mm7mm8mm9mm10mm11mm12mm13mm14mm15mm

1×106 Events

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.

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