Update on the Yield and polarization Study of Undulator based by shwarma

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									Update on the Yield and polarization Study of Undulator based positron source at ANL
Wanming Liu, Haitao Wang, Wei Gai

October 26, 2005 ILC-teleconference meeting

Outline
• The positron yield and polarization of undulator based ILC positron source was studied with a more realistic model. The results are presented in the 1st section. • The yield and polarization of undulator based ILC positron source with different incident ebeam energy are also studied under this model and presented in the 2nd section. • In the last section, we presented the results about the study of influences on the positron yield simulation of the AMD field inside the target.

Motivation
• So far, all the studies have assumed the photons from undulator are 100% polarized. However, the polarization is a function of many variables (such as angle, drive beam energy, and photon energies and harmonics). Here we report on studies of polarized positron production using realistic photons spectrum and show that it requires longer undulators.

Introduction
• The spectrum of photon generated by undulator is determined by [1]
 n dNph 1 106 e2 K 2  ' [ ] ( J n ( x) 2  [ n  ]2 J n ( x) 2 )  dE mMeV 4 0c 2 h 2  2 1 K x

Where,

n

2

1 (1  K 2 )  [n 1  K 2 ]  0 

x  2K



1 (1  K 2 )

n

J n  Bessel functions

•

The amplitude of radiation of helical undulator can be obtained as [1]
Ix( E ) 


n 1



10 6 e 3 K  n n 2 [  ]J n ( x) ( 2  2   n ) 4 0  2 c 2  K x 10 6 e 3 K 2 J n ' ( x) ( 2  2   n ) 4 0  2 c 2 

Iy ( E )  i


n 1



From which we can obtain the polarization information and radiation angle of radiation of all harmonics at given frequency.
[1] : Klaus Flottmann, Investigation toward the development of polarized and unpolarized high
intensity positron sources for linear colliders, DESY 93-161

Schematic layout and processing steps

L

eD

Target



2a

undulator

Capturing optics

collimator 1. Generate photon spectrum, polarization and angle distribution using analytical equations with undulator parameters( K, B) and electron beam energy as variables.
2. Generate photons based on photon spectrum, electron beam parameters (r, z) and undulator length

3. Use collimator parameter (D, a) to select highly circular polarized photons and use them as input for EGS4 code to generate positrons
4. Run PARMELA to simulate the particle capturing optics 5. Calculate positron yield rate and polarization

Case 1: Positron Yield and polarization changing with the iris of collimator
0.8 1.2 Polarization Yield 1

0.65 0.6

0.6 0.4 0.2 0 2.25 2.75 3.25 3.75 Collimator radius (mm) 4.25 4.75

The higher the yield, the lower the polarization of positron beam. The best yield per 100m undulator is about 0.9 where the polarization is 0.6.

0.55 0.5 1.75

The largest radius of collimator exit at 1km is about 3.8mm with positron yield about 0.9 and polarization of 0.6

Yield per 100m

Polarization

The exit of collimator is 1km away from the end of undulator. x, y of electron beam is 100mm. K = 1, lu=1cm.

0.75 0.7

0.8

Photons survived after different collimators

50

1 0.9 0.8

Photon survived (%)

Collimators are located at 1km away from the end of undulator.
The iris radius varies from 2mm to 4.5mm.

40 30 20 10 0 2 3 4 radius of collimator iris (mm)
Photon survived Polarization

0.7 0.6

Photon Polarization

Case 2: Positron Yield and polarization changing with the location of collimator exit
0.8 1.8 ~650m 1.6 1.4 Polarization Yield 1.2 1 0.8 0.6 0.4 0.2 0 400 600 800 Location of Collimator(m) 1000

0.5 0.4 0.3 0.2 0.1 0

The higher the yield, the lower the polarization of positron beam. The best yield per 100m undulator is about 0.9 where the polarization is 0.6.

The nearest location of collimator with radius of 2.5mm is about 650m with yield about 0.9 and polarization of 0.6

Yield per 100m

Polarization

The radius of collimator is 2.5mm. x, y of electron beam is 100mm. K = 1, lu=1cm.

0.7 0.6

Positron Yield and Polarization changing with the incident e- spot size
0.8 0.7 0.65 0.6 0.55 0.5 Polarization Yield 0.45 0.4 1200

The exit of collimator is at 1km away from the end of undulator. The radius of collimator iris 3mm. x, y of electron beam is changing from 50mm to 1.1mm. K = 1, lu=1cm.

0.75 0.7 0.65 0.6 0.55 0.5 0 200 400 600 x (mm) 800 1000

No significant change on positron yield. The polarization drops slightly while increasing the e- beam spot size. The fluctuation is coming from radiation spectrum discretization error. All our simulation has about 5% error due to finite photon sampling in EGS4 simulation.

Yield per 100m

Polarization

Summary
• The best yield for 150GeV ILC undulator based positron source is about 0.9 per 100m with a polarization >60%. • The shortest distance between the end of undulator and the collimator exit need to be about 650m to obtain a best yield while keep the polarization satisfying the ILC requirement. • As long as the undulator field is uniform across the ebeam, the spot size of incident e- beam will not change the positron yield. But a bigger spot size will slightly lower the polarization of positron beam.

Positron Yield and polarization changing with e- energy
0.9 5 4.5 4

The exit of collimator is 800m away from the end of undulator. The radius of collimator iris is 3mm. x, y of electron beam is 100mm. K = 1, lu=1cm.
For a fixed collimator setting, the yield goes up with e- beam energy while the polarization is going down. Different e- beam energy need different collimator to achieve its best performance for a given undulator.

0.8 0.7

Polarization

0.6 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 Energy of e- beam(GeV) 250 300

3

Polarization Yield

2.5 2 1.5 1 0.5 0

Yield per 100m

3.5

Positron Yield and polarization changing collimator location, e- energy 250GeV
0.65 3.5 3 0.6 2.5 0.55 2 1.5

0.5

For this undulator with K=1, lu=1cm, when working with eof energy 250GeV, the best yield per 100m is about 1.3 with a polarization of 0.6.

Polarization Yield

1 0.5

0.45

0.4 1000

1200

1400 1600 1800 2000 Location of collimator(m)

2200

0 2400

Yield per 100m

Polarization

The radius of collimator iris is 2.5mm. x, y of electron beam is 100mm. Incident ebeam energy is 250 GeV. K = 1, lu=1cm.

Positron Yield and polarization changing collimator location, e- energy 100GeV
0.8 0.45 0.4 0.35

Polarization

0.5 0.4

0.25 0.2 0.3 0.2 0.1 0 0 200 400 600 800 Location of Collimator (m) 0.15 0.1 0.05 0 1000

For this undulator with K=1, lu=1cm, when working with eof energy 100GeV, the best yield per 100m is about 0.23 with a polarization of 0.6.

Yield per 100m

The radius of collimator iris is 2.5mm. x, y of electron beam is 100mm. Incident ebeam energy is 250 GeV. K = 1, lu=1cm.

0.7 0.6 Polarization Yield

0.3

The photon spectrum before and after collimator
Before collimator
150GeV, K=1,

After collimator with acceptance angle of 2.1e-6 rad
150GeV, K=1, lu=1cm

More bad polarized photon pass through the same collimator for higher e- energy case. Which explains that for higher eenergy, we need a smaller collimator to maintain the polarization level of positron beam

0.25

0.25
0.2 0.15 0.1 0.05 0 -1 -0.5 0 0.5 Photon Polarization 1 1st Harmonic 2nd harmonic 3rd harmonic 4th harmonic

0.2 0.15 0.1 0.05 0 0.94 Series1 Series2 Series3 Series4

0.96

0.98

1

1.02

Photon Polarization
250 GeV, K=1, lu=1cm

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 -1 -0.5

1st harmonic 2nd harmonic 3rd harmonic 4th harmonic

0.1 0.08 0.06 0.04 0.02 0
1

250GeV, K=1, lu=1cm 1st harmonic 2nd harmonic 3rd harmonic 4th harmonic

0 0.5 Photon Polarization

0.6

0.7 0.8 0.9 Photon Polarization

1

Summary
• For a given undulator, the best positron yield will increase with the increase of incident e- beam energy. • When working at higher e- energy, a collimator with smaller acceptance angle is required to maintain the positron beam polarization level. • To work at lower e- beam energy, a much longer undulator will be required to maintain the positron yield.

The effect of External B field in EGS4 simulation,
Yield 1.4

1.277
With external field Without External field 1.3

1.268

1.2 1.1

The yield of the same case, 1 without both external filed and consideration of phase difference, 0.9 is 1.281 0.8 -12 -10 -8 -6 -4 -2 0

From the results showing here, we conclude that it does not make much difference to consider the AMD field inside the target while doing EGS4 simulation. The phase space distribution of positron exit from target is dominated by multiple scattering process, this has also been confirmed by simulations using GEANT.


								
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