ILC-BDS Collimator Study Adriana Bungau and Roger Barlow The University of Manchester CERN - October 15.

ILC-BDS Collimator Study

Adriana Bungau and Roger Barlow

The University of Manchester

CERN - October 15

Since last time…

Only higher order mode geometric wakefields were implemented in the Merlin code at the last COLSIM meeting

Resistive wakefields were included in the simulations (benchmark with an experiment at SLC)

At PAC - 07: the increase in the bunch size and the decrease in the luminosity due to geometric and resistive wakefields were presented for large offsets

However, large offsets of couple of hundreds of microns are not realistic in a real machine but useful in theory when tried to find the range when the split into modes occurs

Small offsets of several sigmas are more likely to happen Beam jitter in all ILC_BDS collimators Wakefield tests at SLAC in March and July (see Jonny’s talk)

No

Name Type Z (m) Aperture

1 CEBSY1 Ecollimator 37.26 ~



4 CEBSYE

Rcollimator 431.41 ~

5 SP1 Rcollimator 1066.61 x99y99

6 AB2 Rcollimator 1165.65 x4y4

7 SP2 Rcollimator 1165.66 x1.8y1.0

8 PC1 Ecollimator 1229.52 x6y6


10 SP3 Rcollimator 1264.29 x99y99




14 SP4 Rcollimator 1362.91 x1.4y1.0




No Name Type Z (m) Aperture

18 SP5 Rcollimator

1449.84 x99y99

19 PC6 Ecollimator

1491.52 x6y6

20 PDUMP Ecollimator

1530.72 x4y4

21 PC7 Ecollimator

1641.42 x120y10

22 SPEX Rcollimator

1658.54 x2.0y1.6

23 PC8 Ecollimator

1673.22 x6y6

24 PC9 Ecollimator

1724.92 x6y6

25 PC10 Ecollimator

1774.12 x6y6

26 ABE Ecollimator

1823.21 x4y4

27 PC11 Ecollimator

1862.52 x6y6

28 AB10 Rcollimator

2105.21 x14y14

29 AB9 Rcollimator

2125.91 x20y9

30 AB7 Rcollimator

2199.91 x8.8y3.2

31 MSK1 Rcollimator

2599.22 x15.6y8.0

32 MSKCRAB Ecollimator

2633.52 x21y21

33 MSK2 Rcollimator

2637.76 x14.8y9

ILC-BDS colimators

Bunch size - geometric wakefields

- beam parameters at the end of linac:

x = 30.4 10-6 m, y = 0.9 10-6 m

- beam size at the IP in absence of wakefields:

x = 6.51*10-7 m, y = 5.69*10-9 m

- last talk->modes separation at 250 um (on

logarithmic scale!);

- for small offsets, modes separation occurs at

~10 sigmas;

Luminosity - geometric wakefields

- at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 20%

- for a luminosity of L~1038 the offset should be 2-3 sigmas

Resistive wall

pipe wall has infinite thickness; it is smooth; it is not perfectly conducting the beam is rigid and it moves with c; test charge at a relative fixed distance;

bc

cThe fields are excited as the beam interacts with the resistive wall surroundings;

For higher moments, it generates different wakefield patterns; they are fixed and move down the pipe with the phase velocity c;

General form of the resistive wake

Write down Maxwell’s eq in cylindrical coordinates Combined linearly into eq for the Lorentz force components and

the magnetic field Assumption: the boundary is axially symmetric (

are ~ cos mθ and are ~ sin mθ ) Integrate the force through a distance of interest L Apply the Panofsky-Wenzel theorem

sr eBFFF ,|| ,, θ

rFF ,||

sBF ,θ

Lz

c

bzW

mmm 2/1

012

1

)1(

2)(

δπ +−= +

Lz

c

bzW

mmm 2/3

012

' 1

)1(

1)(

δπ += +

The MERLIN code

Previously in Merlin: Two base classes: WakeFieldProcess and

WakePotentials

- transverse wakefields

- longitudinal wakefields

Geometrical wakes:

Some functions made virtual in the base classes Two derived classes:

- SpoilerWakeFieldProcess - does the

summations

- SpoilerWakePotentials - provides

prototypes for W(m,s) functions (virtual) The actual form of W(m,s) for a collimator type is

provided in a class derived from SpoilerWakePotentials

WakeFieldProcess WakePotentials

SpoilerWakeFieldProcess

CalculateCm();CalculateSm();

CalculateWakeT();CalculateWakeL();ApplyWakefield ();

SpoilerWakePotentials

nmodes;virtual Wtrans(s,m);virtual Wlong(s,m);

Implementation of the Resistive wakes

WakeFieldProcess WakePotentials

SpoilerWakeFieldProcess

CalculateCm();CalculateSm();

CalculateWakeT();CalculateWakeL();ApplyWakefield ();

SpoilerWakePotentials

nmodes;virtual Wtrans(s,m);virtual Wlong(s,m);

ResistiveWakePotentials

Modes;Conductivity;pipeRadius;

Wtrans(z,m,AccComp); Wlong(z,m, AccComp);

Resistive wakes

Benchmark against an SLC result

Bunch size - resistive wakefields

For small offsets the mode separation starts at ~10 sigmas

At larger offsets (30-35 sigmas) there are

particles lost in the last collimators

The increase in the bunch size due to resistive wakefields is far greater than in the geometric case

Luminosity - resistive wakes

- at 10 sigmas when the separation into modes occurs, the luminosity is reduced to 10%-for a luminosity of L~1038 the offset should be less than 1 sigma- the resistive effects are dominant!

Bunch Shape Distortion

The bunch shape changes as it passes through the collimator; the gaussian bunch is distorted in the last collimators

But the bunch shape at the end of the linac is not a gaussian so we expect the luminosity to be even lower than predicted

Beam offset in each BDS collimator

No wakefields <y>=4.74e-12; Jitter of 1 nm of maximum tolerable bunch-to-bunch jitter in the train with 300 nm

between bunches; for 1nm: <y>=8.61e-11 Jitter about 100 nm which intratrain ffedback can follow with time constant of ~100

bunches; for 100nm: <y>=5.4e-10 Maximum beam offset is 1 um in collimator AB7 for 1nm beam jitter and 9um for 100 nm

jitter

Beam jitter

Beam jitter of 500 nm of train-to-train offset which intratrain feedback can comfortably capture

The maximum beam offset in a collimator is 40 um (collimator AB7) for a 500nm beam jitter

For 500nm: <y>=2.37e-9

Next plans

Study the wakefields of one collimator for the material damage tests in Japan (Ti coated with Be - emittance dilution and performance with Ti and Be resistivity)

Merlin code development for implementation of ECHO/GDFIDL results

…other suggestions?

ILC-BDS Collimator Study Adriana Bungau and Roger Barlow The University of Manchester CERN - October 15.

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