ILC-BDS Collimator Study

1
ILC-BDS Collimator Study

• Adriana Bungau and Roger Barlow
• The University of Manchester

CERN - October 15
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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
  Jonnys talk)

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ILC-BDS colimators
No Name Type Z (m) Aperture
1 CEBSY1 Ecollimator 37.26
2 CEBSY2 Ecollimator 56.06
3 CEBSY3 Ecollimator 75.86
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
9 AB3 Rcollimator 1264.28 x4y4
10 SP3 Rcollimator 1264.29 x99y99
11 PC2 Ecollimator 1295.61 x6y6
12 PC3 Ecollimator 1351.73 x6y6
13 AB4 Rcollimator 1362.90 x4y4
14 SP4 Rcollimator 1362.91 x1.4y1.0
15 PC4 Ecollimator 1370.64 x6y6
16 PC5 Ecollimator 1407.90 x6y6
17 AB5 Rcollimator 1449.83 x4y4
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
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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 6.5110-7 m, ?y 5.6910-9 m
• last talk-gtmodes separation at 250 um (on
• logarithmic scale!)
• for small offsets, modes separation occurs at
• 10 sigmas

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Luminosity - geometric wakefields

• - at 10 sigmas when the separation into modes
  occurs, the luminosity is reduced to 20
• - for a luminosity of L1038 the offset should
  be 2-3 sigmas

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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

c
The fields are excited as the beam interacts with
the resistive wall surroundings
b
c
For higher moments, it generates different
wakefield patterns they are fixed and move down
the pipe with the phase velocity c
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General form of the resistive wake

• Write down Maxwells 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 m? and are sin m? )
• Integrate the force through a distance of
  interest L
• Apply the Panofsky-Wenzel theorem

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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

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Implementation of the Resistive wakes
WakeFieldProcess
WakePotentials
SpoilerWakeFieldProcess CalculateCm() CalculateS
m() CalculateWakeT() CalculateWakeL() ApplyWake
field ()
SpoilerWakePotentials nmodes virtual
Wtrans(s,m) virtual Wlong(s,m)
ResistiveWakePotentials Modes Conductivity pipe
Radius Wtrans(z,m,AccComp) Wlong(z,m,
AccComp)
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Resistive wakes

• Benchmark against an SLC result

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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

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Luminosity - resistive wakes

• - at 10 sigmas when the separation into modes
  occurs, the luminosity is reduced to 10
• for a luminosity of L1038 the offset should be
  less than 1 sigma
• the resistive effects are dominant!

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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

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Beam offset in each BDS collimator

• No wakefields ltygt4.74e-12
• Jitter of 1 nm of maximum tolerable
  bunch-to-bunch jitter in the train with 300 nm
  between bunches for 1nm ltygt8.61e-11
• Jitter about 100 nm which intratrain ffedback can
  follow with time constant of 100 bunches for
  100nm ltygt5.4e-10
• Maximum beam offset is 1 um in collimator AB7 for
  1nm beam jitter and 9um for 100 nm jitter

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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 ltygt2.37e-9

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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?