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Simulations of fast-ion instability in ILC damping ring. 12 April 2007 @ ECLOUD 07 workshop Eun-San Kim (KNU) Kazuhito Ohmi (KEK). Introduction. We have performed simulations on the fast-ion beam instabilities in ILC damping ring.

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simulations of fast ion instability in ilc damping ring

Simulations of fast-ion instability in ILC damping ring

12 April 2007

@ ECLOUD 07 workshop

Eun-San Kim (KNU)

Kazuhito Ohmi (KEK)

introduction
Introduction
  • We have performed simulations on the fast-ion

beam instabilities in ILC damping ring.

  • We investigated the effects of various different bunch filling patterns, vacuum pressures and feedback system on the fast-ion instabilities.
  • Damping ring lattice is included in the simulations.
simulation method 1
Simulation method (1)
  • Weak-Strong model

- Ions (weak) and beams (strong) are expressed by macroparticles

and point charges, respectively.

- Barycenter motion in beams is only investigated.

  • Interactions between a bunch and ions are considered by Bassetti-Erskine formula.
  • We assume that CO ions exist in the ring and

use 1/6 part of the entire ring lattice for the simulations.

  • Ions are generated at locations that all magnetic components and drift spaces exist.

(Ionization in long drift space is examined by every 2 m.)

  • All electron beams are initially set to zero displacement.
slide4
Simulation method (2)
  • New macroparticles are generated at the transverse position (x,x´,y,y´) of beam where ionization occurs.
  • Incoherent behaviors of ions are obtained by our simulation, but that of the beams, such as emittance growth, can not be computed.
  • We compute the time evolution of the growth of the dipole amplitude of the beam,

where the amplitude is half of the Courant-Snyder invariant Jy = (gy y2 + 2ay y y´ + by y´2)/2 .

simulation method 3
Simulation method (3)

ILC damping ring has a circumference of 6.6 km and trains of 61 to 123, depending on the filling patterns, exist in the ring.

for the fast simulations

One bunch train and 1/6 section of the whole lattice

are included for the simulations.

main parameters of the damping ring
Main parameters of the damping ring

Circumference 6.69 km

Energy 5 GeV

Arc cell type TME

Horizontal tune 52.397

Vertical tune 49.305

Natural chromaticity -63, -62

Momentum compaction factor 4.2 x 10-4

Energy loss/turn 8.69 MeV

Transverse damping time 25.7 ms

Longitudinal damping time 12.9 ms

Norm. emittance 5.04 mm

Natural energy spread 1.28 x 10-3

RF frequency 650 MHz

Synchrotron tune 0.0958

RF acceptance 2.7 %

filling patterns of the damping ring
Filling patterns of the damping ring

Case A B C D E

Bunch spacing / bucket

Number of train

Bunch per train / bucket

Gap between trains / bucket

Bunch per train / bucket

Gap between trains / bucket

Kb : Time between injection/extraction kicker pulses

filling patterns of the damping ring one example
Filling patterns of the damping ring(One example)

nb=2

f1=3

f2=4

f2 bunches in

f2xnbbuckets

f1bunches in

f1xnbbuckets

g2=5

g1=5

g2 buckets

g1 buckets

kb=24

24 buckets

Distance between kicker pulses

(pattern of kb buckets repeated p times)

p=1

slide9
Lattice used in the simulations

~1/6 of the entire ring

slide10
Vertical amplitudes

in different filling patterns

0.23 nT

Case C shows the fastest exponential growth time.

10

slide11
Vertical amplitudes

in different filling patterns

0.23 nT

feedback per 50 turns

11

slide12
Vertical amplitudes vs. vacuum pressures

nb=2

f1=49

~

~

f1 bunches in

f1xnbbuckets

g1=25

slide16
Different bunch spacing in a bunch train

(Same total bunch charge)

bunch spacing (nb) =2

0.97x1010/bunch

25 empty buckets

~

~

bunch spacing (nb) =4

1.94x1010/bunch

25 empty buckets

~

~

bunch spacing (nb) =8

3.88x1010/bunch

25 empty buckets

~

~

slide17
Different bunch spacing in a bunch train

(Same total bunch charge)

0.23 nT

No feedback

in Case A

slide18
One and two trains

with same number of bunches

Case A

25 empty buckets

49 bunches in a train

~

12 empty buckets

12 empty buckets

25 bunches in a train

24 bunches in a train

has electrons of 0.97x1010 per bunch.

empty bucket.

18

slide19
One and two train

with same number of bunches

damping by gap between trains

0.23 nT

No feedback

summary
Summary
  • We performed weak-strong simulations to show aspects on the bunch filling patterns of the fast-ion instability in the ILCDR.
  • The simulation results show that bunch by bunch feedback of ~ 50 turns is enough to suppress the fast-ion instability.
  • We still need more simulation works to understand fully characteristics, in particular of the filling patterns, of the fast-ion instabilities in the ILC DR.
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