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Simulations of fast-ion instability in ILC damping ring

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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)

- 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.

- 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.

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 .

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.

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 %

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

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

Lattice used in the simulations

~1/6 of the entire ring

Vertical amplitudes

in different filling patterns

0.23 nT

Case C shows the fastest exponential growth time.

10

Vertical amplitudes

in different filling patterns

0.23 nT

feedback per 50 turns

11

Vertical amplitudes vs. vacuum pressures

nb=2

f1=49

~

~

f1 bunches in

f1xnbbuckets

g1=25

Growth times vs. vacuum pressures

0.23 nT

Case A

Vertical amplitudes vs. bunch intensity

0.23 nT

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

~

~

Different bunch spacing in a bunch train

(Same total bunch charge)

0.23 nT

No feedback

in Case A

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

One and two train

with same number of bunches

damping by gap between trains

0.23 nT

No feedback

- 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.