*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.

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) 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 y2)/2 .

*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. One bunch train and 1/6 section of the whole lattice are included for the simulations. for the fast simulations

*Main parameters of the damping ringCircumference 6.69 kmEnergy 5 GeVArc cell type TMEHorizontal tune 52.397Vertical tune 49.305Natural chromaticity -63, -62Momentum compaction factor 4.2 x 10-4Energy loss/turn 8.69 MeVTransverse damping time 25.7 msLongitudinal damping time 12.9 msNorm. emittance 5.04 mmNatural energy spread 1.28 x 10-3RF frequency 650 MHzSynchrotron tune 0.0958RF acceptance 2.7 %

Filling patterns of the damping ring Case A B C D E Number of trainBunch spacing / bucketGap between trains / bucketBunch per train / bucketKb : Time between injection/extraction kicker pulsesBunch per train / bucketGap between trains / bucket

*Filling patterns of the damping ring(One example)f2 bunches inf2xnbbucketsf1bunches inf1xnbbucketsg1 bucketsg2 buckets Distance between kicker pulses(pattern of kb buckets repeated p times)24 bucketsnb=2f2=4f1=3kb=24g1=5g2=5p=1

*Lattice used in the simulations ~1/6 of the entire ring

* Vertical amplitudes in different filling patterns Case C shows the fastest exponential growth time.0.23 nT

* Vertical amplitudes in different filling patterns 0.23 nT

feedback per 50 turns

* Vertical amplitudes vs. vacuum pressuresf1 bunches inf1xnbbucketsnb=2f1=49g1=25~~

*Growth times vs. vacuum pressures

Vertical amplitudes vs. feedback number0.23 nTCase A

* Vertical amplitudes vs. bunch intensity

0.23 nT

*Different bunch spacing in a bunch train ~ ~ 0.97x1010/bunch25 empty buckets~ ~ 1.94x1010/bunch25 empty buckets~ ~ 3.88x1010/bunch25 empty buckets bunch spacing (nb) =2 bunch spacing (nb) =4 bunch spacing (nb) =8 (Same total bunch charge)

Different bunch spacing in a bunch train No feedback in Case A0.23 nT (Same total bunch charge)

* ~49 bunches in a train 25 empty buckets25 bunches in a train has electrons of 0.97x1010 per bunch.24 bunches in a train 12 empty buckets 12 empty buckets empty bucket. One and two trains with same number of bunches Case A

*damping by gap between trains One and two train with same number of bunches 0.23 nTNo feedback

*SummaryWe 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.

*30 trainsT*with coupling bump