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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 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 y´2)/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. 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 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 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) 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
Vertical amplitudes vs. feedback number 0.23 nT Case A
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
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.