Electron cloud effects, codes & simulations. K. Ohmi (KEK) ICAP12, Aug, 2012 Rostock
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1 Electron cloud effects, codes & simulations K. Ohmi (KEK) ICAP12, Aug, 2012 Rostock
2 Observation of electron cloud effects Coupled bunch instability ~1 cm bunch e+ Electron cloud ~1m Single bunch fast head-tail instability h: beam harmonic number m: CBI mode Coherent motion of bunch train and electron cloud Electron cloud Coherent motion of a bunch and local electrons
3 Part I Coupled bunch instability due to electron cloud
4 Measurements of electron cloud instability Izawa et.al., Phys. Rev. Lett. 74, 5044 (1995). PF: 2 nd generation light source operated by both of positron and electron beams. E=2.5 GeV L=186 m BPM spectrum for V motion. Electron 354 ma Positron 324 ma & 240 ma Different spectra are observed for e+ or e- storage. Mode spectra depend on beam current.
5 Measurement in KEKB Solenoid ON h: beam harmonic number m: CBI mode measurement vz<<c Solenoid is installed to protects electron cloud near the beam. The mode of the coupled bunch instability depends on the solenoid ON/OFF.
6 Measurement in BEPC & DAFNE Vertical coupled bunch instability in BEPC Horizontal coupled bunch instability in DAFNE M. Zobov, ECLOUD12 BEPC measurement is consistent with that of KEK-PF Slowest mode of horizontal instability is observed in DAFNE.
7 Measurement in LHC. Bartosik et al., ECloud 12 Beam dump has been observed at 25 ns spacing operation. The present physics run is adopted 50 ns spacing, while the design is 25 ns spacing. Horizontal coupled bunch and vertical single bunch instabilities are observed in LHC & SPS.
8 y x Simulation of Electron cloud build-up Model Secondary e- e + beam e - Beam chamber K.Ohmi, PRL,75,1526 (1995) Recipes for electron cloud build-up are written in this paper.
9 Simulation of coupled bunch instability K.Ohmi, PRE55,7550 (1997) K.Ohmi, PAC97, pp1667. Solve both equations of beam and electrons simultaneously Mode spectrum is given by FFT of bunch motion e y + bunches z x Electron cloud ~m
10 Electric(Magnetic) filed, Potential solver Beam-electron force 1. Basetti-Erskine formula and mirror beam 2. Poisson solver Electron space charge, 2D Poisson solver 1. Solve Finite difference equation for cylindrical and rectangular chamber 2. Finite Element Method for ante-chamber No correlation of the electron distribution for s. Longitudinal velocity of electron is negligible for beam velocity. Electron distribution depends only on z=s-ct. In 3D simulation, boundary condition for s is ambiguous.
11 Measurement in KEKB Solenoid ON h: beam harmonic number m: CBI mode measurement vz<<c Solenoid is installed to protects electron cloud near the beam. The mode of the coupled bunch instability depends on the solenoid ON/OFF.
12 Measurement and simulation for BEPC Vertical instability was observed. Mode spectra for electron cloud and ion instabilities FFT of yp
13 Electron distribution and Coupled bunch motion Drift Solenoid White point: beam position passing through the chamber
14 Coupled bunch instability due to electron cloud in bending field Measurement in DAFNE M. Zobov, ECLOUD12 Simulation Horizontal instability is dominant Slowest mode Horizontal coupled bunch instability h=120, m=114, νx=5.2 or m =-1 (m +frac(νx))
15 Coherent motion of beam and electron stripe Electron stripe is formed in bending magnet. The beam and stripe move coherently, then horizontal coupled bunch instability is induced. Electron potential
16 Part II Single bunch instability due to electron cloud
17 PEHT & PEHTS The same purpose code: HEADTAIL, C-MAD, WARP... Simulation of Fast head-tail instability caused by electron cloud Incoherent emittance growth using PEHTS Purpose: to explain beam size blow up observed in KEKB. No sol. Sol. Fukuma et al. measurement at 2001
18 Observations in KEKB Measurement at 2001 Measurement at 2001 Instability has been suppressed in latest measurements with the help of solenoids covered 95% of drift space. Upper sideband νy+aνs (1<a<2) is seen.
19 Observations in PETRA III εy=5pm->100pm R. Wanzenberg, ECLOUD12 Upper sideband νy+aνs (1<a<2) is seen like KEKB.
20 Observations in CesrTA G. Dugan, ECLOUD12 Lower sideband νy-aνs (a~1) is seen contrast with KEKB and PETRA III.
21 Simple modeling (PEHT code) Simulation using Gaussian micro-bunch model Electron cloud Positron bunch y y,x x E z
22 PEHT results Bunch head-tail motion w/wo synchrotron motion. Vertical amplitude of the macro-particles in the longitudinal phase space are plotted. Multi-airbag model (z- ) is used to visualize in these figures. K. Ohmi, F. Zimmermann, PRL85, 3821 (2000).
23 Short range wake field due to electron cloud Vertical wake field given by the numerical method Q=5~10 The same method as the coupled bunch wake (1,1) is consistent with the analytical calculation. (10,10) is twice larger than (1,1). Instability threshold is calculated by the wake force. K. Ohmi, F. Zimmermann, E. Perevedentsev, PRE65, (2001)
24 PIC code (PEHTS modeling) S: strong-strong model 2D-PIC based code Time like variable s is used for beam motion, while t is used for electron motion. z(t) motion for beam can be treated by, where z=s-ct.
25 KEKB: measurement and simulation of fast head-tail instability Beam size blow up observed, and simultaneously synchrobeta sideband observed. J. Flanagan et al., PRL94, (2005) Betatron sideband >νs Measurement at KEKB Tail of train Head of train Simulation (PEHTS) HEADTAIL gave similar results (E. Beneditto showed large cloud gave the sideband signal) ρe,th=0.8x10 12 m -3
26 Possible explanation for the sideband Electron pinching may enlarge the wake field strength. J. Flanagan et al., PRL94, (2005) Mode coupling between m=1 and 2 Static tune shift due to ρe is added.
27 Feedback does not suppress the sideband Bunch by bunch feedback suppress only betatron amplitude. Sideband signal is Integrated over the train Betatron sideband Simulation (PEHTS)
28 Summary Mode spectra due to the coupled bunch instability and synchrotron sideband due to the fast head-tail instability are prominent results of the electron cloud instability. Horizontal coupled bunch instability in DAFNE is reproduce by a simulation. Instability in SPS and LHC will be reproduced Simulations and theory explained the phenomena. The agreement is good. Upper sideband spectrum is solid in experiments, while is sometimes fragile in simulations. Spectrum seen in Cesr-TA has different feature. Simulation can reproduce the spectrum, m=0 mode dominates for ωeσz/c>>1. But...
29 Thank you for your attention
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