Summary: Instabilities Thanks for many interesting talks K. Ohmi

Experiments S. Cousineau (SNS) ep instability at coasting beam operation is observed.  e ~ 2  x80 MHz R. Macek (PSR)  e /  0 ~ M. Tobiyama (KEKB) coupled bunch instability w/wo solenoid. Bunch correlation picks up electron motion. J. Flanagan (KEKB) synchro-beta mode as an evidence of fast head-tail instability due to electron cloud Y. Liu (BEPC-(II)) coupled bunch instability and emittance growth. T. Ieiri (KEKB) tune shift and its current dependence measurements. Estimate the wake force due to electron cloud.

Simulations Sarah Cousineau (ORNL), Proton beam stream instability is simulated by ORBIT. A. Markovik, G. Poeplau (Rostock) Developing a single bunch instability code for ILC. J. Hyunchang (Postech/KEKB) Synchro-beta side band and coherent tune shift K. Sonnad (LBNL) Kick & Transfer method based on PIC J-L. Vay (LBNL) moving frame, adaptive mesh, fresh approach for me.

Theories Y. Liu, longitudinal single bunch effect. Potential well distortion and microwave instability. The threshold is at high cloud density >10 14 m -3. S. Heifets, two-stream instability, obtain beam breakup growth in single path picture of the beam. L. Schachter, Tune shift for electrons distributed at side of chamber. Analytical estimate of the electron cloud distribution in bend and/or wiggler.

Coherent instabilities Long bunch proton beam (  z >10m,  e  z /c>>1) : PSR, ISIS, SNS, JPARC, Single bunch instability is focused. Simulation using many long bunch slicing (>>  e  z /c) and Landau damping due to slippage should be cared. Short bunch proton beam (  z ~<1m,  e  z /c=1~10), RHIC, Tevatron, LHC, Lepton ring Lepton beam (  z ~<1cm,  e  z /c=1~10), Single and multibunch instability should be cared. Simulation using long bunch slicing (>>  e  z /c) and Landau damping due to slippage should be considered. Multibunch instability is equivalent to a beam breakup without Landau damping.

Simulation technique Potential kick & transfer map, so-called second order integrator, is used to guarantee the symplecticity, The potential  x,y,z  is solved by PIC method. Solver: uniform mesh (FFT, FACR), nonuniform mesh

About Simulation Simulation is very different from cases, lepton machine (beam size is very small compare than chamber) and proton beam (similar size). The self consistent simulation, multibunch passage, cloud generation, single bunch instability of each bunch are solved simultaneously. The coupled bunch instability must be treated self-consistently as is already done. In my impression this type self-consistent simulation of single bunch instability with multibunch beam is only possible in linac like HIF. I would like to know reliable method for ring accelerators with self- consistency. Now we decide cloud density first and then study interactions with cloud with the density localized near beam. For proton beam, since the size is comparable with the chamber, boundary condition and whole electron cloud can be treated. It is important to spend resources to include lattice information to study incoherent effects. Various trials, moving frame, adaptive mesh, multigrid, should be encouraged.

Simulation of tune shift Deep issue. Coherent tune is measured in experiments. Single bunch tune or multi bunch tune. Depend on how to measure. Incoherent tune may depend on boundary condition and global cloud distribution (K. Ohmi, S. Heifets, F. Zimmermann, PAC2001). This work should be revised by someone. More study should be done. Coherent tune is given by combination of head-tail effect and incoherent effect. The strong-strong codes (PEHTS, HEADTAIL) should be able to predict tune shift related to the head-tail effect. Since incoherent tune shift is static, it may be taken account by simple summation. Simulations including global cloud distribution may be able to reproduce the whole tune shift. Please try with WARP/POSINST, ORBIT, CMAD, Rostock.

Incoherent emittance growth Single bunch instability can be cured by increase of the slippage factor (  ). How is   infinity? Everything is solved? The answer is no. Nonlinear interaction of electron cloud space charge causes an incoherent emittance growth. Many experiences in beam-beam and space charge effects. Typical nonlinear dynamics phenomena. Electron cloud space charge can be coupled with beam- beam and space charge effects (J. Flanagan, J.Gao).

Experiments J. Flanagan (KEKB) Specific luminosity degradation is observed below the threshold of the single bunch instability. S.Y. Zhang (RHIC) Slow emittance growth correlated to electron cloud induced pressure rise is observed. Y. Liu (BEPC) Beam size blow-up without coherent motion is observed. Chromaticity does not work to suppress the emittance growth. M. Palmer (CESR) Emittance growth with vertical small tune shift << s. Horizontal is further smaller.

Theory & simulation J. Gao, Dynamic aperture and beam lifetime are evaluated by tune shift due to nonlinear interactions of electron cloud, beam-beam and space charge. K. Ohmi, Physical and artificial noises in PIC simulation gives emittance growth due to stochastic diffusion. Electron cloud has noise feature. The cloud density can fluctuate turn by turn (V. Lebedev).

Slow emittance growth Slow emittance growth (min or hour) in proton ring is serious (S.Y.Zhang, W. Fisher). The beam could diffuse even in small tune shift. Space charge limit (~0.1?) in proton ring is applicable to relatively short time storage of the beam (~<1s). How about positron ring. Fast radiation damping ~10ms. For a large tune shift value, it may be serious. ILC damping ring with very low emittance. For the damping time ~10ms, if I say with fearless, tune shift ~0.1 may be allowed from the experience of proton beam, because interaction is not localized. The tune shift limit is 0.05 for localized interaction from beam-beam experiences. If the difference of flat and round beam is important for the tune shift limit, we need study more carefully.

Comments on measurements in positron rings Measurements with current dependence are not suitable for studying the emittance growth: e.g. interferometer. A fast monitor which is capable to measure along bunch train is possible, even if it has current dependence. Monitors without optical component are better to avoid heating problems. Emittance growth due to the wreck of coherent instability should be treated carefully. Sorry I can not comment for proton ring measurements. It is easy to distinguish coherent or incoherent in proton beam, because the difference of the time scale (SY).

Simulation of incoherent emittance growth Beam interacts to cloud with various size (maybe scale to beam size, beta function) at positions of beta function and betatron phase. Whole nonlinear interaction is integration of m-th nonlinear component times  m/2 and its betatron phase factor. Uniform beta and uniform betatron phase advance give an excitation of unphysical structure resonance or unphysical resonance suppression.

Importance of Lattice snowmass 2004 K. Ohmi Nonlinearity of beam-cloud interaction Integrated the nonlinear terms with multiplying  function and cos (sin) of phase difference Nonlinear term should be evaluated with considering the beta function and phase of position where electron cloud exists. Unphysical cancel of nonlinear term may be caused by simple increase of interaction point. F: (non)linear lattice transformation  : cloud interaction

For example (ILD DR arc) Integrate every 2 m along lattice

Ion & dust Similar dynamics of ep instability. Coupled bunch instabilities are observed in experiments. Z. Deming (BEPC-II) Life time Reduction event (LRE), life time self recovered or irrecoverable events, has been observed. Fission of dust, Charge variation are evaluated. E.S. Kim (ILC-DR) Growth rate for various filling pattern. H. Fukuma (Super KEKB) Very fast growth in very high current machine. For KEKB, small tune shift can affect due to a coupling with the beam-beam effect.

Ion instability simulation Q factor of ion oscillation should be included. Weak-strong simulation with a permission of beam dipole motion is reliable to simulate this instability. A bunch and ions are represented by a single macro-particle and many macro- particles, respectively. People who interested in incoherent emittance growth should try strong-strong simulations in which bunches and ions are represented by macro-particles. They should check tune shift value before the heavy job to know whether the job is necessary.

Thanks for the participation of the ECLOUD07 workshop