1. Fast Ion Instability Studies in ILC Damping Ring Guoxing Xia DESY ILCDR07 meeting, Frascati, Mar. 5~7, 2007

2. Outlines Ions-related instabilities Fast ion instability (FII) Simulation of FII Future R&D for FII Summary ILCDR07 meeting, Frascati, Mar. 5~7, 2007

3. Ions related instabilities (1) The ions come from collision ionization process of residual gas in the vacuum chamber by beam particles, or via residual gas ionization and desorption by synchrotron radiation or via beam losses These ions in the beam result in beam emittance growth, beam size blow-up, additional tune shifts and beam lifetime reduction etc. Ion instabilities include conventional ion trapping instability and fast ion instability ILCDR07 meeting, Frascati, Mar. 5~7, 2007

4. Ions related instabilities (2) At conventional storage rings, ion trapping instabilities can be cured by filling the ring partially, e.g, leaving an ion clearing gap of a few us in length In low emittance and high intensity rings, such as ILC damping ring (DR), the effects of ions created during the passage of a single bunch train become important. The so called fast ion instability is one of the most important issues in R&D of ILCDR ILCDR07 meeting, Frascati, Mar. 5~7, 2007

5. Fast ion instability (1)  The residual gas in the vacuum chambers can be ionized by the single passage of a bunch train  The interaction of an electron beam with residual gas ions results in mutually driven transverse oscillations  Ions can be trapped by the beam potential or can be cleared out after the passage of the beam  For ILC damping ring, the growth rate of this instability is high ILCDR07 meeting, Frascati, Mar. 5~7, 2007 Linear theory of FII (Tor, Frank, Stupakov, etc) This instability has been confirmed experimentally in many facilities such as ALS, TRISTAN AR, PLS, Spring-8, ESRF, KEKB HER, ATF DR etc. Characteristics of FII

6. Fast ion instability (2) Linear theory of FII Critical mass Incoherent tune shift The exponential vertical instability rise time # of bunches bunch spacing bunch intensity critical mass incoh. tune shift at train end exponential rise time at train end 26256 ns2.0E105.40.00370.005 s 55343 ns1.0E101.40.00390.004 s Partial pressure of CO is 0.15nTorr; one long bunch train and 30% relative ion frequency spread are assumed here Estimation of FII in OCS6 DR ILCDR07 meeting, Frascati, Mar. 5~7, 2007

7. Fast ion instability (3) Traditional methods to clear ions from electron beam include electrostatic electrodes, beam shaking and gaps in the bunch trains Clearing electrodes may increase the chamber impedance Beam shaking requires dedicated device to drive the ions and beam and may cause coherent transverse instabilities Multi-train fill pattern with regular gaps is an efficient and simple way to remedy of FII Bunch by bunch feedback system? ILCDR07 meeting, Frascati, Mar. 5~7, 2007

8. Fast ion instability (4) Ion line density is If mini-train is introduced in the fill pattern, the diffusion of the ions during the gaps causes a larger size of ion cloud and a lower ion density. In order to evaluate the effects of gaps, an Ion-density Reduction Factor is defined as here, is the diffusion time of ion cloud. IRF is the ratio of the ion density with gaps and without gaps. So the fill pattern can be optimized in terms of obtain the smallest possible IRF (this work is ongoing) ILCDR07 meeting, Frascati, Mar. 5~7, 2007

9. Simulation results on effect of train gaps for ILC DR ( Wang, et al. EPAC06) ρ average [m -3 ] Build-up of CO+ ion cloud at extraction (with equilibrium emittance). The total number of bunches is 5782, P=1 nTorr. IRF=0.017 in this case! with equilibrium emittance ε x = 0.5 nm ε y = 2 pm ILCDR07 meeting, Frascati, Mar. 5~7, 2007 Fast ion instability (5)

10. Simulation of FII (1) Weak-strong approximation Electron beam is a rigid gaussian Ions are regarded as Marco-particles The interaction between them is based on Bassetti-Erskine formula Six collision points in the ring Circumference [m]6695.057 Energy [GeV]5.0 Harmonic number14516 Arc cell typeTME Transverse damping time [ms]25.7 Natural emittance [nm]0.515 Norm. natural emittance [μm]5.04 Horizontal initial emittance [nm]4.599 Vertical initial emittance [nm]4.599 Horizontal equilibrium emittance [nm]0.8176 Vertical equilibrium emittance [pm]2.044 Natural bunch length [mm]6.00 Natural energy spread [10 −3 ]1.28 Average current [mA]402 Mean horizontal beta function [m]13.1 Mean vertical beta function [m]12.5 Bunches per train2820 Particles per bunch2 x 10 10 Bunch spacing [m]1.8 ILCDR07 meeting, Frascati, Mar. 5~7, 2007

11. Simulation of FII (2) Kicks between electrons and ions (based on Bassetti-Erskine formula) ILCDR07 meeting, Frascati, Mar. 5~7, 2007 The ions drift in the space between adjacent bunches linearly

12. Simulation of FII (3) Beam motion between ionization points can be linked via linear optics For the flat beam, we mainly care about the vertical direction (y direction) ILCDR07 meeting, Frascati, Mar. 5~7, 2007

13. Simulation of FII (4) ILCDR07 meeting, Frascati, Mar. 5~7, 2007 Vertical position of bunch centroid in units of σy as a function of number of turns

14. The vertical action of the bunch centroid Simulation of FII (5) ILCDR07 meeting, Frascati, Mar. 5~7, 2007 Vertical centroid action in units of εy as a function of number of turns

15. Vertical oscillation Simulation of FII (6) Oscillation amplitude in units of σy as a function of number of turns ILCDR07 meeting, Frascati, Mar. 5~7, 2007

16. Future R&D for FII (1)  A proposal has been submitted to TB of ATF international collaboration meeting  A plan on experimental studies of FII in ATF DR is ongoing (see Junji’s presentation)  Goals of FII experiment:  Distinguish the two ion effects: beam size blow-up and dipole instability.  Quantify the beam instability growth time, tune shift and vertical emittance growth. Based on the linear model, the growth rate is proportional to the ion density (the related parameters include vacuum pressure, gas species, average beam line density, emittance, betatron functions and beam fill pattern).  Flatness of beam and its effect on FII growth.  Quantify the bunch train gap effect  Beam shaking effect  Provide enough experimental data to benchmark against simulations results. Understand of other measurements (e.g. ALS, PLS and KEKB)  Check effectiveness of feedback system to suppress the FII ILCDR07 meeting, Frascati, Mar. 5~7, 2007

17. Beam centroid oscillation amplitude with respect to number of turns One long bunch train is used in simulation ! The 60 th bunch is recorded here Beam energy [GeV]1.28 Circumference [m]138.6 Harmonic number330 Momentum compaction2.14E-3 Bunch population [×10 9 ]1.6, 3.7 and 6.0 Bunch length [mm]6 Energy spread0.06% Horizontal emittance [mrad]1.4E-9 Vertical emittance [mrad]1.5E-11 Vacuum pressure [nTorr]1 and 5 Parameters of ATF damping ring Future R&D for FII (2) ILCDR07 meeting, Frascati, Mar. 5~7, 2007

18. Future R&D for FII (3) Beam centroid oscillation amplitude with respect to number of turns If we introduce the gaps between the bunch trains, the growth will be greatly reduced ILCDR07 meeting, Frascati, Mar. 5~7, 2007

19. Bunch population1.6E92.0E10 Vacuum pressure [ntorr]1 5 10 Ion density [m -1 ]309 1545 30903862 19312 38625 Critical mass1.28 1.28 1.2816 16 16 Ion oscillation frequency2.4E7 2.4E7 2.4E78.6E7 8.6E7 8.6E7 FII growth time [s]6.8E-5 1.4E-5 6.8E-61.5E-6 3.1E-7 1.5E-7 FII grow. time (10% ion freq. spread) [s]4.0E-4 8.1E-5 4.0E-53.2E-5 6.5E-6 3.2E-6 Tune shift1.9E-5 9.5E-5 1.9E-42.3E-4 1.2E-3 2.4E-3 Analytical estimation of Ion effects in ATF damping ring Future R&D for FII (4) ILCDR07 meeting, Frascati, Mar. 5~7, 2007

20. Summary Fast ion instability is still one of critical issues for R&D of ILCDR Simulation results show that this instability is within control (need further check) R&D of FII should be strengthened further and well coordinated around the world Bunch by bunch feedback systems, up-to-date vacuum technology etc. are closely related to FII There is an excellent opportunity to characterize FII systematically at ATF DR and to compare to simulation results ILCDR07 meeting, Frascati, Mar. 5~7, 2007

21. Thanksforyourattention! Thanks for your attention !

22. Linear theory The growth time of FII is closely related to the beam sizes, the larger the value σ y 3/2 (σ x +σ y ) 3/2, the larger the characteristic FII growth time. It is possible to use the up-to-date feedback system (~0.1ms) to damp the FII growth. Critical mass, ion density, FII growth time, ion oscillation frequency, ion angular frequency, FII growth time in presence of ion angular frequency variation, and the coherent tune shift due to ions ILCDR07 meeting, Frascati, Mar. 5~7, 2007