Fast Ion Instability Studies in ILC Damping Ring

Fast Ion Instability Studies in ILC Damping Ring Guoxing Xia DESY ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Outlines • • • Ions-related instabilities Fast ion instability (FII) Simulation of FII Future R&D for FII Summary ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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 ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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 07 meeting, Frascati, Mar. 5~7, 2007

Fast ion instability (1) 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 ØThe residual gas in the vacuum chambers can be ionized by the single passage of a bunch train ØThe interaction of an electron beam with residual gas ions results in mutually driven transverse oscillations ØIons can be trapped by the beam potential or can be cleared out after the passage of the beam ØFor ILC damping ring, the growth rate of this instability is high ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Fast ion instability (2) • Linear theory of FII Critical mass Estimation of FII in OCS 6 DR 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 2625 6 ns 2. 0 E 10 5. 4 0. 0037 0. 005 s 5534 3 ns 1. 0 E 10 1. 4 0. 0039 0. 004 s Partial pressure of CO is 0. 15 n. Torr; one long bunch train and 30% relative ion frequency spread are assumed here ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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? ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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) ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Fast ion instability (5) ( Wang, et al. EPAC 06) ρaverage [m-3] with equilibrium emittance εx = 0. 5 nm εy = 2 pm Simulation results on effect of train gaps for ILC DR Build-up of CO+ ion cloud at extraction (with equilibrium emittance). The total number of bunches is 5782, P=1 n. Torr. IRF=0. 017 in this case! ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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] Energy [Ge. V] 6695. 057 5. 0 Harmonic number 14516 Arc cell type TME 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 [m. A] 402 Mean horizontal beta function [m] 13. 1 Mean vertical beta function [m] 12. 5 Bunches per train 2820 Particles per bunch 2 x 1010 Bunch spacing [m] 1. 8 ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Simulation of FII (2) • Kicks between electrons and ions (based on Bassetti-Erskine formula) • The ions drift in the space between adjacent bunches linearly ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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) ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Simulation of FII (4) Vertical position of bunch centroid in units of σy as a function of number of turns ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Simulation of FII (5) The vertical action of the bunch centroid Vertical centroid action in units of εy as a function of number of turns ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Simulation of FII (6) Vertical oscillation Oscillation amplitude in units of σy as a function of number of turns ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Future R&D for FII (1) q A proposal has been submitted to TB of ATF international collaboration meeting q A plan on experimental studies of FII in ATF DR is ongoing (see Junji’s presentation) q Goals of FII experiment: Ø Distinguish the two ion effects: beam size blow-up and dipole instability. Ø 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). Ø Flatness of beam and its effect on FII growth. Ø Quantify the bunch train gap effect Ø Beam shaking effect Ø Provide enough experimental data to benchmark against simulations results. Understand of other measurements (e. g. ALS, PLS and KEKB) Ø Check effectiveness of feedback system to suppress the FII ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Future R&D for FII (2) Parameters of ATF damping ring Beam energy [Ge. V] 1. 28 Circumference [m] 138. 6 Harmonic number 330 Momentum compaction 2. 14 E-3 Bunch population [× 109] 1. 6, 3. 7 and 6. 0 Bunch length [mm] 6 Energy spread 0. 06% Horizontal emittance [mrad] 1. 4 E-9 Vertical emittance [mrad] 1. 5 E-11 Vacuum pressure [n. Torr] 1 and 5 One long bunch train is used in simulation ! The 60 th bunch is recorded here Beam centroid oscillation amplitude with respect to number of turns ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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 ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Future R&D for FII (4) Analytical estimation of Ion effects in ATF damping ring Bunch population 1. 6 E 9 2. 0 E 10 Vacuum pressure [ntorr] 1 5 10 Ion density [m-1] 309 1545 3090 3862 19312 38625 Critical mass 1. 28 16 16 16 Ion oscillation frequency 2. 4 E 7 8. 6 E 7 FII growth time [s] 6. 8 E-5 1. 4 E-5 6. 8 E-6 1. 5 E-6 3. 1 E-7 1. 5 E-7 FII grow. time (10% ion freq. spread) [s] 4. 0 E-4 8. 1 E-5 4. 0 E-5 3. 2 E-5 6. 5 E-6 3. 2 E-6 Tune shift 1. 9 E-5 9. 5 E-5 1. 9 E-4 2. 3 E-4 1. 2 E-3 2. 4 E-3 ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

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 ILCDR 07 meeting, Frascati, Mar. 5~7, 2007

Thanks for your attention !

Linear theory 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 The growth time of FII is closely related to the beam sizes, the larger the value σy 3/2(σx+σy)3/2, the larger the characteristic FII growth time. It is possible to use the up-to-date feedback system (~0. 1 ms) to damp the FII growth. ILCDR 07 meeting, Frascati, Mar. 5~7, 2007