Longitudinal Coupled Bunch Instability - PowerPoint Presentation

Longitudinal Coupled Bunch Instability in MEIC Electron Collider Ring R. Li

Outline Motivation Mechanism of LCBI Experimental ObservationsSuppression SchemesPEPII ResultsLCBI in MEIC (Wang), (Ahmed, Yunn, Krafft)Summary (Thanks Shaoheng for many input and discussions)

1. Motivation Coupled Bunch Instabilities (CBI) are the most important instabilities encountered in a storage ring in multibunch operation. These instabilities may amplify beam oscillations or blow up emittances, preventing a high current operation and limit beam performance.Longitudinal coupled bunch instability is the most severe problem in storage rings (with E<3 GeV and I >200mA before PEPII)The narrow-band impedances of RF HOM are the main source of CBIs.

Current limit in Various Machines Facility Energy (GeV)Maximumcurrent(mA) Max curren (mA) with feedback CESR 5.5220 550PLS 2180 400 PEPII 3.1 410 (str. HOM damping) 2400 MEIC 5 350 3000 MEIC 3 40 3000 (?) If rely on natural synchrotron radiation damping Weaker syn rad damping More susceptible to HOM kick

Motivation (con’d) Recently, during the discussion of the possibility of using top-off inection for e-collider ring in MEIC, the issue of current threshold at E=3 GeV was brought up Design goal: I= 3 A at E= 3 GeV It is a concern whether this current can be achieved. Here we review this instability from beam dynamics point of view, and compare our parameters with the state of art to see where R&D efforts are necessary.Parameters in MEIC Design Report

2. Mechanism of LCBI Single bunch spectra Multiple passage of bunch in time In frequency domain Multibunch Operation   As bunches going through cavities, HOM modes will be excited by earlier bunches and will act on later bunches MEIC: M =0.224 MHz,   = 3 GeV , 1.70kHz; 5 GeV , 2.76kHz; 12 GeV , 6.57kHz  

HOM of an RF cavity vs. for an RF cavity with adjacent beam pipe   Narrowband Impedances : Excitation of localized EM modes with high Q (Q>>1) below cut-off frequency of vacuum chamber Impact:Robinson-instability (related to the fundamental mode)Longitudinal and transverse coupled bunch instability (related to HOM)

Early ReferencesF. J. Sacherer, IEEE Trans. Nucl . Sci. NS-24 (1977) 1393. ZAP User’s Manual, M. Zisman, S. Chattopadhyay and J. Bisognano, 1986.A. Chao, Physics of Collective Beam Instabilities in High Energy Accelerators,1993.

Mechanism of LBCI For long range wake, all particles in the bunch see the same wakefield . So we can treat the bunch as a macroparticle. The longitudinal coordinates of the bunch at n-th bunch is .   The equation of motion:     Wake voltage on the n- th bunch due to HOM of RF cavity:     HOM effects Assume even fill of the ring: n- th bunch interact with m- th bunch back k period           k      

Dynamical Equation     Expansion Beam loading s yn. freq. shift Coupled bunch effect     Bunch coupling For th mode, we let , we get the growth rate:     Bunch frequency

Examples: Longitudinal impedance s pectra and impedance threshold of various SR sources using 500 MHz RF-systems (F. Marhauser et al, PAC2001) Conservative assumptions: Every HOM coincides with an instability driving beam frequencyImpedances for Nc cavities are the sameA single HOM mode can be responsible for LCBI     Let   Given a , and , o ne can get maximum Impedance for each freq allowable for the LCBI to be damped by syn. rad.  

Individual Bunch Oscillating Modes Dipole (a=1) Quadruple (a=2) Sextuple (a=3)Octupole (a=4)(K. Schindl, CERN)Rigid bunch oscillationHigher order bunch shapeoscillation

Coupled Bunch Motion for a M-bunch Beam Dipole mode (a) 4-bunch operation in a storage ring (b) Coupled bunch mode in 4-bunch operation ( )   (K. Schindl , CERN)   For M bunches there are M modes: =0,1,  

Resonance frequency   Example: SRS at UK M =3.123 MHz =70 kHz   Instability occurs at MHz Beam execute a synchrotron oscillation w ith a dipole coupled bunch mode:   (McIntosh, SRS) E=2 GeV , mA .   mA when the 6T superconducting wiggler is not operational   Example: PLS E=2.5 GeV , M =1.068 MHz =9.6 kHz   TM011, MHz , mA (beam loss) TM020, MHz , mA (beam loss)   Example: MEIC e-ring E=3 GeV , mA (due to syn. rad. damping) .   =0.224 MHz, =3.5 kHz  

At current threshold, the synchrotron sidebands in the BPM spectrum begin to grow rapidly in amplitude vs. current Amplitude of oscillation grows as current increases, until at a higher current the quadruple CBI are observed with bunch shape oscillation3. Experimental Observation Example: Measured synchrotron spectra of a two bunch, 400 MeV e-beam at Duke Storage Ring I=13.17 mAI=13.94 mAI=14.15 mA

The longitudinal feedback system is designed to suppress longitudinal instabilities by providing additional damping to the electron beam. The longitudinal motion of an electron is ) syn rad. damping wake voltage feedback voltage or The net growth is   (J. Fox, SLAC) 4. LCBI Suppression Schemes

Measures to fight LCBI Decrease growth rate     Reduce by Damping HOM by orders of magnitudes Avoid overlapping of beam spectral line with HOM impedance   Increase synchrotron radiation damping rate Using wiggler insertion Increase Landau damping by increase spread of   Using Landau cavity Using uneven fill Increase damping rate by LFB system Expansive broadband electronic solution      

LCBI Suppression Techniques Minimization of Impedance (HOM damping) Tuned damper to reduce shunt impedance of the strongest HOM HOM frequency tuning by cavity temperature adjustment mode strength changedIncrease Laudau DampingSpread of synchrotron tune (Landau cavity) Uneven-fill causes damping from fill-induced tune spread Increase SR damping using wiggler insertion Implement systematic differences in all cavities to spread HOM resonance frequency across a number of revolution harmonics Active Feedback Systems Longitudinal feedback systemTransverse feedback system

Landau Cavity NSLS-II: Longitudinal phase space portrait with and without Landau cavity Increase bunch length to increase Touschek life time Increase spread of synchrtron frequency to increase Landau damping for LCBI

5. PEPII Results Design Parameters

The State of Art for LBF System design achieved

Growth time for LER in Design Report increased by 100 times via HOM damping ms. LFB can control growth time within 0.3 ms , meaning 45 turns.   (A. Wolski, Int. Sch. For Linear Collider)

=2.85 ms   =0.03ms  

6. LCBI in MEIC E = 5 GeV SRF cavity 750MHz N cavity =20 HOM: TM011 near 1.3 GHz=1.3 kΩ Feedback system: factor 10Syn rad. Damping time: =18.5 ms  At the verge of instability feedback (Thanks for Shaoheng Wang for information and discussion)

Discussion MEIC e-ring, assuming cavity impedance remains the same for 3 and 5 GeV .Direct comparison with PEPII results of controlling =2.85 ms suggest that with additional R&D effort MEIC e-ring design goal at 3 GeV may be within reach.Expert assessments on the dependence of LFB on design parameters will give more complete picture. E = 5 GeVNcavity =20, =1.3 kΩ HOM: TM011 near 1.3 GHz =0.013 Syn rad. Damping time: =18.5 ms   =2.3 ms   =1.5 ms   Assuming LFB gives ms , LCBI can be controled .  

Compared to PEPII LER case   Obtained using CEBAF 1.5 GHz cavity HOM impedance ( undamped HOM) ZAP calculation for e-ring Using CEBAF cavities (S. Ahmed)

LCBI for Proton Ring The CBI are stabilized by Landau damping from the synchrotron frequency spread within the bunches induced by the non-linearities of the RF bucket. The synchrotron mode is Landau damped if the shifted mode frequency lies within the effective spread of the bunch. Coupled-bunch instabilities were observed in several proton rings at about N p =10 13. Instabilities are also expected in MEIC p-ring. In MEIC p-ring, Np=2.1 1013 Mode Growth time (µs) a = 1 668.5 679.5 714.2 a = 2 1633.5 1655.8 1745.7 ZAP calculation for p-ring Using CEBAF cavities (S. Ahmed)

7. SummaryThe mechanism and suppression scheme of longitudinal coupled bunch instability are reviewed MEIC design parameters of I=3 A for e-ring at E=3 GeV is very challenging and may be beyond the state of art.Requires dedicated R&D of HOM damping and LFB development