Electron Cloud Effects in SuperB T. Demma, INFN-LNF SuperB Workshop LAL, Orsay , 15-18/02/2009

PLAN OF TALK Electron Cloud Effects Electron Cloud Single Bunch Instability Linear Theory Simulations Electron Cloud Build-Up Straight Solenoid Dipole Quadrupole Mitigation Techniques Work in progress Conclusions

Electron Cloud Effects The electron cloud develops quickly as photons striking the vacuum chamberwall knock out electrons that are then accelerated by the beam, gain energy, and strike the chamber again, producing more electrons. The peak secondary electron yield (SEY) of typical vacuum chamber materials is >1 even after surface treatment, leading to amplification of the cascade. The interaction between the electron cloud and a beam leads to the electron cloud effects such as single- and multi-bunch instability, tune shift, increase of pressure and so on.

Linear Theory of Single Bunch Instability K. Ohmi, et Al. , Phys. Rev Linear Theory of Single Bunch Instability K.Ohmi, et Al., Phys.Rev.E65,2002. The oscillation frequency of electrons under a bunch population (Nb= 5.52×1010 ) is given by The number of oscillations is: The threshold of electron cloud density for a given bunch population is given by where 4

Input Parameters for HEADTAIL SuperB LER (june ‘08) Beam energy E[GeV] 4 circumference L[m] 1800 bunch population Nb 5.52x1010 bunch length σz [mm] 5 horizontal emittance εx [nm rad] 2.8 vertical emittance εy [pm rad] 7 hor./vert. betatron tune Qx/Qy 43.57/21.59 synchrotron tune Qz 0.017 hor./vert. av. beta function <βx>[m]/ <βy>[m] 20/20 momentum compaction  3.2e-4

Emittance growth due to fast head-tail instability Head-Tail (CERN) june’08 param.s The interaction between the beam and the cloud is evaluated at 10 different positions around the SuperB ring for different values of the electoron cloud density. The threshold density is determined by the density at which the growth starts:

Emittance growth due to fast head-tail instability Head-Tail (CERN) june’08 param.s The interaction between the beam and the cloud is evaluated at 10 different positions around the SuperB ring for different values of the electoron cloud density. Electron in the cloud moves only vertically. The threshold density is:

Electron cloud buildup simulation Cloud buildup was calculated by code “ECLOUD” developed at CERN. Assumptions: - Round or elliptical Chambers - Uniform production of primary electrons on chamber wall. - A reduced number of primary electrons is artificially used in order to take into account the reduction of electron yield by the ante-chamber.

Build Up Input Parameters for ECLOUD Bunch population Nb 5.52x1010 Number of bunches nb 500 Bunch spacing Lsep[m] 0.6 Bunch length σz [mm] 5 Bunch horizontal size σx [mm] 0.3 Bunch vertical size σy [mm] 0.012 Chamber hor. Aperture hx [mm] 50 Chamber vert. aperture hy [mm] Photoelectron Yield Yeff 0.1 Primary electron rate dλ/ds 0.0024 Photon Reflectivity R 100% Max. Secondary Emission Yeld δmax 1.0-1.5 Energy at Max. SEY Εm [eV] 250 SEY model Cimino-Collins ((0)=0.5)

Build Up in Drift Space (95% antechamber protection)

e-cloud Density at Center of Beam Pipe 95% prot. δmax=1 δmax=1.1 δmax=1.2 δmax=1.3 The central e-cloud density is always above the threshod th.=5*1011 m-3

Build Up in Drift Space (99% antechamber protection) For δmax=1.2 the central e-cloud density is below the threshod th.=5*1011 m-3

Electron Cloud Buildup in a 50G Solenoidal Field

Build Up in the SuperB arcs: Dipoles For δmax=1.3 the central e-cloud density is below the threshod th.=6*1011 m-3

Build Up in the SuperB arcs: Quadrupoles

Mitgation Techniques Preliminary simulations indicate that a peak secondary electron yield close to 1.2 and an antechamber protection of 99% results in a cloud density close to the instability threshold. Planned use of NEG coatings and solenoids in SuperB free field regions (~75% of LER cirmumference, no wigglers) can help. In magnetic field region, external solenoid field are not effective in build-up of electron cloud. In SuperB all chambers would be TiN coated inside the beam channel to reduce the SEY. Studies of mitigation techniques (grooves in the chamber walls, clearing electrodes) are in progress for other accelerators, we can profit of these studies to plan mitigation in SuperB.

Mitigation Techniques: SEY reduction M. Pivi et. al, SLAC

Mitigation Techniques: SEY reduction (cont.) M. Pivi et. al, SLAC

Mitigation Techniques: Clearing Electrodes

Clearing Electrode Test chamber was installed into a wiggler magnet Y. Suetsugu, KEK Test chamber was installed into a wiggler magnet Beam current (Ib) ~1600 mA Bunch spacing (Bs) 4 ~16 ns Wiggler magnet. Magnetic field: 0.77 T Effective length: 346 mm Aperture (height): 110 mm Placed at the center of pole SR: 2x1017 photons/s/m Test chamber Electrode Gate Valve Gate Valve Inside view Beam 20 Monitor 2018/6/9 2008/12/10 INFN 2008/12/10 INFN

Clearing Electrode Effect of electrode potential Y. Suetsugu, KEK Effect of electrode potential Drastic decrease in electron density was demonstrated by applying positive voltage. 1585 bunches (Bs ~ 6 ns) ~1600 mA Vr = 1.0 kV B = 0.77 T [Logarithmic scale] Vr = -1 kV ~1x1012 e-/m3 Electron density decreased to 1/10 at Velec = + 100 ~ 200 V 1/100 at Velec = + 300 ~ 400 V -500 V Velec = 0 V Velec [V] Ie [A] +500 V Collectors 21 2018/6/9 2008/12/10 INFN 2008/12/10 INFN

Conclusions and Outlook Simulations indicate that a peak secondary electron yield of 1.2 and 99% antechamber protection result in a cloud density below the instability threshold in free field regions. Planned use of coatings (NEG, TiN..) and solenoids in SuperB free field regions (~75% of LER cirmumference, no wigglers) can help. Studies on mitigation techniques offers the opportunity to plan activity for SuperB. • Work is in progress to: estimate other effects: multi-bunch instability, tune-shift. compare the results with other codes (PEHTS, PEI, K.Ohmi; POSINST, M.Furman,M.Pivi). benchmark codes using: grow-damp and tune-shift measurements at DAFNE pressure measurements vs solenoid field intensity at PEPII (S.Novokhatski)

Spare Slides

Electron cloud at DAFNE e+ current limited to 1.2 A by strong horizontal instability Large positive tune shift with current in e+ ring, not seen in e- ring Instability depends on bunch current Instability strongly increases along the train Anomalous vacuum pressure rise has been oserved in e+ ring Solenoids installed in free field regions strongly reduce pressure but have no effect on the instability Instability sensitive to orbit in wiggler and bending magnets Main change for the 2003 was wiggler field modification

Tracking simulation e+ bunches z y ~m x K.Ohmi, PRE55,7550 (1997) K.Ohmi, PAC97, pp1667. Electron cloud e+　bunches z y ~m x Solve both equations of beam and electrons simultaneously, giving the transverse amplitude of each bunch as a function of time. Fourier transformation of the amplitudes gives a spectrum of the unstable mode, identified by peaks of the betatron sidebands.

Bunch train evolution x [m] bunch 1.2 A in 120 equispaced bunches

Mode spectrum and growth rate Measurment Simulation I[mA]/nb /T0 1000/105 73 1200/120 100 750/105 56 900/120 95 500/105 600/120 130

e-cloud density evolution 1 turn 5 turn 10 turn 15 turn 20 turn 25 turn