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Electron Cloud, IBS, and Fast Ion Update

Electron Cloud, IBS, and Fast Ion Update. T. Demma, INFN-LNF Thanks to A.Chao and K.Ohmi SuperB General Meeting March 16-19 2010, LAPP-Annecy. Plan of Talk. Electron Cloud effects Multiparticle simulation for IBS Conventional calculation of IBS Code structure

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Electron Cloud, IBS, and Fast Ion Update

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  1. Electron Cloud, IBS, and Fast IonUpdate T. Demma, INFN-LNF Thanks to A.Chao and K.Ohmi SuperB General MeetingMarch 16-19 2010, LAPP-Annecy

  2. Plan of Talk • Electron Cloud effects • Multiparticle simulation for IBS • Conventional calculation of IBS • Code structure • Comparison with conventional theories • Fast Ion Instability simulation with Updated Parameters

  3. Simulation of single-bunch instability • Simulations were performed using CMAD (M.Pivi): • Parallel bunch-slices based decomposition to achieve perfect load balance • Beam and cloud represented by macroparticles • Particle in cell PIC code 9-point charge deposition scheme • Define at input a cloud density level [0<r<1] for each magnetic element type • Good code benchmarking • Tracking the beam (x,x’,y,y’,z,d) in a MAD lattice by 1st order and 2nd (2nd order switch on/off) transport maps • MAD8 or X “sectormap” and “optics” files as input • Apply beam-cloud interaction point (IP) at each ring element Input parameters (Sep.09 conf.) for CMAD

  4. Emittance growth due to fast head-tail instability (LNF conf.) =7x1011e-/m-3 <5x1011e-/m-3 The interaction between the beam and the cloud is evaluated at 40 different positions around the SuperB HER (LNF option) for different values of the electoron cloud density. The threshold density is determined by the density at which the growth starts:

  5. Head-Tail Instability Threshold Instability occurs if: LNF conf. where cent. ande,th are obtained from simulations.

  6. e-cloud summary • Simulations indicate that a peak secondary electron yield of 1.2 and 99% antechamber protection result in a cloud density close to the instability threshold. • Planned use of coatings (TiN, ?) and solenoids in SuperB free field regions can help. • Ongoing studies on mitigation techniques (grooves in the chamber walls, clearing electrodes) offers the opportunity to plan activity for SuperB. • Clearing electrodes has been designed, built, and are ready for installation in DAFNE during this stop of the machine. • • Work is in progress to: • estimate other effects: multi-bunch instability, tune-shift, ... • New: • More realistic simulations taking into account the full SuperB lattice (~1300 IPs) are currently running on several hundreds of the Grid-SCoPE cluster cores. Thanks to S.Pardi (INFN, Naples)

  7. IBS Calculations procedure • Evaluate equilibrium emittances ei and radiation damping times ti at low bunch charge • Evaluate the IBS growth rates 1/Ti(ei) for the given emittances, averaged around the lattice, using K. Bane approximation* • Calculate the "new equilibrium" emittance from: • For the vertical emittance use* : • where r varies from 0 (y generated from dispersion) to 1 (y generated from betatron coupling) • Iterate from step 2 * K. Kubo, S.K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams," Phys. Rev. ST Accel. Beams 8, 081001 (2005)

  8. IBS in SuperB LER (lattice V12) v=5.812 pm @N=6.5e10 h=2.412 nm @N=6.5e10 • Effect is reasonably small. Nonetheless, there are some interesting questions to answer: • What will be the impact of IBS during the damping process? We have calculated the equilibrium emittances in the presence of IBS, but the beam is extracted before it reaches equilibrium… • Could IBS affect the beam distribution, perhaps generating tails? z=4.97 mm @N=6.5e10

  9. Algorithm for Macroparticle Simulation of IBS • The lattice is read from a MAD (X or 8) file containing the Twiss functions. • A particular location of the ring is selected as an Interaction Point (S). • 6-dim Coordinates of particles are calculated (Gaussian distribution at S). • At S location the scattering routine is called. • Particles of the beam are grouped in cells. • Particles inside a cell are coupled • Momentum of particles is changed because of scattering. • Invariants of particles and corresponding grow rate are recalculated. • Particles are tracked at S again through a one-turn 6-dim R matrix (under test). S

  10. Zenkevich-Bolshakov algorithm For two particles colliding with each other, the changes in momentum for particle 1 can be expressed as: with the equivalent polar angle effand the azimuthal angle  distributing uniformly in [0; 2], the invariant changes caused by the equivalent random process are the same as that of the IBS in the time interval ts

  11. Code Benchmarking (Gaussian Distribution) DAFNE Optical Functions 1/Th1/Tv1/Ts [s-1] Multiparticle Bane # of macroparticles: 104 Grid size: 5xx5yx5z Cell size: x/2xy/2 CIMP

  12. Intrinsic Random Oscillations

  13. IBS Status • The effect of IBS on the transverse emittances is about 30% in the LER and less then 5% in HER that is still reasonable if applied to lattice natural emittances values. • Interesting aspects of the IBS such as its impact on damping process and on generation of non Gaussian tails may be investigated with a multiparticle algorithm. • A code implementing the Zenkevich-Bolshakov algorithm to investigate IBS effects is being developed • Benchmarking with conventional IBS theories gave good results. • Tracking routine is sill under test. • Radiation damping and quantum excitation routines will be implemented soon.

  14. Fast Ion Instability Characteristics of FII • 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 • Multi-train fill pattern with regular gaps is an efficient and simple way to remedy of FII

  15. Simulation of FII • 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 •  function variation are taken into account • The effect of a bunch-by-bunch feedback system is included (damping time 50 turns) • Assumptions for SuperB: CO ions Ni[m-1]=0.046xP[Pa]xppb P=0.3x10-8 Pa SuperB LER IONTR developed by Ohmi san

  16. Simulation of FII (4) Lgap=40ns Lgap=20ns Ntrain=5 Nb=50 Lsep=4ns Lgap=180ns

  17. Simulation of FII (5) Nb=100 Nb=150 Ntrain=2 Lgap=40ns Lsep=4ns Nb=200

  18. Fast Ion Instability Summary • Fast Ion Instability has been simulated for SuperB updated parameters using Ohmi san code iontr • Preliminary results show that: • Beam oscillations are suppressed by the feedback system for Lgap  40 ns, while considerable residual oscillation remains for Lgap ≤ 20 ns. • With Lgap= 40 ns, the instability is suppressed by the feedback system for Nb = 100, but it is not suppressed for longer trains, Nb ≥ 150.

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