1. Electron Cloud, IBS, and Fast Ion Update
T. Demma, INFN-LNF
Thanks to A.Chao and K.Ohmi
SuperB General Meeting March , 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
Beam energy E[GeV]
6.7
circumference L[m]
1370
bunch population Nb
5.74x1010
bunch length σz [mm] 5
horizontal emittance εx [nm]
1.6
vertical emittance εy [pm] 4
hor./vert. betatron tune Qx/Qy
40.57/17.59
synchrotron tune Qz
0.01
hor./vert. av. beta function
20/20
momentum compaction 
4.04e-4

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
June 2008
January 2009
March 2009
int [1015m-2] solenoids
int [1015m-2] no solenoids
SEY=1.1
95%
0.06
2.1
0.09
2.5
0.22
2.7
99%
0.02
0.25
0.04
0.3
0.7
SEY=1.2
2.8
0.27
3.2
0.45
6.5
0.045
0.71
0.82
0.07
2.4
SEY=1.3
20.2
2.9
25.7
5.4 25
0.94
1.3
4.1
4.5 13
Sep.2009
int [1015m-2] solenoids
0.1
0.07
0.3
2.0
0.7
Instability occurs if:
where cent. ande,th are obtained from simulations.
LNF conf.

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, (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 eff and 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/Th 1/Tv 1/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 SuperB LER IONTR developed by Ohmi san
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
Circumference [m]
1258.4
Energy [GeV]
4.18
Harmonic number
1998
Trans. damping time [ms] 40
Horizontal emittance [nm]
2.4
Vertical emittance [pm]
6.15
Natural bunch length [mm]
5.00
Natural energy spread [10−4]
6.68
Bunches per train
978
Particles per bunch
5.5 x 1010
Bunch spacing [ns] 4

16. Simulation of FII (4)
Lgap=20ns
Lgap=40ns
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.