1. Intra-Beam Scattering modeling for SuperB and CLIC
Mauro Pivi work performed while at SLAC
High Luminosity Workshop
27-30 May, 2013

2. Analytical 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?
Could IBS affect the beam distribution, perhaps generating tails?
z=4.97 mm
@N=6.5e10
Theo Demma 2012

3. Intra-Beam Scattering (IBS) Simulation Algorithm: CMAD
IBS applied at each element of the Ring
CMAD parallel code: Collective effects & MAD
Lattice read from MADX files containing Twiss functions and transport matrices
At each element in the ring, the IBS scattering routine is called. At each element:
Particles of the beam are grouped in cells.
Particles inside a cell are coupled
Momentum of particles is changed because of scattering.
Particles are transported to the next element.
Radiation damping and excitation effects are evaluated at each turn.
Vertical dispersion is included
Code: Electron Cloud + IBS + Radiation Damping & Quantum Excitation
M. Pivi, T. Demma (SLAC, LAL), A. Chao (SLAC)
27-30 May, 2013

4. IBS - 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
SIRE code uses similar implementation (A. Vivoli Fermilab, Y. Papaphilippou CERN)
27-30 May, 2013
high L

5. IBS modeling: animation

6. IBS evaluation in SuperB
Parameter
Unit
Value
Energy
GeV
4.18
Bunch population
1010
6.5
Circumference m
1257
Emittances (H/V)
nm/pm
1.8/4.5
Bunch Length mm
3.99
Momentum spread %
0.0667
Damping times (H/V/L) ms
40/40/20
N. of macroparticles -
105
N. of grid cells
64x64x64
Bane
Piwinski
IBS-Track/CMAD
- IBS-Track
- C-MAD
One turn evolution: compare codes
One turn evolution: compare codes and theory
M. Pivi, T. Demma
27-30 May, 2013

7. IBS evaluation for CLIC DR
Energy (GeV)
2.86
emitx (m)
5.554e-11
emity (m)
e-13
Deltap
e-3
sigmaz (m)
Ideal lattice
CMAD simulations compare with theory: one turn evolution of emittance growth in the CLIC Damping Ring.

8. IBS Distribution study
Parameter
c2799
Confidence Z
<1e-6 X Y
0.6920
M. Pivi (SLAC), T. Demma (INFN)

9. Previous work at CERN: SIRE IBS Distribution study
Parameter
c2999
Confidence
Dp/p
3048.7
<1e-15 X
1441.7 Y
1466.9
Parameter
Value
Eq. ex (m rad)
2.001e-10
Eq. ey (m rad)
2.064e-12
Eq. sd
1.992e-3
Eq. sz (m)
1.687e-3
A. Vivoli , Y. Papaphilippou CERN

10. ‘Equivalent’ Long term Emittance Evolution in SuperB LER
These preliminary simulations are performed using a factor F=10 faster damping time and a factor 10 larger beam intensity
tx = 10-1 x 40 ms
ty = 10-1x 40 ms
ts = 10 -1x 20 ms
For SuperB V12 LER
Nb= 2x x1010

11. IBS in SuperB Damping Ring
Beam injection
with IBS
without IBS
ex (m)
ez (m)
Injection
1100e-9
1.5e-4
Extraction w/ IBS
25e-9
3.3e-6
Extraction w/o IBS
23e-9
2.97e-6
Evolution of emittance with radiation damping and IBS
Just 1 IP per tun is considered here

12. IBS evaluation next steps
Code validation: benchmark recent experiments made at CesrTA and SLS with simulations
Tau-Charm factory estimate gives larger IBS growth than SuperB because of larger beam intensity and lower energy
Code predictions: long term beam evolution in Tau-Charm and CLIC Damping Rings
Included magnet vertical misalignments and vertical dispersion
Next: Include magnet rotation and coupling also to closely benchmark experimental data (CesrTA, SLS)

13. Summary
Developed multi-particle simulation codes for Intra-beam scattering
Codes in agreement with theoretical models
Estimations for Super-B
Plans for methodical evaluation of IBS in Tau-Charm are needed.

14. Thanks to:
M. Boscolo, M. E. Biagini, A. Chao