1. Modelling and measurements of bunch profiles at the LHC FB
Stefania Papadopoulou, Fanouria Antoniou, Yannis Papaphilippou
24/6/16

2. Contents Beam profiles at FB -The q Gaussian distribution function
-LHC beam profiles
SIRE code
-IBS effect at FB, comparison with MADX

3. The q Gaussian distribution
The emittance evolution at LHC FB energy is dominated by the IBS effect.
In the case of LHC, the interplay between IBS and a series of other effects, can enhance the tails of the beam distributions, which may become non-Gaussian.
In many cases, the bunch profiles in the LHC, appear to have heavier tails than a normal distribution.
In order to describe them more accurately, the q-Gaussian function, is used. This distribution has a probability density function given by:
3 parameters
In the heavy tail domain (1 < q < 3)
for q =1
Gaussian function

4. Beam profiles at FB
low frequency excitation (MD453), Miriam

5. Beam profiles at FB B1 B2 G.Trad
Fit parameters for B1
6/11/15 00:00
Gaussian; s
0.33
q Gaussian; s and q
0.33 and 1.15
Fit parameters for B2
6/11/15 00:00
Gaussian; s
0.33
q Gaussian; s and q
0.33 and 1
G.Trad
low frequency excitation (MD453), Miriam

6. Beam profiles at FB B1 B2 G.Trad
Fit parameters for B1
6/11/15 00:00
Gaussian; s
0.33
q Gaussian; s and q
0.33 and 1.15
Fit parameters for B2
6/11/15 00:00
Gaussian; s
0.33
q Gaussian; s and q
0.33 and 1
G.Trad
low frequency excitation (MD453), Miriam

7. Beam profiles at FB B1 B2 G.Trad
Fit parameters for B1
6/11/15 01:00
Gaussian; s
0.34
q Gaussian; s and q
0.34 and 1
Fit parameters for B1
6/11/15 01:00
Gaussian; s
0.34
q Gaussian; s and q
0.34 and 1
G.Trad
low frequency excitation (MD453), Miriam

8. Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa
Forbidden by e-cloud
+ Q’ + octupoles
Forbidden by Q’ + octupoles
Can give stability issues if coupling is not fully corrected
Nominal
2015
Tune scans Fill4785, Gianni and Annalisa

9. Beam profiles at FB Tune scans Fill4785, Gianni and Annalisa
Forbidden by e-cloud
+ Q’ + octupoles
Forbidden by Q’ + octupoles
Can give stability issues if coupling is not fully corrected
Nominal
2015
Tune scans Fill4785, Gianni and Annalisa

10. Beam profiles at FB
Tune scans Fill4785, Gianni and Annalisa

11. Beam profiles at FB
Tune scans Fill4785, Gianni and Annalisa

12. Beam profiles at FB
Tune scans Fill4785, Gianni and Annalisa

13. developed by A. Vivoli and M. Martini and revised by Fanouria
SIRE
Software for IBS and Radiation Effects (a Monte Carlo multiparticle simulation code)
developed by A. Vivoli and M. Martini and revised by Fanouria
Inputs
-The optics along a lattice (MADX twiss file).
-The parameters file.
-The particles distribution (default: Gaussian distribution).
Computing IBS (and Radiation Effects)
-Particles are tracked from point to point in the lattice by their invariants.
-At each point of the lattice the scattering routine is called.
-6-dim coordinates of particles are calculated.
-Particles of the beam are grouped in cells.
-The intrabeam collisions between pairs of macro-particles are iteratively computed, the momentum of particles is changed because of scattering.
-Invariants of particles are recalculated.
-Radiation damping and excitation effects are evaluated at the end of every loop.
Outputs
-The beam distribution is updated and the rms beam emittances are recomputed, giving finally the evolution of the emittance and particle distribution in time.
The analytical models that describe the IBS effect assume Gaussian beam distributions. In the case of non-Gaussian beam distributions no theoretical models exist. SIRE calculates IBS for any distribution.

14. SIRE Parameters file Fastrun NIBSruns nturnstostudy ncellx ncellz
ncells
numpart
The Fastrun is applied in order to speed up the simulation.
-the IBS is applied in oneturn and the growth rate per particle is calculated
-the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep.
-continue tracking with the interpolated distribution
Number of timesteps that the time is divided to calculate IBS
Number of turns (total time)
Number of cells in each plane
Number of macroparticles

15. SIRE Parameters file Fastrun NIBSruns nturnstostudy ncellx ncellz
ncells
numpart
The Fastrun is applied in order to speed up the simulation.
-the IBS is applied in oneturn and the growth rate per particle is calculated
-the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep.
-continue tracking with the interpolated distribution
Number of timesteps that the time is divided to calculate IBS
Number of turns (total time)
Number of cells in each plane
Number of macroparticles
In order to avoid combinations which give very small #macroparticles/cell, it was observed (by Fanouria) that 5macroparticles/cell is the optimal minimum number.

16. SIRE Parameters file scanning tested Parameters (at injection) Nominal
Fastrun
NIBSruns
nturnstostudy
ncellx
ncellz
ncells
numpart
The Fastrun is applied in order to speed up the simulation.
-the IBS is applied in oneturn and the growth rate per particle is calculated
-the emittance per particle is recalculated based on the exponential IBS growth in a specific timestep.
-continue tracking with the interpolated distribution
Number of timesteps that the time is divided to calculate IBS
Number of turns (total time)
Number of cells in each plane
Number of macroparticles
scanning
In order to avoid combinations which give very small #macroparticles/cell, it was observed (by Fanouria) that 5macroparticles/cell is the optimal minimum number.
tested
Parameters (at injection)
Nominal
HiLumi
ex,y [mm]
3.5 2
4s bunch length [ns]
1.2 1
Bunch population [1011]
2.3
lattice recurrences
Elements of the lattice with twiss functions differing of less than prec.% are considered equal

17. Scanning ncells and #mp
30min at FB, full optics
Scanning ncells and #mp
Nominal
HiLumi

18. Reduced lattice
As the LHC has a large number of elements (more than 11000), the computational time that SIRE needs to track the distribution for all of them along the ring is very long.
The IBS growth rates were calculated for the LHC’s full optics, using the IBS module of the MADX, based on the B-M formalism.
The optimal minimum number of IBS kick points around the lattice, without affecting the overall effect, are identified.
Finally, the reduced lattice used in SIRE has only 92 points (much lower computational time). so

19. 30min at FB, reduced lattice
Scanning ncells and #mp
Nominal
HiLumi

20. 30min at FB, reduced lattice
Choose the optimal case of ncells and #mp, for both nominal and HiLumi parameters.
Parameters
Nominal
HiLumi
#mp/cell 5
#mp
135000
160000
ncellx·ncelly·ncells
27000
31950
SIRE runs many times (cause there are random generators) then the mean values are compared with the B-M result from MADX.

21. 30min at FB, reduced lattice
Optimal case parameters
Nominal
+2%
+3%
HiLumi
+16%
+12%

22. Summary and next steps
Non-Gaussian beam profiles with heavy tails use of the q-Gaussian distribution function.
The benchmarking with B-M (MADX) is very good for the 30min at FB.
SIRE: IBS tends to develop tails of the particle distribution.
Use q Gaussian as an input distribution in SIRE.
At the LHC FT , the IBS effect becomes weaker while SR damping becomes more pronounced. After the longitudinal beam manipulations during the energy ramp, the longitudinal bunch profiles arrive at FT with a clearly non-Gaussian shape interplay between IBS and SR in this regime, the impact on the evolution of the bunch characteristics and finally on the luminosity.
Acquire beam profiles more regularly.

23. J. D Bjorken, S. K. Mtingwa, Intrabeam Scattering, Part. Accel. Vol
J.D Bjorken, S.K. Mtingwa, Intrabeam Scattering, Part. Accel. Vol. 13, p (1983).
M. Martini, A. Vivoli, “INTRA-BEAM SCATTERING IN THE CLIC DAMPING RINGS”, CERN-ATS , 2010.
M. Martini, A. Vivoli, “Effect of intrabeam scattering and synchrotron radiation damping when reducing transverse emittances to augment the LHC luminosity”, sLHC Project Report 0032, 2010.
E. M. F. Curado and C. Tsallis, “Generalized statistical mechanics: connection with thermodynamics”, 1992 J. Phys. A: Math. Gen
W. Thistleton, J.A. Marsh, K. Nelson, C. Tsallis, “Generalized Box-Mller Method for Generating q-Gaussian Random Deviates”, 2006.
A. Piwinski, Proc. 9th Int. Conf. on High Energy Accelerators, Stanford, 1974.
P. Zenkevich, O. Boine-Frankenheim, A. Bolshakov, Last advances in analysis of intrabeam scattering in the hadron storage rings, Nucl. Instr. and Meth. A 577 p (2007).
F. Antoniou, F. Zimmermann, Revision of Intrabeam Scattering with Non-Ultrarelativistic Corrections and Vertical Dispersion for MAD-X“, CERN-ATS
MAD-X homepage, URL .
M. Kuhn, Emittance Preservation at the LHC, Master Thesis, University of Hamburg/CERN, Geneva, Switzerland 2013.

24. Thank you!

25. 30min at FB, reduced lattice
Optimal case parameters
Nominal
+2%
+3%
HiLumi
+12%
+16%

26. Beam profiles at FB t=0 t=22min Juan Juan
wait for the next fill with nominal bunches and acquire new data. If they keep the bunches some time in the machine it would be possible to see the evolution of the profile at flat bottom.
I took measurements of the nominal bunch in Beam 1 every 5 seconds. Each measurement contains 100 traces acquired every 100 turns, so you can average them to get a smoother profile. The files are standard HDF5 files.
Juan
Juan

27. Beam profiles at FB nominal bunches log G.Trad Fit parameters t=0
Gaussian; s
0.28
q Gaussian; s and q
0.27 and 1.31
G.Trad

28. Fits(HB2)
Growth time [h] 1
70.028 2
48.295 3
4.036 4
6.078 5
4.378 6
14.077 7
10.965 8
8.503 9
7.698 10
8.075

29. Fits(HB1)
Growth time [h] 1
6.085 2
20.94 3
13.144 4
22.651 5 6
24.798 7
23.915 8
65.694 9
15.446 10

30. Beam profiles at FB G.Trad low frequency excitation (MD453), Miriam
Fit parameters for B1
5/11/15 23:00
Gaussian; s
0.35
q Gaussian; s and q
0.34 and 1.14
Fit parameters for B2
5/11/15 23:00
Gaussian; s
0.34
q Gaussian; s and q
0.34 and 1
G.Trad
low frequency excitation (MD453), Miriam

31. Beam profiles at FB G.Trad low frequency excitation (MD453), Miriam
Fit parameters for B1
5/11/15 23:00
Gaussian; s
0.35
q Gaussian; s and q
0.34 and 1.14
Fit parameters for B2
5/11/15 23:00
Gaussian; s
0.34
q Gaussian; s and q
0.34 and 1
G.Trad
low frequency excitation (MD453), Miriam

32. Nominal Fit parameters t=0 t=30min Gaussian; s 0.337 0.339
q Gaussian; s and q
0.293 and 2.16
0.295 and 2.19 (+1.4%)
Nominal

33. Nominal Fit parameters t=0 t=30min Gaussian; s 0.337 0.339
q Gaussian; s and q
0.293 and 2.16
0.295 and 2.19 (+1.4%)
Nominal

34. HiLumi Fit parameters t=0 t=30min Gaussian; s 0.334 0.352
q Gaussian; s and q
0.291 and 2.17
0.304 and 2.26 (+4%)

35. Why non Gaussian if SIRE has this distribution as default?
Parameters
LHC
CLIC DRs
#mp
<160000
200000
ncellx·ncelly·ncells
<27000

36. Nominal 3qgauss:(1-a/b+a/b.*exp((x.^2/2).*(-1+q).*b)).^(1/2+1/(1-q))
Fit parameters
t=0
t=30min
Gaussian; s
0.328
0.336
q Gaussian; s and q
0.289 and 2.14
0.294 and 2.17 (+1.4%)
Nominal
3qgauss:(1-a/b+a/b.*exp((x.^2/2).*(-1+q).*b)).^(1/2+1/(1-q))

37. HiLumi Fit parameters t=0 t=30min Gaussian; s 0.322 0.346
q Gaussian; s and q
0.287 and 2.12
0.303 and 2.27 (+7.1%)

38. Nominal
horiz.
t=0
t=30min

39. Nominal
longit.
t=0
t=30min