1. Preliminary results of the PTC/ORBIT convergence studies in the PSB
LIS meeting 16/04/2012
Vincenzo Forte

2. OVERVIEW Aim of the study Logical path D.O.E. Results
Conclusions and future implementations
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

3. Aim of the study
Preliminary study for finding the optimal conditions for PTC/ORBIT space-charge simulations in terms of convergence and computational costs
How far do we have to push in simulations settings to obtain reasonable results with less computational costs?
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

4. Logical path Externally created (MadX, …) Internally modified (tables)
Lattice setup
Inject starting 6-D matched distribution
Externally created (Mathematica, …)
PTC ORBIT basic settings
Adding of space charge Orbit routines
PTC-ORBIT
1000 turns tracking
RMS emittance
95-99% emittance
tunes
Results analysis
Plots and tunes footprints
Best settings choose
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

5. D.O.E. Made externally through Mad-X Lattice setup
Modified internally through tables
Lmax = 1, w.p. Qx = 4.27, Qy= 4.43 (“resonances - safe” area)
Simple lattice
(double harmonic, tables at 0 value, no acceleration, no C.O.D.)
Inject starting 6-D matched distribution
PTC ORBIT basic settings
Adding of space charge Orbit routines
1000 turns tracking
RMS emittance
95-99% emittance
tunes
Results analysis
Best settings choose
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

6. Inject starting 6-D matched distribution PTC ORBIT basic settings
D.O.E.
Lattice setup
Externally-made distribution through Mathematica script
Ekin = 160 MeV
Normalized transverse emittances: ex=3 (mm-mrad) - ey=2 (mm-mrad) (source: official Excel datasheet on SC-webpage) Un-normalized transverse emittances: ex=4.9 (mm-mrad) - ex=3.3 (mm-mrad)
Matched 6-D distribution (without SC)
250th, 500th, 1000th macro-particles used
Number of particles per bunch = 1.5 * 1.65e12 (official) = 2.475e12 -> “extreme” conditions for space charge
Fringe fields included
Inject starting 6-D matched distribution
PTC ORBIT basic settings
???
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

7. Inject starting 6-D matched distribution PTC ORBIT basic settings
D.O.E.
Lattice setup
Externally-made distribution through Mathematica script
Matched 6-D distribution (without SC)
250th, 500th, 1000th macro-particles used
RF voltages (h=1) 8kV, (h=2) 4kV -> Ts ~ 750 turns
Inject starting 6-D matched distribution
PTC ORBIT basic settings ax bx ay by hx
hpx
Lattice (PTC)
0.8762e-5
5.5940
e-3
3.6225
e-3
250 th (Matlab post p.)
1.0819e-4
5.5890
0.0022
3.6187
-9.4e-4
500 th (Matlab post.p.)
e-4
5.5903
e-4
3.6186
7.8642e-4
1000 th (Matlab post p.) *
-1.81e-5 *
6.5791e-4
* Beta functions statistical precision increases with number of m.p.
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

8. Inject starting 6-D matched distribution
D.O.E.
Lattice setup
1000th M.p. distribution
Longitudinal
dp/p = , T = ns
4T dW = eV.s
Bunching Factor = <I>/Ipeak  0.6 (histogram analysis)
Inject starting 6-D matched distribution
PTC ORBIT pre-tracking settings
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

9. Adding of space charge Orbit routines
D.O.E.
Lattice setup
Inject starting 6-D matched distribution
PTC ORBIT basic settings
Longitudinal space charge adding
Potential-based transverse space-charge (2 ½ D) adding
“chamber” definition
Nxbins, Nybins
Adding of space charge Orbit routines
1000 turns tracking
RMS emittance
95-99% emittance
tunes
Results analysis
Best settings choose
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

10. D.O.E.
1000 turns tracking
RMS emittance
95-99% emittance
tunes
Results analysis
Best settings choose
no. sc.
64 x 64
128 x 128
256 x 256
250th
500th
1000th
Nxbins/Nybins
N.mp.
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

11. D.O.E. Computational costs criteria Best settings choose
Lattice setup
Inject starting 6-D matched distribution
PTC ORBIT basic settings
Adding of space charge Orbit routines
1000 turns tracking
RMS emittance
95-99% emittance
tunes
Results analysis
Computational costs criteria
Convergence criteria
Best settings choose
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

12. Results – first without space charge…y
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

13. Results – first without space charge…
If NoSc. with 1000th is our reference -> Error’s order ~ 10^-3
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

14. Results – computational time criteria
On lxbatch machines, “engpara” queue, 8 nodes required, over 1000 turns
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

15. Results – convergence criteria – best cases – a footprint…
- 4th order resonances plotted
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

16. Results – convergence criteria – the best two cases…
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

17. Results – convergence criteria – best cases difference
The error is in the order of 10^-3 (same as in the linear case !!!)
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

18. Results – convergence criteria – best cases – 95, 99% x emittances
In horizontal 95% emittance is better for 1000th – 256 x 256
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

19. Results – convergence criteria – best cases – 95, 99% y emittances
In vertical 95% emittance is good enough even for 500 th M.p. – 256 x 256
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

20. Results – worst case
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

21. Results – a little better…
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

22. Results – “a little better” vs. best cases…
128 x 128 growth ratio order ~10^-2 (RMS)
256 x 256 growth ratio order ~10^-3 (RMS) -> better accuracy
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

23. Conclusions
Thanks to this preliminary study we had an indication for a starting setting for transverse space charge simulations: 500th – 256x256 could be almost ever enough for RMS emittance behavior and halo formation studying…
We should increase the computational power for longer simulations.
Question #1 -> Between 95% or 99% emittance, which should we choose to study the halo formation?
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte

24. Future implementations
Question #2 -> Which basic settings should we use (i.e. intensity and starting emittance) in the future as “final” PSB characteristics?
Longer simulations required (more turns, i.e. a few synch. periods)
“Lmax” effect -> beta function w-length is about 40 m in PSB ->Lmax up to 4 m (now 1 m) -> less S.C. nodes for integration! -> less CPU time but … what about physics?
Bumps introduction (static -> dynamic tables)
New scripts creation for “off-line” post-processing (FFT analysis for tunes, …)
Effects of shorter dipole magnets on the emittance growth with space charge
Errors in lattice introduction (misalignments and field errors) -> resonance analysis… long term
Preliminary results of the PTC/ORBIT convergence studies in the PSB - Vincenzo Forte