1. Multi-Turn Extraction studies and PTC
M. Giovannozzi
PS and its model
MTE principle
Trapping simulations and PTC
Computing higher order fixed points
Outlook
Acknowledgements: A. Franchi, S. Gilardoni, C. Hernalsteens, R. de Maria, F. Schmidt
09/11/2011
MG - ABP PTC review

2. PS and its model - I The PS in a nutshell: Hundred main magnets
Combined function magnets (dipole and quadrupole fields)
Each main magnet is made of two half-unit (focusing and defocusing).
Each half unit is made of five blocks.
The main magnet is bent.
Additional coils are used to control the working point (tunes and chromaticity – see next slide).
The circumference is 200 p m.
The lattice features ten super periods.
Ideal application for PTC!
09/11/2011
MG - ABP PTC review

3. PS and its model - II Courtesy S. Gilardoni 09/11/2011
MG - ABP PTC review

4. PS and its model - III The PS model:
Thin multipoles are used to reproduce non-linear chromaticity measurements.
Quadrupolar, sextupolar, octupolar multipoles are enough to reproduce experimental observations.
Six three parameters (F/D half-units three multipoles each).
09/11/2011
MG - ABP PTC review

5. Multi-Turn Extraction (MTE)
The main ingredients of multi-turn extraction:
The beam is separated in the transverse phase space using
Nonlinear magnetic elements (sextupoles ad octupoles) to create stable islands.
Slow (adiabatic) tune-variation to cross an appropriate resonance.
This approach has the following beneficial effects:
Losses are reduced (virtually to zero. No mechanical device to slice the beam is used).
The phase space matching is improved with respect to the present situation.
The beamlets have the same emittance and optical parameters.
09/11/2011
MG - ABP PTC review

6. Transverse dynamics - I
Extraction: s
Injection: s
09/11/2011
MG - ABP PTC review

7. Transverse dynamics - II
Phase space at septum
09/11/2011
MG - ABP PTC review

8. Evolution of beam distribution
Horizontal beam profiles in section 54 have been taken during the capture process (total intensity ~2.1×1013).
09/11/2011
MG - ABP PTC review

9. CAPTURE_PTC - I Script code developed by A. Franchi.
PTC is used for the tracking.
Initial conditions are divided into various sets for different batch jobs.
5D script code (no synchrotron motion included) with transverse and momentum distributions included.
Possibility to specify the time-dependence of magnets’ strength.
Post processing included: islands recognition, dispersion computation for islands (implemented according to definition).
09/11/2011
MG - ABP PTC review

10. CAPTURE_PTC - II
Key weak point: impossible to change dynamically strength inside PTC.
Particles’ coordinates are written out after one turn.
The parameters are changed (horizontal tune, strength of sextupoles and octupoles).
Final coordinates are used as initial coordinates for a new turn.
Overall, the CPU-time is NOT used very effectively!
Limitations on number of turns/initial conditions
PTC/ORBIT will allow to overcome this issue and CAPTURE_PTC will be re-written in PTC/ORBIT.
The way the non-linearities of the PS main magnet are modelled should be changed (from thin multipoles to distributed errors).
09/11/2011
MG - ABP PTC review

11. CAPTURE_PTC - III
Capabilities of TRACKING_PTC Plain tracking Aperture model
09/11/2011
MG - ABP PTC review

12. CAPTURE_PTC - III
Example of simulation of the splitting process. Distributions at the location of the magnetic septum.
09/11/2011
MG - ABP PTC review

13. Other PTC-based tools - I
Transverse phase space portrait (trivial)…another script code developed around PTC_TRACK (A. Franchi).
SS01, qx=0.261, qy=0.30
SS01, qx=0.261, qy=0.30
nl coupling corrected
The h2,0, h1,1, h0,2 can be computed easily with PTC_NORMAL
09/11/2011
MG - ABP PTC review

14. Other PTC-based tools - II
Recently the possibility of working around a fixed point different than the origin was introduced (R. de Maria)!
The fixed point at the centre of each stable island is a closed orbit.
The possibility of computing it and to use it as a reference orbit opens up many possibilities:
Computation of optical parameters of islands (PTC_TWISS around the fixed point)
Computation of normal forms around the fixed point.
All this is available with madx_dev.
The current implementation imposes to build a lattice that is N times the original machine, where N is the order of the resonance.
09/11/2011
MG - ABP PTC review

15. Fixed point trajectory: h1,1 ≠ 0 Four times PS circumference
Applications - I
Fixed point trajectory: h1,1 ≠ 0
Four times PS circumference
09/11/2011
MG - ABP PTC review

16. Applications - II b-functions: h1,1 ≠ 0
Optics perturbation for the islands: island-dependent
09/11/2011
MG - ABP PTC review

17. Applications - III b-functions : h1,1 ≠ 0
Optics perturbation for the islands: island-dependent
09/11/2011
MG - ABP PTC review

18. Applications - IV
Optics perturbation for the islands: island-dependent
Dispersion : h1,1 ≠ 0
09/11/2011
MG - ABP PTC review

19. Applications - V
Chromaticities and momentum compaction for the islands: island-independent (h1,1 ≠ 0).
Total momentum spread about ±10-3.
09/11/2011
MG - ABP PTC review

20. Applications - VI
Optics perturbation for the islands: island-dependent
Dispersion : h1,1 = 0
09/11/2011
MG - ABP PTC review

21. Applications - VII
Chromaticities and momentum compaction for the islands: island-independent (h1,1 = 0).
Total momentum spread about ±10-3.
09/11/2011
MG - ABP PTC review

22. Outlook PTC proved to be very useful for MTE!
Latest simple developments opened up new possibilities.
PTC/ORBIT is the tool for tracking (even without space charge) thanks to time-dependence of magnet’s strength.
Documentation not always easy to understand:
trial and error approach
oral transmission from colleagues
proved to be very effective in building experience...
09/11/2011
MG - ABP PTC review