1. MAD-X V3 with Space Charge via Macros (2010) Benchmarking (GSI) with other Codes Implementing Space Charge directly into MADX-SC V5 (2012)  latest version (2013) by present MAD-X custodian L. Deniau Application to the Fermilab Debuncher and comparison with ORBIT Frozen space charge model in MAD-X with adaptive intensity and sigma calculation on behalf of Valery Kapin Acknowledgements: Y. Alexahin, G. Franchetti, F. Schmidt, P. Zenkevich

2. V. Kapin (F. Schmidt)SC-132 MAD-X V3 with Space Charge for Debuncher (V. Kapin 2010) Utilizing the BB elements to create a frozen space charge model but adapting emittances and Twiss parameters for the sigma determination. Using the MAD-X Macro technique for all operations Phase-I: Lattice Preparation Splitting the elements (at least once) and introduce SC kicks in between Making sure that the lattice is stable including SC and proper sigma values (  next slide) Transferring thick lattices into thin ones (symplectic and only way to track in MAD-X) Phase-II: Running (turn-by-turn due to Macro procedures) Time varying magnet strengths, phase trombone Emittance and sigma recalculation after every turn via TWISS Output (losses, emittances, etc)

3. V. Kapin (F. Schmidt)SC-133 The 2nd order ray tracing integrator for a number of S-C kicks

4. V. Kapin (F. Schmidt)SC-134 Procedure to determine Beam Sizes with large SC Tune Swings TWISS fails for integer and/or half integer tunes  Trick to avoid it: turn on SC tune-shift in small steps and let tunes converge at each step Lines represent Laslett formula Reference: Valery Kapin talk at GSI 2009

5. Y.Alexahin, A.Drozhdin, N.Kazarinov, “direct space charge in Fermilab Booster with MAD8”, Beams-doc-2609-v1, 2007 Unfortunately TRACK module of MAD8 (frozen, only executable file) does not permit to have more than 200 BB elements. Thereby the particle tracking has been fulfilled with 197 BB elements with average distance between ~ to 2.4 m. Number of particle Beam emittance Red – horizontal, blue – vertical Turn by Turn run of MAD8 under control of Mathematica

6. V. Kapin (F. Schmidt)SC-136 BB-sizes for 6D simulations Conte & MacKay, “Intro to Phys. Part. Acc”, 1991, 5.5 Dispersion: trajectories x(s) is composed of two parts: a)betatron oscillations x  (s), and particular solution due to dispersion x D (s)=D(s)  p. b)Statistically beam size is   tot =    + [ D(s)  p ] 2 Beam size in bends ( D x  0)  is increased for beam with  p

7. V. Kapin (F. Schmidt)SC-137 Tracking with many BB in 6D S.C. kicks by BB-elements for non-linear tracking; (C.O. shifts are included; a total number BB-elements is not limited); Thin-lens tracking with MADX (similar to MAD8) with lattice conversion by MAKETHIN command Transverse BB-forces are modulated according to longitudinal Gaussian distribution. Two versions: a) given “fake” harmonical oscillations (GSI- 2009) b)  T from real 6D tracking (FNAL-2010)

8. V. Kapin (F. Schmidt)SC-138 Benchmarking with 4D & 6D simulations using MADX + Sp.Ch. for SIS18 model (GSI, 2009) vs. G. Franchetti (GSI), MICROMAP S. Machida (RAL), SIMPSON G. Franchetti, “Code Benchmarking on Space Charge Induced Trapping”: http://www-linux.gsi.de/~giuliano/

9. V. Kapin (F. Schmidt)SC-139 Benchmarking SIS18 steps 1-5 for 4D 1) Benchmarking of the Phase Space MADX with BBs

10. V. Kapin (F. Schmidt)SC-1310 2) Benchmarking of the tunes versus particle amplitude. Sextupole OFF.

11. V. Kapin (F. Schmidt)SC-1311 3) Benchmarking of the tunes versus particle amplitude, with sextupole ON.

12. V. Kapin (F. Schmidt)SC-1312 4) Benchmarking of the Tunes versus particle amplitude, with sextupole ON

13. V. Kapin (F. Schmidt)SC-1313 5) Benchmarking of phase space with space charge and sextupole on at Qx = 4.3504 MAD-X with BB’s MICROMAP SIMPSONS

14. V. Kapin (F. Schmidt)SC-1314 6) Benchmarking SIS18 for 6D (fake longitudinal motion) Trapping test particle during 1 synchrotron oscillation Evolution of the transverse rms emittance of a bunch (1000particles)

15. V. Kapin (F. Schmidt)SC-1315 The MACRO technique of MAD-X is working fine but typically one ends up with very complex logic  Therefore quite unpractical for new applications. Macros are inherently slow! Therefore the idea was to reduce the use of Macros as much as possible and to modify the code to do most of the work directly within MAD-X. In detail: Time varying multipoles via turn-by-turn TFS tables Time varying phase trombone (Forest/Schmidt: Don’t use them!) Time varying RF cavity voltage Include the sigma and emittance determination after each turn Allow for stop&go for the MAD-X tracking routine to allow intermediate TWISS calculation at start and the locations of the SC elements Input via several TFS tables. MADX-SC V5 (2012)

16. V. Kapin (F. Schmidt)SC-1316 Frank has left the MAD-X project 2 years ago. Laurent Deniau at CERN has taken over till then. Frank has been a manager of the code with limited involvement in the actual code writing other than the PTC part. In particular, the core of the code in C has been written exclusively by Hans Grote. In a state of emergency Frank had to be ready to fix the code quickly. MAD-X is not well suited for this task since deferred evaluation does not easily allow to put element parameters back into the database. Various C routines were needed but Hans did not have to help! MAD-X Status

17. V. Kapin (F. Schmidt)SC-1317 Lattice with variable Parameters M.J.Syphers, “Status of Mu2e Operating Scenario”, Feb, 2010 Beams-doc-3556  Mu2e experiment  Accelerator issue: 8 GeV Accumulator and Debuncher storage rings are used  Compact bunches (<200ns,  <0.025) are prepared in Accumulator ring  Bunches are transferred to Debuncher ring and extracted out to the experiment using 3-rd order resonant extraction with spill times ~150ms. A stable, slow spill with a very intense proton beam is a big challenge.

18. V. Kapin (F. Schmidt)SC-1318 N_macro_surv vs Turn Number for the Debuncher Timing on CERN computer Macro version ~20-24h MADX-SC ~2-4h MAD-X V3 with Macros MADX-SC V5

19. V. Kapin (F. Schmidt)SC-1319 Ex,y_rms vs Turn Number for the Debuncher MADX-SC V5MAD-X V3 with Macros

20. V. Kapin (F. Schmidt)SC-1320 Longitudinal Emittance vs Turn Number for the Debuncher MAD-X V3 with Macros MADX-SC V5

21. Slow extraction in Debuncher using Orbit Simulations with Orbit code (PIC + matrices) by Vladimir Nagaslaev 3-order resonance with variable tune Qx and sext. str. K2 First “strange” results for extraction: “intensity drop” intensity vs turns Need to simulate in a lattice with variable parameters (Qx, K2)

22. V. Kapin (F. Schmidt)SC-1322 Simulation Tasks: Compare MADX and ORBIT space-charge simulations using the Debuncher lattice in ORBIT(6x6matr.)-style (created by V. Nagaslaev) Compare simulations for lattices with MAD-style (MAD-8 -> MADX) and ORBIT-style (6x6 matr.) Valery’s task was the code validations and comparisons. The design of slow extraction is used “as is” and out of his scope. “Intensity drop” was resolved simply at the beginning: Valery advised to make mesh refinements PIC: “Total Beam size increases at slow extraction => mesh number should be increased to keep the cell size”

23. V. Kapin (F. Schmidt)SC-1323 Simulations with ORBIT by V. Nagaslaev Ramps are given in tables; Npart in bunch ~ 2.5e12

24. V. Kapin (F. Schmidt)SC-1324 MADX-SC is going to be used at CERN as their frozen model tool for space charge studies. Any developments, bugfixes etc will be provided to Fermilab. Most probable I (Valery Kapin) and Yuri Alexahin will use it and CERN will hopefully help in case of problems and/or further developments. There has already been request by both BNL and GSI to apply it for their machines. Code, examples and help has been offered by CERN. In the meantime the code has been implemented into the latest version of MAD-X but a careful checking remains to be done. Documentation will soon be provided  responsibility F. Schmidt Future Developments

25. V. Kapin (F. Schmidt)SC-1325 Reserve

26. V. Kapin (F. Schmidt)SC-1326 Self-consistent (linear) BB-sizes Space-charge kicks simulated by the 1st order MATRIX for linear TWISS calculations; Linearly self-consistent beam sizes calculated by iterations with the TWISS; Analytical Laslett's formula and numerical iterations provide near the same tune shifts (for coasting beam !!!)