1 / 34

Summary of GSI Visit July 2013

Summary of GSI Visit July 2013. Benchmarking of MICROMAP with MAD-X/PTC/SixTrack Analysis of Resonances in 4D: In particular non-linear normal Sextupole Coupling Resonance Q x + 2 Q y = n Intense Collaboration with Giuliano Franchetti.

urbain
Download Presentation

Summary of GSI Visit July 2013

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Summary of GSI Visit July 2013 • Benchmarking of MICROMAP with MAD-X/PTC/SixTrack • Analysis of Resonances in 4D: In particular non-linear normal Sextupole Coupling Resonance Qx + 2 Qy= n • Intense Collaboration with Giuliano Franchetti GSI visit

  2. Benchmarking of MICROMAP with MAD-X/PTC I • MAD-X Twiss: 2nd order terms included agrees with EXACT Hamiltonian up to this order; non-symplectic due to missing higher orders, SC with rescaling turn by turn • PTC: approximate (kicks), exact or non-exact, always symplectic, very high orders included • Sixtrack: always symplectic, non-exact, second order • MICROMAP: always symplectic, non-exact, first order GSI visit

  3. Benchmarking of MICROMAP with MAD-X/PTC II • Set-up of the PS an example with minimal set of elements, MAD-X clean-up via seqedit • Conversion to MICROMAP more efficient now • Perfect agreement of 4D parameters: tunes, TWISS and dispersion! • Chromaticity off by 16% in horizontal plan due to lack of EXACT Hamiltonian • ➔ SC comparison eagerly awaited!!! GSI visit

  4. Resonance Categorization Fodo with single Sextupole ➔ unstable motion at sextupole resonance, no islands Stabilization via octupole ➔ islands Sextupole (constant strength) distributed around a ring ➔ first order resonance compensated no islands; detuning with amplitude; large scale chaos Random Errors balances resonance and detuning ➔ anything possible! GSI visit

  5. Resonances in Tune diagram 1D Resonance 2D coupled Resonance  Fixlines 2D crossing Resonances  2D Fixpoints Dynamic Aperture

  6. DA in 1D ParticleLoss Dynamic Aperture

  7. 1D close-up LOSS Dynamic Aperture

  8. 2D Stable and Chaos Dynamic Aperture

  9. 2D Fixpoints Vertical Horizontal Horizontal Dynamic Aperture

  10. 2D Fixlines Full Projection Cut in Phase Space Stable Chaos Dynamic Aperture

  11. Simple Toy PS Fodo with 1 Sextupole per Fodo GSI visit

  12. Resonance Qx + 2Qy Large Island Tube GSI visit

  13. X-Y PX-PY GSI visit

  14. Stroboscope Large Island Tube GSI visit

  15. Resonance Qx + 2Qy Small Island Tube GSI visit

  16. X-Y PX-PY GSI visit

  17. Stroboscope Small Island Tube GSI visit

  18. Resonance Qx + 2Qy on Fix-Line GSI visit

  19. X-Y PX-PY GSI visit

  20. Stroboscope on Fix-Line GSI visit

  21. Determining the Fix-Line Standard Technique I • As in 1D the expectation is that particles are trapped in the island torus around the fix-line. • To understand this mechanism in detail on has to determine the fixline. • With this knowledge one can construct a normal plane to the fix-line which will allow to find the extent of the torus structure and the unstable fixlines. • The motion in the plane can be interpreted as a secondary Poincaré section of motion! In fact, in this plane the motion around the fix-line resembles a 1D resonance. GSI visit

  22. Determining the Fix-Line Standard Technique I I • First step is to put a particle somewhere into the island structure. • The method works by restricting the motion in one plane to a wedge say with positive values and best in the linearly normalized phase space (I have called this stroboscoped motion above). • The opening angle of the wedge is the free parameter in this technique. • In the other plane one will then find a number of islands according to the nx * Qx + ny * Qy = n resonance. • The analysis has to be restricted to one of these islands. • The average of all 4 coordinates represents a good approximation of the stable fix-line. • The technique is very time consuming since a sufficient amount of data has to be available in the restricted phase space: however with 2000 turns a good approximation of the fix-line could be found in 7 steps. GSI visit

  23. Determine Fix-line Y-Py X-Px GSI visit

  24. Determining the Fix-Line Using artificial Damping • Experiments at LEP some 13 years ago have shown that in the presence of 4d stable fix-points the particle motions is damped to those fix-points rather than (0,0). • The mechanism works because motion around the fix-point the particles increase there amplitude which can be seen as pseudo energy “gain”. • Therefore, if the damping is not too strong the motion will zoom into the fix-point until the damping and the energy “gain” balances out. • This should generally work in higher dimensions. • One side-effect of this finding is that in presence of weak damping the resonance structure is preserved in all phase space! • A fine-tuning of the damping as a function of the distance to the resonance and/or fix-line should improve the convergence of the technique. GSI visit

  25. Lep: Damping at 4th order GSI visit

  26. Damping in 1D in Simulation GSI visit

  27. Damping in 2D in Simulation GSI visit

  28. Additional Tools • Originally I had hoped that NormalForm would allow to determine detuning and resonance strength. • Although true in principle, the trouble is that this technique is divergent in the vicinity of resonance structures. Therefore, despite the valuable information gained (direction of detuning and good prediction far from resonances) one could not determine the precise location of the resonance structures. • Another tool is the harmonic analysis which decomposes the particle motion into a set of lines. • Despite best efforts one could not yet determine the fix-lines with the help of this complete decomposion into lines. More effort will be invested. • However, the island tune can be nicely determine as a set of side-bands. GSI visit

  29. FFT Large Island Tube GSI visit

  30. FFT Small Island Tube GSI visit

  31. FFT on Fix-Line GSI visit

  32. Next Steps • The simulations will intensify both with MICROMAP and MAD-X-SC. • We will have to define and revisit the Random Part of the multipole components ➔ newest value from Simone in collaboration with the magnet experts. • MAD-X-SC is not yet under MPI but work has been started on that. • The plan is to finish the analysis of the 2012 PS experiments by the end of the year 2013 and spring 2014 at the latest. • The 2D resonance analysis will be brought to conclusion including 2D fix-points (2 separate resonance conditions full-filled: E.G. 3Qx and 4Qy) which is an additional challenge ➔ publication in planning GSI visit

  33. Fix-points motion 3Qx AND 4Qy GSI visit

  34. Fix-points motion 3Qx AND 4Qy X-Y PX-PY GSI visit

More Related