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dynamic aperture optimization work for the CLIC DR

dynamic aperture optimization work for the CLIC DR. Mauro Pivi, CERN/SLAC June 27, 2012 CLIC DR collaboration meeting. TME cell phase advance – identity transformation. Goal: set the phase advance of the TME cells to cancel high order multi-poles and increase dynamic aperture [1]

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dynamic aperture optimization work for the CLIC DR

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  1. dynamic aperture optimization work for the CLIC DR Mauro Pivi, CERN/SLAC June 27, 2012 CLIC DR collaboration meeting

  2. TME cell phase advance – identity transformation • Goal: set the phase advance of the TME cells to cancel high order multi-poles and increase dynamic aperture [1] Procedure: • Set the Vertical phase advance in the arc TME cell to obtain an identity transformation (phase adavanceis an integer number) every N cells • Re-match the phase advance of FODO cell in the straights to re-obtain the nominal global tunes • Correct chromaticity [1] PEP-X report, SLAC-PUB-14785 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  3. TME cell phase advance – identity transformation use, fodo !! Mauro jun 2012 ************** cell vary, kqdw , step=1.e-5, upper=11, lower=-11 vary, kqfw , step=1.e-5, upper=11, lower=-11 constr,#e, mux = 0.256647 , muy = 0.098547 ! original: mux = 0.256, muy = 0.105500 lmdif,calls=2000,tolerance=1.0e-8 endmatch • MAD main steps: use, tme cell vary, kqf1 , step=1.e-5, upper=11, lower=-11 vary, kqf2 , step=1.e-5, upper=11, lower=-11 constr,#e, mux=0.37500 muy=0.0833333 ! original: mux = 0.4080, muy = 0.0500, lmdif endmatch use, ring ! mauro: commented this below harmon hvary, ks2x2, step=0.01 hvary, ks2y1, step=0.01 htune, qx'=0.0, qy'=0 hchromaticity endharm 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  4. Optics FODOcell TME cell 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  5. Phase advance space • “Nominal” TME cell phase advances: mux = 0.408, muy = 0.05 mux varied: 0.333333 0.34375 0.375 0.40625 0.416667 0.4375 0.46875 0.5 muy varied: 0.03125 0.0416667 0.0625 0.0833333 (0.09375) 0.125 96 TME cells, mu=1/96/i Index: i, 96/i, 1/96/i mux muy

  6. Identity transformation of vertical phase advance every N - TME cells Examples: • “CLIC DR - mux=0.375, muy=0.0625” • “CLIC DR - mux=0.38541, muy=0.0625” nominal mod ph.adv dp=0.0 dp=0.01 nominal mod ph.adv dp=0.0 dp=0.01 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  7. Identity transformation of vertical phase advance every N- TME cells • Probably best case so far: mux=0.375 muy=0.083333 (multiple 2p) nominal mod ph.adv Off momentum dynamic aperture, dp=1% On momentum dynamic aperture, dp=0% Dynamic aperture increase for on- and off-momentum particles. The beam sizes are also shown.

  8. CLIC DR: set phase advance per TME cell • “Nominal” TME cell phase advance was: mux= 0.408, muy = 0.05 • Then set TME cell phase advance to mux=0.375 muy=0.0833 (identity transformation every 12 TME cells) • Nominal working point nx=48.349, ny=10.394. • Beam size relevant for dynamic aperture: sx=297mm, sx=38mm • Used optics .seq posted at: https://twiki.cern.ch/twiki/bin/view/CLIC/DampingRings • In this particular case, Horizemittanceincreases 8-9% 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  9. Phase advance considerations: analytical parameterization of TME cell Keeping the phase advances μx,y/2*p< 0.5 assures that chromaticitiesare kept to low enough values (by Fanouria Antoniou) Detuning Factor (top) and horizontal (bottom, left) and vertical (bot- tom, right) chromaticities as a function of the horizontal and vertical phase advances.

  10. General treatment - Perturbation of sextupoles • Following [1], based on the Lie Algebra method, the transfer map M of the beam-line can be decomposed in where A-1 is linear symplectic to transform into normalized coordinates and R is rotational map with phase advances as angles. In particular f3 and f4 depends on the sextupolestrenghtS and: where yX,yy are phase advances from last sextupole to end of beam line (an achromat in PEP-X) [1] PEP-X report, SLAC-PUB-14785 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  11. Summary and future plans for the CLIC DR • Initial work: increased dynamic aperture with identity transformation of phase advance every N - TME cells • Systematic studies are needed to evaluate best phase advance per cell to improve dynamic aperture • Optimize working points • Frequency map analysis • Space charge effect: need to scan the dynamic aperture vs space charge tune shift to account for Dn~0.1 • In addition, apply more standard techniques: increase number of sextupole families, include harmonic sextupoles, cell symmetry 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

  12. Thanks to M.H. Wang (SLAC), Fanouriaand Yannis 27 June, 2012 CLIC DR coll. meeting Mauro Pivi, CERN/SLAC

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