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PAMELA lattice and magnets - Deriving the parameters needed for Zgoubi Kai Hock 28/4/13

PAMELA lattice and magnets - Deriving the parameters needed for Zgoubi Kai Hock 28/4/13. PAMELA. Closed orbit and Twiss parameters for a 100 MeV proton, computed using a Matlab script based on equations from the Zgoubi manual.

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PAMELA lattice and magnets - Deriving the parameters needed for Zgoubi Kai Hock 28/4/13

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  1. PAMELA lattice and magnets - Deriving the parameters needed for Zgoubi Kai Hock 28/4/13

  2. PAMELA Closed orbit and Twissparameters for a 100 MeVproton, computed using a Matlab script based on equations from the Zgoubimanual. These must be obtained using Zgoubi first, before moving on to dynamic aperture calculation.

  3. Lattice parameters 1 cell Packing factor, a = 0.48 No. of cells, Ncell = 12 r0 = 6.251 m Obtained from PAMELA papers. Lcell L L L L = 0.314 m L L Triplet length = 5L = aLcell F D F r0 q q = 2p/Ncell

  4. Suggested reference path for Zgoubi Likely to be closer to closed orbit because of symmetry. Start closed orbit search here. New cell F D F New reference r0 q q = 2p/Ncell

  5. Lattice parameters needed for Zgoubi d1 = 5L/2 q1 = tan-1(d1/r0) r1 = r0/cosq1 q2 = p/Ncell – q1 d2 = r1cos q2 d1 q1+q2 q1+q2 F D F d2 d2 r1 r0 q2 q1

  6. Magnet parameters k = 38 B0 = 1.67 T for F magnet B0 = -2.44 T for D magnet r = r0+x Along radial direction in each magnet, By = B0(r/r0)k.

  7. Field created by multipole expansion Taylor expand about r=r0: To obtain Bx, replace each term by multipole: Check that real part agrees with previous equation for By. This works because each multipole term satisfies Maxwell’s equations. Since x, y << r0, it may be possible to truncate the series. This graph compares N = 3 with the actual field.

  8. Magnet parameters for Zgoubi Zgoubi requires the magnetic field (magnitude) at pole tip. To find this, we first write down an expression for a multipole term. Comparing with a sum of multipole fields Bn: the nth order multipole field is given by: Consider a pole tip on the x axis at distance R0 from reference path. This pole tip is at x=R0, y=0. So at the pole tip, the field is:

  9. For future comparison: These results are obtained using a multipole expansion up to N=3, and for a 100 MeV proton.

  10. References PAMELA Design Report http://www.hep.manchester.ac.uk/u/hywel/papers/proton/PamelaPDR.pdf S. Sheehy, et al, “PAMELA: LATTICE DESIGN AND PERFORMANCE”, Proceedings of PAC09, Vancouver, BC, Canada http://accelconf.web.cern.ch/AccelConf/PAC2009/papers/fr5pfp001.pdf H. Witte, et al, “PAMELA MAGNETS - DESIGN AND PERFORMANCE”, Proceedings of PAC09, Vancouver, BC, Canada http://accelconf.web.cern.ch/AccelConf/PAC2009/papers/mo6pfp073.pdf S. Sheehy, Design of a Non-Scaling Fixed Field Alternating Gradient Accelerator for Charged Particle Therapy, PhD Thesis, Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:d9cd977c-35db-45cc-ad33-67710fc3e82f

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