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PS2 Aperture Model

PS2 Aperture Model. Wolfgang Bartmann and Brennan Goddard PS2 Meeting, 24-Jan 2008. Calculation of the Aperture. A x = K β [ √ (N  σ )+ D x dp/p ] + Align + M ech + Sagitta x + Traj max A x [ m] horizontal aperture K β = 1.1 optical mismatch factor

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PS2 Aperture Model

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  1. PS2 Aperture Model Wolfgang Bartmann and Brennan Goddard PS2 Meeting, 24-Jan 2008

  2. Calculation of the Aperture Ax = Kβ[ √(Nσ)+ Dxdp/p ] + Align + Mech + Sagittax + Trajmax • Ax[m] horizontal aperture • Kβ= 1.1 optical mismatch factor • N = 3.5 Number of betatron sigma opening • σx = √(βx εnx /βγ) [m] horizontal betatron sigma • εnx = 15e-6 [mrad] hor. normalised emittance • βγ = 5.167 relativistic βγ at 4 GeV • dp/p = 0.005 [m] momentum spread • εl = 0.6 [eVs] dp1/2 = εl/(π ½ bunch length) • bunch length = 20 [ns] • Align = 0.001 [m] alignment precision • Mech = 0.000 [m] mechanical precision (included in magnet gap) • Sagittax = 0.0179 [m] horizontal sagitta in main dipoles • Trajmax = 0.004 [m] maximum orbit excursion PS2 Aperture Model

  3. Reminder: PS2 FODO Optics PS2 Aperture Model

  4. Minimum Apertures from calculation(optics values from elements’ centre) PS2 Aperture Model

  5. Minimum and proposed aperturehorizontal PS2 Aperture Model

  6. Minimum and proposed aperturevertical PS2 Aperture Model

  7. Apertures for the different elementsAperture type: Rectellipse PS2 Aperture Model

  8. Available horizontal aperture PS2 Aperture Model

  9. Available vertical aperture PS2 Aperture Model

  10. Follow ups • Take optics values at the beginning and the end of the elements… • Refine apertures for Inj/Extr elements • Define aperture standard to compare different lattices… • Keep all main element physical sizes and compare available aperture • Or derive minimum gaps for (e.g.) 3.5 sigma PS2 Aperture Model

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