PS 2 Aperture Model Wolfgang Bartmann and Brennan
PS 2 Aperture Model Wolfgang Bartmann and Brennan Goddard PS 2 Meeting, 24 -Jan 2008
![Calculation of the Aperture Ax = Kβ [ √(N σ)+ Dx dp/p ] +](http://slidetodoc.com/presentation_image_h2/0a4f1064af571ff6821dba99b346d31a/image-2.jpg "Calculation of the Aperture Ax = Kβ [ √(N σ)+ Dx dp/p ] +")
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) εnx = 15 e-6 [m rad] βγ = 5. 167 relativistic βγ at 4 Ge. V dp/p = 0. 005 [m] momentum spread εl = 0. 6 [e. V s] dp 1/2 = 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 24 -Jan 2008 [m] horizontal betatron sigma PS 2 Aperture Model hor. normalised emittance 2
Reminder: PS 2 FODO Optics 24 -Jan 2008 PS 2 Aperture Model 3
![Minimum Apertures from calculation (optics values from elements’ centre) Element Rect: half width [mm]](http://slidetodoc.com/presentation_image_h2/0a4f1064af571ff6821dba99b346d31a/image-4.jpg "Minimum Apertures from calculation (optics values from elements’ centre) Element Rect: half width [mm]")
Minimum Apertures from calculation (optics values from elements’ centre) Element Rect: half width [mm] Rect: half height [mm] MB 59. 3 29. 6 QF 60. 4 18. 0 QD 29. 3 35. 2 LSF 57. 8 18. 6 LSD 30. 7 33. 7 BPH 58. 9 18. 5 BPV 30. 6 33. 9 MDH 58. 1 33. 8 MDV 31. 1 33. 5 24 -Jan 2008 PS 2 Aperture Model 4
Minimum and proposed aperture horizontal 24 -Jan 2008 PS 2 Aperture Model 5
Minimum and proposed aperture vertical 24 -Jan 2008 PS 2 Aperture Model 6
![Apertures for the different elements Aperture type: Rectellipse Element Rect: half width [mm] Rect:](http://slidetodoc.com/presentation_image_h2/0a4f1064af571ff6821dba99b346d31a/image-7.jpg "Apertures for the different elements Aperture type: Rectellipse Element Rect: half width [mm] Rect:")
Apertures for the different elements Aperture type: Rectellipse Element Rect: half width [mm] Rect: half height [mm] Ell: hor. half axis [mm] Ell: vert. half axis [mm] MB 70 30 - - QF - - 65 65 QD - - 65 65 LSF - - 65 65 LSD - - 65 65 BPH - - 65 65 BPV - - 65 65 MDH 70 40 - - MDV 40 70 - - 24 -Jan 2008 PS 2 Aperture Model 7
Available horizontal aperture 24 -Jan 2008 PS 2 Aperture Model 8
Available vertical aperture 24 -Jan 2008 PS 2 Aperture Model 9
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 24 -Jan 2008 PS 2 Aperture Model 10
- Slides: 10
