CI Courses / Winter 2016

Transcription

1 CI Courses / Winter 2016 MADX I Methodical Accelerator Design Design of a FODO Ring Dr. Öznur Mete, Dr Robert Apsimon University of Lancaster The Cockcro@ InsBtute of Accelerator Science and Technology Contact: o.mete@lancaster.ac.uk r.apsimon@lancaster.ac.uk

2 CI Courses / MADX Introduction Reminder LECTURE 1 Introduction Design and compute a regular lattice Exercise 1 Adjust basic machine parameters LECTURE 2 Induce machine imperfections and perform corrections Introduce straight sections Design injection and extraction sections LECTURE 3 Design a dispersion suppressing lattice Determine the energy acceptance of your machine using MADX-PTC

3 CI Courses / MADX Introduction 3 Exercise 1 In this exercise Design a machine for protons at a momentum of 20 GeV/c with the following basic parameters: Circumference = 1000 m Quadrupole length Lq = 3.0 m Ring consists of 20 FODO cells Dipole length is 5 m and maximum field strength is 3 T Use your lecture note for lattice design: Define a FODO lattice according to the boundary condition (position of dipole and quadrupoles). Find the optics (strength of dipoles and quadrupoles) so that βmax=100 m. Implement it in MADX format using thin lenses for all elements and verify your calculations.

4 CI Courses / MADX Introduction 4 Step 1 Given: Circumference = 1000 m Quad length = 3.0 m 20 FODO cells Dipole length = 5 m Maximum dipole field = 3 T How many dipole magnet should you use per cell?

5 CI Courses / MADX Introduction 5 Step 1 = 1 (m 1 )=0.3 B(T ) p(gev/c) L(m) =0.3 3(T )5(m) 20(GeV/c) =0.225(rad) Total number of dipoles per cell = = /Cell

6 CI Courses / MADX Introduction 6 Step 2- Define the lattice / positions of dipoles and quadrupoles Adjust the dipoles so that they will be all at an equal distance from each other. l D L Cell 0.15L Cell 0.35L Cell 0.65L Cell 0.85L Cell

7 CI Courses / MADX Introduction 7 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 100 m. Given: Circumference = 1000 m Quad length = 3.0 m 8 FODO cells Dipole length = 5 m Maximum dipole field = 3 T Condition: max ˆ 100 m How many dipole magnet should you use per cell?? 32 dipole magnets / 4 per cell. Calculate the phase advance per cell.

8 CI Courses / MADX Introduction 8 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m. Cell length L Cell = 1000m 20 = 50m Max beta function for FODO cell ˆ = (1 + sin µ 2 )L cell sinµ = 100 Find the phase advance ˆ L 1/2 = 1+sin µ 2 sin µ 2 cos µ 2 = 100m 25m =4 But how?

9 CI Courses / MADX Introduction 9 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m. Calculate the phase advance. ˆ L 1/2 = 1+sin µ 2 sin µ 2 cos µ 2 Following an indirect method, find the solution for f(μ/2) for a μ/2 satisfying βmax/l1/ f(x) = (1+sinx) / (sinx cosx) f(µ) Target µ = rad ( o ) Phase advance for one cell µ = o f(µ/2) µ/2

10 CI Courses / MADX Introduction 10 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m. Given: Circumference = 1000 m Quad length = 3.0 m 8 FODO cells Dipole length = 5 m Maximum dipole field = 3 T Condition: max ˆ 100 m How many dipole magnet should you use per cell?? 32 dipole magnets / 4 per cell. Calculate the phase advance per cell. Cell length 125m and the phase advance is o. Calculate the quadrupole strengths and the focal lengths.

11 CI Courses / MADX Introduction 11 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m. Remember the equation relating the phase advance and the focal length of a quadrupole magnet for a FODO cell: sin µ 2 = L Cell 4f Q f Q = 1 k Q l Q f Q = L Cell 4sin µ 2 = 50m 4sin(21.5 o ) = 34m l D L Cell 0.15L Cell 0.35L Cell k Q = 1 f Q l Q = 1 34m3m = L Cell 0.85L Cell

12 CI Courses / MADX Introduction 12 Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m. Given: Circumference = 1000 m Quad length = 3.0 m 8 FODO cells Dipole length = 5 m Maximum dipole field = 3 T Condition: max ˆ 100 m How many dipole magnet should you use per cell?? 32 dipole magnets / 4 per cell. Calculate the phase advance per cell. Cell length 50m and the phase advance is o. Calculate the quadrupole strengths and the focal lengths. Quadrupole focal length is 34m and quad strength is 9.8x10-3 m -2.

13 CI Courses / MADX Introduction 13 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. Prepare the sequence file (ex1.seq). Prepare MADX commands file (ex1.madx). Run your file from the command line: madx < ex1.madx

14 CI Courses / MADX Introduction 14 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. Prepare the sequence file (ex1.seq).

15 CI Courses / MADX Introduction 15 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. Prepare MADX commands file (ex1.madx).

16 CI Courses / MADX Introduction 16 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. command line output

17 CI Courses / MADX Introduction 17 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. Plot the dispersion function for your ring. madx.ps

18 CI Courses / MADX Introduction 18 Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations. survey.out Survey Plot z (m) x (m)