CI Courses / Winter 2016 - The Cockcroft Institute · CI Courses / MADX Introduction Dr Ö. Mete...
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Dr. Öznur Mete, Dr Robert Apsimon University of Lancaster The Cockcro@ InsBtute of Accelerator Science and Technology Contact: [email protected] [email protected] CI Courses / Winter 2016 MADX I Methodical Accelerator Design Design of a FODO Ring
Transcript of CI Courses / Winter 2016 - The Cockcroft Institute · CI Courses / MADX Introduction Dr Ö. Mete...
Dr.ÖznurMete,DrRobertApsimonUniversityofLancaster
TheCockcro@InsBtuteofAcceleratorScienceandTechnologyContact:
[email protected]@lancaster.ac.uk
CI Courses / Winter 2016MADX I
Methodical Accelerator Design Design of a FODO Ring
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction
Reminder
LECTURE 1
❖Introduction
❖Design and compute a regular lattice
❖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
Exercise 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 3
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.
Exercise 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction
Exercise 1
4
Circumference = 1000 mQuad length = 3.0 m20 FODO cellsDipole length = 5 mMaximum dipole field = 3 T
Given:
‣ How many dipole magnet should you use per cell?
‣ Step 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 5
� =1⇥(m�1) = 0.3
B(T )p(GeV/c)
L(m)
� = 0.33(T )5(m)20(GeV/c)
= 0.225(rad)
Total number of dipoles per cell =2�
0.225= 28⇥ 3.5 � 4/Cell
Exercise 1
‣ Step 1
Dr Ö. Mete and Dr R. ApsimonCI 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.
Exercise 1
0.15LCell
0.35LCell
0.65LCell
0.85LCell
lDLCell
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 7
‣ How many dipole magnet should you use per cell??
❖ 32 dipole magnets / 4 per cell.
‣ Calculate the phase advance per cell.
Circumference = 1000 mQuad length = 3.0 m8 FODO cellsDipole length = 5 mMaximum dipole field = 3 T
Given:
Exercise 1
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 100 m.
Condition:
�max
⌘ �̂ ⇡ 100m
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 8
Cell length
Max beta function for FODO cell
Find the phase advance
But how?
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m.
Exercise 1
LCell =1000m
20= 50m
�̂
L1/2=
1 + sinµ2
sinµ2 cosµ
2
=100m
25m= 4
�̂ =(1 + sinµ
2 )Lcell
sinµ= 100
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 9
�̂
L1/2=
1 + sinµ2
sinµ2 cosµ
2Calculate the phase advance.
‣ Following an indirect method, find the solution for f(μ/2) for a μ/2 satisfying βmax/L1/2.
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m.
Exercise 1
µ/20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
f(µ/2
)
0
5
10
15
20
25
30f(x) = (1+sinx) / (sinx cosx)
f(µ)Target µ = 0.75325 1.9791 rad (43.15792 113.3939o)
Phase advance for one cell
µ = 43.16o
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction
Exercise 1
10
‣ 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 32.14o.
‣ Calculate the quadrupole strengths and the focal lengths.
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m.
Circumference = 1000 mQuad length = 3.0 m8 FODO cellsDipole length = 5 mMaximum dipole field = 3 T
Given:
Condition:
�max
⌘ �̂ ⇡ 100m
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 11
sinµ
2=
LCell
4fQfQ =
1kQlQ
‣ Remember the equation relating the phase advance and the focal length of a quadrupole magnet for a FODO cell:
0.15LCell
0.35LCell
0.65LCell
0.85LCell
lDLCell
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m.
Exercise 1
fQ =LCell
4sinµ2
=50m
4sin(21.5o)= 34m
kQ =1
fQlQ=
134m3m
= 9.8 � 10�3
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 12
‣ Step 3- Find the optics (dipole and quadrupole strengths) providing a maximum beta function of 300 m.
Circumference = 1000 mQuad length = 3.0 m8 FODO cellsDipole length = 5 mMaximum dipole field = 3 T
Given:
‣ 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 43.16o.
‣ Calculate the quadrupole strengths and the focal lengths.❖ Quadrupole focal length is 34m and quad strength is 9.8x10-3 m-2.
Exercise 1
Condition:
�max
⌘ �̂ ⇡ 100m
Dr Ö. Mete and Dr R. ApsimonCI 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
Exercise 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 14
❖ Prepare the sequence file (ex1.seq).
‣ Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations.
Exercise 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 15
❖ Prepare MADX commands file (ex1.madx).
‣ Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations.
Exercise 1
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 16
command line output
Exercise 1
‣ Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations.
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 17
madx.ps
Plot the dispersion function for your ring.
Exercise 1
‣ Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations.
Dr Ö. Mete and Dr R. ApsimonCI Courses / MADX Introduction 18
survey.out
Exercise 1
‣ Step 4- Implement it in MADX format using thin lenses for all elements and verify your calculations.
x (m)-400 -300 -200 -100 0 100
z (m
)
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0
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![HIE-ISOLDE HEBT beam optics studies with MADX...Beam design and beam optics studies for the HIE-ISOLDE transfer lines [1, 2] have been carried out in MADX [3], and benchmarked against](https://static.fdocuments.net/doc/165x107/60aa044b38d1b849ad1106c3/hie-isolde-hebt-beam-optics-studies-with-madx-beam-design-and-beam-optics-studies.jpg)
