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Introduction to Accelerator PhysicsPart 4
Pedro Castro / Accelerator Physics Group (MPY)Hamburg, 24th July 2018
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Page 2
Circular accelerators: the synchrotron
vacuum chambermagnet
accelerating device
injector
straight sections
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 3
Low Energy Antiproton Ring (LEAR) at CERN
Circular accelerators: the synchrotron
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 4
Dipole magnet
beam
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 5
vacuum chambermagnet
accelerating device
injector
straight sections
Circular accelerators: the synchrotron
(circular motion)
� ⊥ �� → � = ���� ⊥ �� → � = ��
�� = �
� → � = (�)������� = ��������
�
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 6
Electromagnet
permeability of iron = 300…10000 larger than air
�
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Page 7
Dipole magnet
beam
air gap
flux lines
beam
Ampere’s law:
�
���� = � ������
+� ���"�#
= $�
� �%��� �����
+� �%& ��"�#
= $�
� �%& ��"�#
= �'%& = $�
� = %&$�'
gap height
N
S
���� = �( )*�+(, = $�
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Page 8
Dipole magnet cross section
increase B � increase current, but power dissipated P = � ∙ ��� large conductor cables
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Page 9
Dipole magnet cross section
water cooling channels
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Page 10
Dipole magnet cross section
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Page 11
Dipole magnet
beam
iron
currentloops
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Page 12
Dipole magnet cross section
C magnet + C magnet = H magnet
beam
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Page 13
Dipole magnet cross section (another design)
beam
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Page 14
Dipole magnet cross section (another design)
beam
water cooling tubes
current leads
Power dissipated: 2IRP ⋅=
beam
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Page 15
Superconductivity12.5 kAnormal conducting cables
12.5 kAsuperconducting cable
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Page 16
increase B � increase current, but power dissipated P = � ∙ ��� large conductor cables� saturation effects
Saturation of iron
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Page 17
I [A]
Saturation of iron: 1.6 – 2 T
B vs H curve for iron
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 18
Superconducting dipole magnets
superconducting dipoles
LHC
HERA
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Page 19
Superconducting dipole magnets: cross section
Tevatron HERA RHIC LHC
Fermilab DESY Brookhaven CERNChicago (USA) Hamburg (Germany) Long Island (USA) Geneva (Switzerland)
4.5 T 5.3 T 3.5 T 8.3T
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018
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Page 20
Superconducting dipole magnets
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Page 21
Dipole field inside 1 conductor
B
Ampere’s law:
r
�� ∙ ��� = ���� = 201� = %&01�2
2: uniform current density
2
� = %&22 1
θr
θµsin
20 rJ
Bx −=
θµcos
20 rJ
By =
�
�� ∙ ��� = %&�( )*�+(,
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Page 22
Dipole field inside 2 conductors
densitycurrentuniform=J
J JB Br
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Page 23
Dipole field inside 2 conductors
JJ
0=J
densitycurrentuniform=J
θµsin
20 rJ
Bx −=
θµcos
20 rJ
By =
)sinsin(2 22110 θθµ
rrJ
Bx +−=
)coscos(2 22110 θθµ
rrJ
By −=
.
superposition:
one conductor:
1θ1r
2θ2r
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Page 24
Dipole field inside 2 conductors
JJ
0=J
densitycurrentuniform=J
θµsin
20 rJ
Bx −=
θµcos
20 rJ
By =
1θ1r
2θ2r
)cos(cos 2211 θθ rrd −+=
2211 sinsin θθ rrh ==
0)sinsin(2 22110 =+−= θθµ
rrJ
Bx
dJ
rrJ
By 2)coscos(
20
22110 µθθµ =−=
.
one conductor:
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Page 25
Dipole field inside 2 conductors
JJ
constant vertical field
B.
beam
dJ
By 20µ=
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Page 26
.B
56 mm
15 mm x 2 mm
From the principle … to the reality…
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Page 27
LHC dipole coils in 3D
p beam
p beam
15 mm x 2 mm
Aluminium collar
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Page 28
LHC dipole coils in 3D
Bp beam
p beam
I
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Page 29
Computed magnetic field
Bferromagnetic iron
nonmagnetic collars
56 mm
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Page 30
LHC dipole magnet (cross -section)
beam tubes
superconducting coils
nonmagnetic collars
ferromagnetic iron
steel container for He
insulation vacuum
supports
vacuum tank
1 m
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Page 31
p
p
Superconducting dipole magnetsLHC dipole magnet interconnection:
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Page 32
Summing-up of this part
Circular accelerators: the synchrotron
RF cavities:pill-box cavity
superconducting cavities
Dipole magnets:normal conducting dipoles
superconducting dipoles
| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018