Introduction to Accelerator Physics · Page 15 Superconductivity 12.5 kA normal conducting cables...

Introduction to Accelerator PhysicsPart 4

Pedro Castro / Accelerator Physics Group (MPY)Hamburg, 24th July 2018

Circular accelerators: the synchrotron

vacuum chambermagnet

accelerating device

injector

straight sections

| Introduction to Accelerator Physics | Pedro Castro, 24th July 2018

Low Energy Antiproton Ring (LEAR) at CERN



Dipole magnet

beam


vacuum chambermagnet

accelerating device

injector

straight sections


(circular motion)

� ⊥ �� → � = �� ⊥ �� → � = ��

�� = �

� → � = (�)�� = ��

�


Electromagnet

permeability of iron = 300…10000 larger than air

�

Dipole magnet

beam

air gap

flux lines

beam

Ampere’s law:

�

�� = � ��

+� ��"�#

= $�

� �%��

+� �%& ��"�#

= $�

� �%& ��"�#

= �'%& = $�

� = %&$�'

gap height

N

S

�� = �( )*�+(, = $�

Dipole magnet cross section

increase B � increase current, but power dissipated P = � ∙ �� large conductor cables


water cooling channels

Dipole magnet

beam

iron

currentloops


C magnet + C magnet = H magnet

beam

Dipole magnet cross section (another design)

beam

Dipole magnet cross section (another design)

beam

water cooling tubes

current leads

Power dissipated: 2IRP ⋅=

beam

Superconductivity12.5 kAnormal conducting cables

12.5 kAsuperconducting cable

increase B � increase current, but power dissipated P = � ∙ �� large conductor cables� saturation effects

Saturation of iron

I [A]

Saturation of iron: 1.6 – 2 T

B vs H curve for iron


Superconducting dipole magnets

superconducting dipoles

LHC

HERA

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


Superconducting dipole magnets

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 =

�

�� ∙ �� = %&�( )*�+(,

Dipole field inside 2 conductors

densitycurrentuniform=J

J JB Br


JJ

0=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


JJ

0=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:


JJ

constant vertical field

B.

beam

dJ

By 20µ=

.B

56 mm

15 mm x 2 mm

From the principle … to the reality…

LHC dipole coils in 3D

p beam

p beam

15 mm x 2 mm

Aluminium collar

LHC dipole coils in 3D

Bp beam

p beam

I

Computed magnetic field

Bferromagnetic iron

nonmagnetic collars

56 mm

LHC dipole magnet (cross -section)

beam tubes

superconducting coils

nonmagnetic collars

ferromagnetic iron

steel container for He

insulation vacuum

supports

vacuum tank

1 m

p

p

Superconducting dipole magnetsLHC dipole magnet interconnection:

Summing-up of this part


RF cavities:pill-box cavity

superconducting cavities

Dipole magnets:normal conducting dipoles

superconducting dipoles


Contact

Deutsches Elektronen-Synchrotron

www.desy.de

Pedro [email protected]

Introduction to Accelerator Physics · Page 15 Superconductivity 12.5 kA normal conducting cables...

Documents

Transcript of Introduction to Accelerator Physics · Page 15 Superconductivity 12.5 kA normal conducting cables...