Introduction to superconducting magnets* · A Brief History of the Superconductivity US Particle Accelerator School – Grand Rapids, MI – June 2012 2 ... First theoretical works

Mauricio Lopes – FNAL

Introduction to superconducting magnets*

US Particle Accelerator School – Grand Rapids, MI – June 2012

* From: “Superconducting Accelerator Magnets” by Paolo Ferracin, Ezio Todesco, Soren O. Prestemon and Helene Felice, January 2012

A Brief History of the Superconductivity

US Particle Accelerator School – Grand Rapids, MI – June 2012 2

Heike Kamerlingh Onne

1908 – Successfully liquified helium (4.2 K) 1911 – Discovered the superconductivity while measuring the conductivity of Mercury as function of temperature 1913 – Nobel prize


1933 – Walther Meissner and Robert Ochsenfeld discover perfect diamagnetic property of supeconductors. 1935 – First theoretical works on SC by Heinz and Fritz London 1950 – Ginzburg and Landau proposed a macroscopic theory for SC.

Meissner effect

A Brief History of the Superconductivity

Why using SC magnets?


𝐵𝑟 =𝑃

𝑞=

𝐾2 + 2𝐾𝐸𝑜

𝑞𝑐

Example: Lets calculate the magnetic rigidity for a 1 TeV proton:

𝐵𝑟 ≈1 𝑇𝑒𝑉

𝑐≈ 3333 𝑇. 𝑚

Let us assume a maximum field of 1.5 T; the circumference of such machine will be:

𝑟 = 2222 𝑚 𝐶 = 2𝜋𝑟 ≈ 14 𝑘𝑚

The Tevatron was the first machine to use large scale superconductor magnets with a 4.2 T in a 6.3 km circumference!

Critical surface


Critical surface for different SC materials


10

100

1,000

10,000

100,000

1,000,000

0 5 10 15 20 25 30 35

Applied Field, T

S

up

erc

on

du

cto

r C

riti

cal C

urr

en

t D

en

sit

y,

A/m

m²

YBCO: Tape, || Tape-plane, SuperPower (Usedin NHMFL tested Insert Coil 2007)

YBCO: Tape, |_ Tape Plane, SuperPower (Usedin NHMFL tested Insert Coil 2007)

Bi-2212: non-Ag Jc, 427 fil. round wire, Ag/SC=3(Hasegawa ASC-2000/MT17-2001)

Nb-Ti: Max @1.9 K for whole LHC NbTi strandproduction (CERN, Boutboul '07)

Nb-Ti: Nb-47wt%Ti, 1.8 K, Lee, Naus andLarbalestier UW-ASC'96

Nb3Sn: Non-Cu Jc Internal Sn OI-ST RRP 1.3mm, ASC'02/ICMC'03

Nb3Sn: Bronze route int. stab. -VAC-HP, non-(Cu+Ta) Jc, Thoener et al., Erice '96.

Nb3Sn: 1.8 K Non-Cu Jc Internal Sn OI-ST RRP1.3 mm, ASC'02/ICMC'03

Nb3Al: RQHT+2 At.% Cu, 0.4m/s (Iijima et al2002)

Bi 2223: Rolled 85 Fil. Tape (AmSC) B||, UW'6/96

Bi 2223: Rolled 85 Fil. Tape (AmSC) B|_, UW'6/96

MgB2: 4.2 K "high oxygen" film 2, Eom et al.(UW) Nature 31 May '02

MgB2: Tape - Columbus (Grasso) MEM'06

2212 round wire

2223 tape B|_

At 4.2 K Unless Otherwise Stated

Nb3Sn Internal Sn

Nb3Sn 1.8 K

2223 tape B||

Nb3Sn ITER

MgB2 film

MgB2

tape

Nb3Al: RQHT

1.9 K LHC

Nb-Ti

YBCO B||c

YBCO B||ab

NbTi Parameterization


7.1

0

0 1C

CCT

TBTB

where BC0 is the critical field at zero temperature (BC0 ~14.5 T)

7.1

0_

11),(

cccrefc

c

T

T

B

B

B

B

B

C

J

TBJ

where JC_ref is the critical current density at 4.2 K and 5 T (JC_ref ~ 3000 A/mm2); C, , and are fitting parameters:

C ~ 31.4 T ~ 0.63 ~ 1.0 ~ 2.3

(Lubell’s formula)

(Bottura’s formula)

Nb3Sn Parameterization


22

0

2

)(1

),(1

)(),,(

cc

cT

T

TB

B

B

CTBJ

)(77.11

)(31.01

)(1

),(

0

2

0

2

00

cccc

c

T

TLn

T

T

T

T

B

TB

where:

2/17.1

_0 1)( mCC

7.1

_0 1),( mcc BTB

3/17.1

_00 1)( mcc TT

and:

= 900 = -0.003 Tc0_m = 18K C0_m = 48500 AT1/2/mm2 (for Jc = 3000 A/mm2 @ 4.2 K and 12 T)

(Summer’s formula)

Strand Fabrication


Superconducting cables

• Most of the superconducting coils for particle accelerators are wound from a multi-strand cable.

• The advantages of a multi-strand cable are: – reduction of the strand piece length; – reduction of number of turns

• easy winding; • smaller coil inductance

– less voltage required for power supply during ramp-up; – after a quench, faster current discharge and less coil voltage.

– current redistribution in case of a defect or a quench in one strand.

• The strands are twisted to – reduce interstrand coupling currents (see interfilament coupling currents)

• Losses and field distortions

– provide more mechanical stability

• The most commonly used multi-strand cables are the Rutherford cable and the cable-in-conduit.


Superconducting cables • Rutherford cables are fabricated by a cabling machine.

– Strands are wound on spools mounted on a rotating drum.

– Strands are twisted around a conical mandrel into an assembly of rolls (Turk’s head). The rolls compact the cable and provide the final shape.


Superconducting cables

• The final shape of a Rutherford cable can be rectangular or trapezoidal. • The cable design parameters are:

– Number of wires Nwire

– Wire diameter dwire

– Cable mid-thickness tcable

– Cable width wcable

– Pitch length pcable

– Pitch angle cable (tan cable = 2 wcable / pcable) – Cable compaction (or packing factor) kcable

– i.e the ratio of the sum of the cross-sectional area of the strands (in the

direction parallel to the cable axis) to the cross-sectional area of the cable.

• Typical cable compaction: from 88% (Tevatron) to 92.3% (HERA).

cablecablecable

wirewirecable

tw

dNk

cos4

2



Cable insulation

• The cable insulation must feature – Good electrical properties to withstand

high turn-to-turn voltage after a quench.

– Good mechanical properties to withstand high pressure conditions

– Porosity to allow penetration of helium (or epoxy)

– Radiation hardness

• In NbTi magnets the most common insulation is a series of overlapped layers of polyimide (kapton).

• In the LHC case: – two polyimide layers 50.8 µm thick

wrapped around the cable with a 50% overlap, with another adhesive polyimide tape 68.6 µm thick wrapped with a spacing of 2 mm.


Superconducting Magnets Design Perfect dipole

-60

0

60

-40 0 40

+

+-

-

-60

0

60

-40 0 40

+

+-

-

A wall-dipole, cross-section A practical winding with flat cables

1 - Wall dipole (similar to the window frame magnet)


Superconducting Magnets Design Perfect dipole

2 - Intersecting ellipsis

-60

0

60

-40 0 40

+

+-

-

-60

0

60

-40 0 40

+

+-

-

Intersecting ellipses A practical (?) winding with flat cables


Intersecting Cylinders


within a cylinder carrying uniform current j0, the field is perpendicular to the radial direction and proportional to the distance to the center r: Combining the effect of the two cylinders Similar proof for intersecting ellipses

2

00 rjB

0sinsin2

2211

00

rrrj

Bx

sj

rrrj

By2

coscos2

00

2211

00

Superconducting Magnets Design Perfect dipole 3 – Cos() current distribution

-60

0

60

-40 0 40

+

+-

-j = j0 cos


Superconducting Magnets Design Perfect quadrupole


-60

0

60

-40 0 40

+

+

- - j = j 0 cos 2

- -

+

+

Quadrupole as an ideal cos2

-60

0

60

-40 0 40

+

+

- -

- -

+

+

Quadrupole as two intersecting ellipses

Dipole design using sector coils


-60

0

60

-40 0 40

+

+-

-j = j0 cos

+

+

-

-

w

r

1

1

)(n

n

ref

nR

zCzB

n

ref

ref

nz

R

R

IC

0

0

2

0

0

0

01

cos

2

1Re

2 z

I

z

IB

ddjI

sin2cos

22 00

1 wj

ddj

B

wr

r

Multipoles of a dipole sector coil


wr

r

n

n

refwr

r

n

n

ref

n ddinRj

ddinRj

C 1

1

0

1

0)exp(

)exp(

22

r

wRjB

ref1log)2sin(

0

2

n

rwr

n

nRjB

nnn

ref

n

2

)()sin(2 221

0

for n = 2

for n > 2

wrr

jRB

ref 11

3

)3sin(2

0

3

33

4

0

5

11

5

)5sin(

wrr

jRB

ref

for =/5 (36°) or for =2/5 (72°) B5=0 for =/3 (60°) B3=0

Multi-sector dipole coil


0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

1

23

wrr

jRB

ref 11

3

3sin3sin3sin 123

2

0

3

33

123

4

0

5)(

11

5

5sin5sin5sin

wrr

jRB

ref

0)5sin()5sin()5sin(

0)3sin()3sin()3sin(

123

123

(48°,60°,72°) or (36°,44°,64°) are some of the possible solutions

[0°-43.2°, 52.2°-67.3°] sets also B7 = 0 !

Multi-sector dipole coil


0)3sin()3sin()3sin()3sin()3sin( 12345




0)11sin()11sin()11sin()11sin()11sin( 12345 (B3, B5 and B7) = 0

[0°-33.3°, 37.1°- 53.1°, 63.4°- 71.8°] sets (B3, B5, B7 , B9 and B11) = 0!

Examples


0

20

40

60

0 20 40 60x (mm)

y (

mm

)RHIC main dipole - 1995 Tevatron main dipole - 1980

0

20

40

60

0 20 40 60x (mm)

y (

mm

)

Two layer design


0

50

0 50

1

2

r

w

wrwrwrrB

2

11)3sin(

11)3sin( 213

3323315)2(

1

)(

1)5sin(

)(

11)5sin(

wrwrwrrB

0

20

40

60

80

0 20 40 60 80x (mm)

y (

mm

)

72o

37o

0

15

30

45

60

75

90

0.0 0.1 0.2 0.3 0.4 0.5 0.6

w/r (adim)

Angle

(deg

rees)

a1 - first branch a2 - first branch

a1 - second branch a2 - second branch

1 2

21

Tevatron main dipole

Quadrupole design using sector coils


-50

0

50

-50 0 50

+

+

+

+

--

- -

r w

1

1

)(n

n

ref

nR

zCzB

n

ref

ref

nz

R

R

IC

0

0

2

2

0

0

2

0

0

2

2cos

2

1Re

2 z

RI

z

RIB

refref

ddjI

r

wRjdd

RjB

refwr

r

ref1ln2sin

42cos

28

0

0

2

0

2

Multipoles of a quadrupole sector coil


44

5

0

6

11

6

)6sin(

wrr

jRB

ref

88

8

0

10

11

10

)10sin(

wrr

jRB

ref

for =/6 (30°) one has B6 = 0

for =/10 (18°) or =/5 (36°) one sets B10 = 0

It follows the same philosophy of the Dipole design!

Examples


Tevatron main quadrupole

0

20

40

0 20 40 60 80x (mm)

y (

mm

)

RHIC main quadrupole

0

20

40

0 20 40 60 80x (mm)

y (

mm

)

~[0°-12°, 18°-30°] ~[0°-18°, 22°-32°]

0

20

40

0 20 40 60 80x (mm)

y (

mm

)

LHC main quadrupole

~[0°-24°, 30°-36°]

Peak field and bore field ratio (l)


0

20

40

60

80

0 20 40 60 80x (mm)

y (

mm

)

LHC main dipole – location of the peak field

0

20

40

60

80

0 20 40 60 80x (mm)

y (

mm

)

RHIC main dipole – location of the peak field

0

20

40

60

80

0 20 40 60 80x (mm)

y (

mm

)

Tevatron main dipole – location of the peak field

Peak field and bore field ratio (l)


1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 20 40 60 80width (mm)

l (

adim

)

1 layer 60

1 layer 48-60-72

1 layer 42.8-51.6-67

1 layer three blocks

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 20 40 60 80width (mm)

l (

adim

)

1 layer 60

1 layer 48-60-72

1 layer 42.8-51.6-67

1 layer three blocks

Fit

w

arrw 1~),(l a ~ 0.045

Examples


1.0

1.1

1.2

1.3

0.0 0.5 1.0 1.5 2.0equivalent width w/r

l [

adim

]

TEV MB HERA MB

SSC MB RHIC MB

LHC MB Fresca

MSUT D20

HFDA NED

Operational Margin


24 %

Lorentz Forces


• A superconducting accelerator magnet has a large magnetic stored energy

• A quench produces a resistive zone

• Current is flowing through the magnet

• The challenge of the protection is to provide a safe conversion of the magnetic energy to heat in order to minimize – Peak temperature (“hot spot”) and temperature gradients in the magnet

– Peak voltages

• The final goal being to avoid any magnet degradation – High temperature => damage to the insulation or stabilizer

– Large temperature gradient => damage to the conductor due to differential thermal expansion of materials

Joule Heating Voltages (R and L)

Quench protection



Quench

Normal zone growth

Detection

Power supply

switched off Protection

heaters Extraction Quenchback

Trigger protection options

Current decay in the magnet

I

t

Magnetic energy

Converted to heat by Joule heating

General quench protection diagram

The faster this chain happens the safer is the magnet

Training


Magnetization


Magnetization


Magnetization


Summary


• Design and Fabrication of Superconducting Magnets belong to a different Universe

• Although the mathematical formulation for the field generation is shared, the design of superconducting magnets involves many other aspects:

o Thermal considerations o Mechanical Analysis o Fabrication techniques o Quench Protection o Material Science

• If one is interested to learn more about superconducting magnet, one should

attend to the Superconducting Accelerator Magnets USPAS course. The material for that course can be found at:

http://etodesco.web.cern.ch/etodesco/uspas/uspas.html

Next…


Unusual design examples

Documents

Introduction to superconducting magnets* · A Brief History of the Superconductivity US Particle Accelerator School – Grand Rapids, MI – June 2012 2 ... First theoretical works