Applied superconductivity P. Tixador - CRYOCOURSE...

Cryocourse 2011Grenoble September 2011

Appliedsuperconductivity

P. Tixador

2

2011

2011: very special yearOne Hundred Years of Superconductivity

(April 8, 2011)

3

SC market

MRI + NMRPhysics

instruments

Energy Electronics

Total: 4300 MEuros (2009)

4

Main SC applications

27 km(100 km)

40 MW(900 MW)

26 000

5

Outline

Part I: Introduction Part II: SC electromagnetic behavior Part III: Composite structure Part IV: AC losses Part V: Quench Part VI: SC conventional materials Part VII: High Tc superconductors

Cryocourse 2011Grenoble Sept. 2011


I. Introduction

Pascal TIXADOR2

The beginning

Once upon a timein Leiden …

Pascal TIXADOR3

Step 1: July 10, 1908

First productionof liquid helium

HKO invented big science:lab. of international status (coldfactory) with a strong andnumerous technical support

Pascal TIXADOR4

Introduction - history

1908 First He liquefaction by H. Kammerling Onnes New unexplored territories opened Leiden “coldest place on earth” up to 1923

1911 Discovery of superconductivity for Mercury (Hg) April 8, 1911 “Mercury practically zero”

Pascal TIXADOR5

Kammerling Onnes’s notebook

“Mercury practically zero”

Pascal TIXADOR6

Discovery of superconductivity

ρ(T) metal studies

G. HolstOctober 26, 1911

Pascal TIXADOR7


1908 : He liquefaction 1911 : superconductivity discovery 1933 : Meissner effect 1957 : BCS microscopic theory 1958 : type II superconductors (NbSn, NbZr) 1960 : high current density in NbSn 1963 : quantum effects predictions by B. Josephson 1964 : first large scale SC application (Argonne bubble chamber)

1968 : multifilament composite definition (Rutheford Lab.) 1974 : CERN bubble chamber (830 MJ)

Pascal TIXADOR8

CERN bubble chamber (BEBC)

Øint = 3.7 mBo = 3.5 T

Wmag = 800 MJ

Pascal TIXADOR9


1908 : He liquefaction 1911 : superconductivity discovery 1933 : Meissner effect 1957 : BCS microscopic theory 1958 : type II superconductors (NbSn, NbZr) 1960 : high current density in NbSn 1963 : quantum effects predictions by B. Josephson 1964 : first large scale SC application (Argonne bubble chamber) 1968 : multifilament composite definition (Rutheford Lab.) 1974 : CERN bubble chamber (830 MJ) 1982 : first MRI images (commercial SC application)

Pascal TIXADOR10

SC applications MRI & NMR

600 MHz14.1 T

1 GHz23.4 T

26 000in operation

3T Philips®

11.7 T CEA

Pascal TIXADOR11

Introduction - history 1908 : He liquefaction 1911 : superconductivity discovery 1933 : Meissner effect 1957 : BCS microscopic theory 1958 : type II superconductors (NbSn, NbZr) 1960 : high current density in NbSn 1963 : quantum effects predictions by B. Josephson 1964 : first large scale SC application (Argonne bubble chamber) 1968 : multifilament composite definition (Rutheford Lab.) 1974 : CERN bubble chamber (830 MJ) 1982 : first MRI images (commercial SC application) 1987 : high Tc discovery 2007 : LHC starting, the biggest cryogenic and SC system

Pascal TIXADOR12

LHC the biggest cryogenic and SC system

1232 dipoles392 main quadrupoles

+ experiences (ATLAS,CMS…..)

ATLAS

CMS

Hello!

Hello!

Pascal TIXADOR13

LHC the biggest cryogenic and SC system

Hello!

Pascal TIXADOR14

Zero resistivity

0

2

4

6

8

0 50 100 150 200 250

Res

isti

vit

y (

µ!

.m)

T (K)

YBaCuO

Tc

Pascal TIXADOR15

Zero resistivity ?

Zero : no sense from experimental point of view===> lower value

τ measurement ==> R(ρ) meas.I. C. : t = 0 ; I = Io

!

RI + LdI

dt= 0

!

I = Ioe"t

# # =L

R

Pascal TIXADOR16

Miles and Files experiment (1962)

Experimental time constants :Run 1 : τ = 144 000 years ==> ρ < 10-25 Ωm

Field decreasing measurement ==> τ

Hours

Pascal TIXADOR17

Current supply

ich

IscIps

Powersupply

Heater

SCcoil

SC shunt with thermal control- heating : normal state, high resistance- no heating : SC state

(SC shunt with magnetic control too)

Pascal TIXADOR18

SC coil supply : end of cycle

Ips = 0 Isc

Ish

Isc

Ips

Ish

isc

time

Cur

rent

s

SC coil in persistent mode- no power supply- ultra stable current

Pascal TIXADOR19

Limits of non dissipative state

Three main limits

Temperature - Tc

Magnetic field - Hc / H*

Current density Jc

Pascal TIXADOR20

Critical temperature

0

50

100

150

200

1900 1920 1940 1960 1980 2000

Cri

tica

l te

mp

eratu

re (

K)

Years

Hg PbNb

3Sn

Nb3Ge

BaLaCuO

YBaCuO

BiSrCaCuO

HgBaCaCuO

HgBaCaCuO under pressure

TlBaCaCuO

N2 liquid (77 K)

He liquid (4.2 K)

MgB2

Pascal TIXADOR21

Critical current density Jc

Jc = Jc (T, B, ε) + orientation (SHTS)

0

500

1000

1500

2000

0 2 4 6 8 10 12 14

Jc (T) 10 T, 0,1 %

Nb3Sn

Jc (

A/m

m2)

T (K)

0

500

1000

1500

0 0,2 0,4 0,6 0,8 1

Jc( ) 10T, 4K

Nb3Sn

Jc (

A/m

m2)

Déformation (%)

!

!

0

2000

4000

6000

8000

10000

0 5 10 15 20

Jc(B) 4,2 K 0,1%

Nb3Sn

Jc (

A/m

m2)

B (T)

Pascal TIXADOR22


Jc = Jc (T, B, θ, ε)

0,1

1

10

100

1000

0 2 4 6 8 10

Bi-2223 PIT

Je (

MA

/m2)

B (T)

20 K

77 K

// ab plans

// c axis

// ab plans

// c axis

10

100

1000

0 2 4 6 8 10

Bi-2223 PIT

B // ab plans

Je (

MA

/m2)

B (T)

20 K

35 K

50 K

77 K

AMSC data

Pascal TIXADOR23


Jc = Jc (T, B, θ, ε) Stress effect

Conventional PITAMSC documents

Reinforced PIT

Pascal TIXADOR24

What is Jc ?

Jc criteria Electric field

0.1 µV/cm

1 µV/cm

Resistivity

ρ = 10-14 Ωm

Above Jc SC is dissipative

0,0

5,0

10,0

15,0

0 50 100 150 200 250

Ele

ctri

c fi

eld

(µ

V/c

m)

Current (A)

! = 10"14 # m

10 µV/cm

1 µV/cm

CurrentI

!

E =V

l

Pascal TIXADOR25

Empirical E(J) law - “n” value

Experimental E(I) curve (Bi-2223 /PIT @ 77 K, 0 T)

0

0,5

1

1,5

2

0 10 20 30 40 50

E (

µV

/cm

)

I (A)

39.5 A

Pascal TIXADOR26

Empirical E(J) law - “n” value

0

0,5

1

1,5

2

0 10 20 30 40 50

E (

µV

/cm

)

I (A)

39.5 A

"n" ! 17E = k I

16,83Empirical law

around Ic (Jc) :

E = Ec (I/Ic)n

Exponent n : “n value”Important quantity“quality” criteria

Magnet design, stability“n” is called alsoresistivity transition index

Pascal TIXADOR27

Critical surface

Tc & Hc: intrinsic Jc: elaboration Surface (deformation)

Important for SCstrand structure

SC in normal state : ρn high λ low

Nb3Sn

NbTi

Température(K)

Densité de courant

(MA/m2)

Induction magnétique

(T)

14 T25 T

Azote

liquide

(77 K)

Hélium

liquide

(4,2 K)

YBaCuO

10 K18 K

92 K

10 000

110 K

BiSrCaCuO

Current density

Fluxdensity

Temperature(K)



II. SC electromagneticbehaviour

2 Pascal TIXADOR

Superconductor behavior

Maxwell equations valid Curl E = -∂B/∂ t Curl H = j

Superconductor relation B (H) E (J)

3 Pascal TIXADOR

Macroscopic SC B(H) relation

MACROSCOPICALY (> 1/100 µm)a superconducting material

can be considered as non magneticexcept for very little fields

B = µo H

4 Pascal TIXADOR

Macroscopic SC B(H) relation

B

H

Hc2Hc1 Working area

5 Pascal TIXADOR

Macroscopic SC E(J) relation

0,0

5,0

10,0

15,0

0 50 100 150 200 250

Ele

ctri

c fi

eld

(µ

V/c

m)

Current (A)

Experimental E(I) curve

→ Relation valid forlocal current density

→ Infinite stiffness

0,0

5,0

10,0

15,0

Ele

ctri

c fi

eld

(µ

V/c

m)

Local current density (A/mm2)

Jc

MODEL

6 Pascal TIXADOR

E(J) relation - Critical State Model

Currentdensity

Electricfield

+Jc

-Jc

Critical statemodel

Local current density

ONLY THREE VALUES

→ O→ + Jc

→ - Jc

7 Pascal TIXADOR

E(J) relation - Bean model

Bean model:Critical state model

+Jc constant (B independent)

Bean model very usedfor analytical relations

8 Pascal TIXADOR

Bean model application

J=It/SResistive wire :

- uniform current density J = It/S

Transport current (It) distribution

Superconductive wire :-current density 0 / +Jc / -Jc (CSM)JcO

9 Pascal TIXADOR

Transport current distribution

JcO JcO JcO

-Jc

JcO

-Jc

-JcO

Time

Transport current

10 Pascal TIXADOR

Critical state model - “n” value

SC model in a finite element code FLUX3D®

Superconducting element:- non magnetic material, B = µo H- power law for E(J), E = Ec (J/lJl) (lJl/Jc)n

n = 1 resistive materialn = ∞ (high) critical state model

11 Pascal TIXADOR

Current distribution - single filament

-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1

i/Ic

t

SCCurrentsource

12 Pascal TIXADOR

To “decouple”: Litz wireFull transposition

Current distribution - multi filament

Filaments ”coupled” (twisted or not)

Currentsource …

9 filaments

Matrix

-1

-0,75

-0,5

-0,25

0

0,25

0,5

0,75

1

i/Ic

t

13 Pascal TIXADOR

Current distribution in a tape

B. Dutoit, EPFL

14 Pascal TIXADOR

Magnetization of a superconductor

Response of a SC to amagnetic field Lenz law Critical state model

J = O or ± Jc

Curl B = 0 or Curl B = µo Jc

HeHe

15 Pascal TIXADOR

Magnetization of a superconductor-M

oo

ooo

oo

o

4.2 K

non irradiatedirradiated

o. Experimental curve- Nb

-R.H. Kernohan et S.T. Sekula, 1967

16 Pascal TIXADOR

Magnetization of a superconductor

HeHe

17 Pascal TIXADOR

Experimental results

Magnetization measurement

18 Pascal TIXADOR

Magnetization curve (YBCO pellet)

-0,4

-0,2

0

0,2

0,4

0 0,2 0,4 0,6 0,8 1

µo M (T)

µoH

ext (T)

µo H

p

Courtesy

X. Chaud

19 Pascal TIXADOR

Remanent magnetization

20 Pascal TIXADOR

Remanent magnetization, field profile 2/2

21 Pascal TIXADOR

Floating magnet experiment

Interactions betweena YBCO pellet and

a permanent magnet

22 Pascal TIXADOR

Floating magnet - F(z)

-2

0

2

4

6

8

10

0 5 10 15 20 25

Fz

(N)

z (mm)

z

Magnet

SC

-0,4

-0,2

0

0,2

0,4

0 0,2 0,4 0,6 0,8 1

µo M (T)

µoH

ext (T)

µo H

p

F ≈ M Grad He Vsc

23 Pascal TIXADOR

Critical state model - “n” value

SC model in a finite element code FLUX3D

Superconducting element :- non magnetic material, B = µo H- power law for E(J):

n = 1 resistive material

n = ∞ (high) critical state model!

E = Ec

J

Jc

"

# $

%

& '

n

J

J

!

" =Ec

Jc

#

$ %

&

' (

24 Pascal TIXADOR

Plate submitted to an external field

2.4 mm

Be Be

0

5

10

15

20

0 10 20 30 40

E (

µV

/cm

)

J (MA/m2)

n = 500

n = 10n = 5

n = 1

Jc = 19,5 MA/m2

-60

-40

-20

0

20

40

60

0 5 10 15 20B (

mT

) t (ms)

15 ms

18 ms

Bmax

= 60 mT

(2 !o H

p)

25 Pascal TIXADOR

Plate submitted to an external field

Be Be

⊗

.

.

.

⊗

⊗

Be

Be Be

⊗

.

.

.

⊗

⊗

Be = µo Hp

Be Be.

.

.

⊗

⊗

⊗

.

.

.

⊗

⊗

⊗

Be

26 Pascal TIXADOR

Current distribution at t = 15 ms

0

100

200

300

400

0 0,2 0,4 0,6 0,8 1 1,2

t = 15 ms (B = - Bmax

)

n = 500

n = 1

n = 5

n = 10

J (

MA

/m2)

x (mm)

0

10

20

30

40

50

0 0,2 0,4 0,6 0,8 1 1,2

t = 15 ms (B = - Bmax

)

n = 500

n = 5

n = 10

J (

MA

/m2)

x (mm)

27 Pascal TIXADOR

Current distribution at t = 18 ms

-150

-100

-50

0

50

0 0,2 0,4 0,6 0,8 1 1,2

t = 18 ms

n = 500

n = 10

n = 5

n = 1J (x

) (M

A/m

2)

x (mm)

-40

-20

0

20

40

0 0,2 0,4 0,6 0,8 1 1,2

t = 18 ms

n = 500

n = 10

n = 5

J (x

) (M

A/m

2)

x (mm)

28 Pascal TIXADOR

Critical state model : conclusion

Critical state model valid for “n” > 10Valid for superconducting materials

Critical state model valid for HTSsuperconducting materials



III. Composite structure

2 Pascal TIXADOR

Orders of magnitude 1/4

Conventional superconductors operate at temperaturesclose to zero (5 K) and the specific heats are very low

0,001

0,01

0,1

1

10

10 100

Cp (

J/c

m3/K

)

T (K)

Cuivre

Hélium

NbTiTc

Specific heat :Internal material

brake againsttemperature rise

3 Pascal TIXADOR

Order of magnitude 2/4

W = Vol cp ∆T => ∆T = E / V cpEnergy

Volume

Specific heat

Temperature rise

NbTi @ 4 K: cp = 0. 005 J/cm3/K

0.005 J/cm3 ==> ∆T = 1 K

THERMAL EQUATION IN ADIABATIC CONDITIONS

4 Pascal TIXADOR


Temperature margin and related energy for NbTi

0,01

0,1

1

10

-0,2 0 0,2 0,4 0,6 0,8 1

Tcs

-To (K)

I/Ic

0 T

10 T

6 T

5 000

50 000

500

50

MQE (J/m3)

4 T

8 T

4 K andAdiabaticconditions

5 Pascal TIXADOR

Perturbations - origins

Mechanics wire motion under Lorentz force, micro-slips winding deformations, isolation failures, cracks

Electromagnetic flux-jumps AC loss

Nuclear events particles in particle accelerator magnets neutron flux in fusion

Thermics current leads, instrumentation wires heat leaks through thermal insulation, degraded cooling

6 Pascal TIXADOR

Perturbations - spectrum

Courtesy L. Bottura

7 Pascal TIXADOR


B

B = 5 T ; J = 1000 MA/m2 ; d = 1 µmJ B d = 5000 J/m3 = 0.005 J/cm3 => ∆T = 1 K

Displacement of a SC strand of a distance d

F = I B L = J B S L

W = F d = J B d Vol

d

J

!

"

8 Pascal TIXADOR

Real conditions - cooling effects

1

10

100

1000

10000

0 0,2 0,4 0,6 0,8 1

MQE

(µJ)

I/Ic

Bath He I

Adiabatic

NbTi strand@ 1.8 KLHC - CERN

P. Bauer, CERN

9 Pascal TIXADOR

Order of magnitude - conclusions

SC state very “unstable” Small temperature margins Low energy absorption possibilities

SC very sensitive to disturbances No wire displacement

Suitable structure to stabilize the sensitive SC state

Multifilament twisted composite

10 Pascal TIXADOR

Minimum propagating zone 1/3

Normal zone heating: WJoule = ρn J2 L S

Cooling by axial conduction: Wcond = 2 λ S ∂T/∂z

Normal zoneHeating : propagation

Cold SC zonescooling

ToTc

L/2

T

z3/2 L

superconductingsuperconducting normal

0

11 Pascal TIXADOR


If WJoule > Wcond ==> zone extension

If WCond > WJoule ==> zone resorption

Minimum propagatinglength

Heating of the normal zone :

Cooling by axial conduction :

!

WJoule = "n J2L S

!

WCond = 2 " S#T

# z

!

LMPZ =2 " Tc #To( )

$n J2

12 Pascal TIXADOR


Great interest for a materialwith high thermal and electrical conductivities

100

101

102

103

104

105

0 0,2 0,4 0,6 0,8 1 1,2

L' MPZ/LMPZ

ß

Cu

SSC/Stot

ρSC = 4 10-7 ΩmρCu = 2 10-10 Ωm

kSC = 0.3 W/m/KkCu = 400 W/K/m

!

LMPZ =2 " Tc #To( )

$n J2

13 Pascal TIXADOR

Mimimum propagation zone

Conclusion 1:

To embed the superconductor in a good

thermal and electrical conductor (Cu)

14 Pascal TIXADOR

Minimum propagation quench energy

F. Trillaud, CEA Saclay

15 Pascal TIXADOR

Minimum propagation quench energy

F. Trillaud, CEA Saclay

16 Pascal TIXADOR

Flux jump 1/5

“Flux jumps”at low temp.Experimental

Magnetizationcurves

J.L. Tholence et al.Solid State Com.,Vol. 65, 1988

17 Pascal TIXADOR

Flux jump 1/5

Flux jump :

thermal-magnetic instability due to

∂ cJ/∂T < O

18 Pascal TIXADOR

Flux jump 2/5

Thermal eventWire motionResin crack

∆T1

Decrease of Jc∂Jc/∂ t < 0 ∆Jc

∆Jc => variation of BFlux jump

(Curl B = µo Jc)dB/dt => electric field E(Curl E = - ∂B/∂ t)

Dissipated energy Q (∆Jc)Losses (E Jc)

∆T1 > ∆T1 => runaway INSTABLE

∆T2∆T2 < ∆T1 => resorption

STABLE

19 Pascal TIXADOR

Flux : calculation in a particular case

Be Be

Slab

x

zy

Lz = ∞

Ly = ∞2a

20 Pascal TIXADOR

Slab submitted to an external field

Be Be

⊗

.

.

.

⊗

⊗

Be

Be Be

⊗

.

.

.

⊗

⊗

Be = µo Hp

Be Be

⊗

.

.

.

⊗

⊗

Be > µo Hp

21 Pascal TIXADOR

Flux jump

BeBe

+Jc-Jc

∆Jc

2a

!

ptotal (t) = p(x) dx dy dz

slab

"""

!

ptotal (t) = µoJcdJc

dt

2a3

3LyLz

0 ≤ x ≤ a

!

E(x) = µo

dJc

dt

1

2x2 " a x

#

$ %

&

' (

p = E Jc : losses

!

p(x) = µo JcdJc

dt

1

2x2 " a x

#

$ %

&

' (

- Consequence of a Jc reduction (Be constant)

22 Pascal TIXADOR

!

"slab

Flux jump

BeBe

+Jc-Jc

∆Jc

2a

!

ptotal (t) = µoJcdJc

dt

2a3

3LyLz

!

ptotal (t) =dQ

dt

Energy dissipated by ∆Jc:

!

Qtotal = µoJc"Jca2

32aLyLz

!

Qtotal = µoJc"Jca2

3#slab

- Consequence of a Jc reduction (Be constant)

23 Pascal TIXADOR

Flux jump

BeBe

+Jc-Jc

∆Jc

2a

Energy dissipated by ∆Jc :

!

Qtotal = µoJc"Jca2

3#slab

!

Qtotal = µoJc"Jc"T

#

$ %

&

' ( )T

a2

3*slab

Slab in fully penetration

24 Pascal TIXADOR

Flux jump

Perturbation ∆T1

Decrease of Jc∂Jc/∂ t < 0 ∆Jc

∆Jc => variation of BFlux jump

(Curl B = µo Jc)dB/dt => electric field E(Curl E = - ∂B/∂ t)

Dissipated energy Q (∆Jc)Losses (E Jc)

∆T2∆T2 < ∆T1 => resorption

STABLE

25 Pascal TIXADOR

Flux jump

∆T1 ==>

Worst conditions : adiabatic conditions,energy absorbed only by the SC

Stability condition: ∆T2 < ∆T1

=> Limited size for stability <=

!

Qtotal = µoJc"Jc

"T#T

1

a2

3$slab

!

"T2

=Qtotal

c p #slab= µoJc

$Jc

$T"T

1

a2

3 cp

!

a <3 cp

µoJc"Jc

"T

Temperature rise of the SC:

26 Pascal TIXADOR

Flux jump - adiabatic criterion

!

" f <#

2

cp

µoJc$Jc

$T

Max diameter for stable flux jump:

!

Jc(T ,B) " J

c(T

o,B)

Tc(B) #T

Tc(B) #T

o

!

" f <#

2

cp Tc (B) $To( )µo Jc

2(To,B)

Adiabatic criterion

27 Pascal TIXADOR

Flux jump

SC must be subdivised into µm size filamentsBetween the filaments: Cu

Stability, protection

!

" f <#

2

cp Tc (B) $To( )µo Jc

2(To ,B)

cp = 5000 J/m3/KJc (4.2 K ; 5 T) = 3000 MA/m2

Tc (5 T) = 8 Ka < 64 µm NbTi

Experience shows that this value is pessimistic

Max diameter for stable flux jump:

28 Pascal TIXADOR

Temperature effect

0,001

0,01

0,1

1

10

10 100

Cp (

J/c

m3/K

)

T (K)

Cuivre

Hélium

NbTiTc

29 Pascal TIXADOR

Flux jump

Magnetizationexperimentalcurves

J.L. Tholence et al.Solid State Com.,Vol. 65, 1988

30 Pascal TIXADOR

Mimimum propagation zone

Conclusion 1 (MPZ):To embed the superconductor in a goodthermal and electrical conductor (Cu)

Conclusion 2 (Flux jump):To subdivide the superconductor in µm

size filaments

Filaments in a good thermal and electricalconducting matrix

31 Pascal TIXADOR

Problem

Electromagnetic coupling of the

filaments by the resistive matrix

32 Pascal TIXADOR

Coupling

Be Be

SCslab

SCslab

Res.slab

33 Pascal TIXADOR

Coupling

!

"

Be

!

L

A.N. : L = 100 m, ρt = 0.2 nΩmτ = 52 106 s (60 days ….)

Resistive areas : damping

+ other limit: Lc

Time constant of the dampingcurrents:

!

" #1

12µo

L2

$t

!

"t : transverse matrix resistivity

Diffusion(amag = ρ/µo)

34 Pascal TIXADOR

Coupling

!

"

Be

!

t >> "

« Coupled » slabs

!

"

Be

« Uncoupled » slabs

35 Pascal TIXADOR

Coupling

Be BeBe = Bmax sin (2πf) t

Current density(MA/m2)

!

1

f>>

1

12µo

L2

" t

!

1

f<<

1

12µo

L2

" t

36 Pascal TIXADOR

Coupling - decoupling filaments

M. N. Wilson« SC magnets »

Same phenomena for filaments

« Coupled » filaments, behaveas a single « big » filament

Unstable flux jump

« Decoupled » filaments,behave as independant

filamentsStable flux jump

37 Pascal TIXADOR

Coupling - decoupling filaments

Coupled filaments (twist pitch = 300 mm)

Decoupled filaments(twist pitch = 0.03 mm)

38 Pascal TIXADOR

To avoid coupling: twisting

Lp: twist pitch

!

" #1

12µo

L2

$t

Low

Filament twisting

Filament decoupling toavoid flux jump:

Limit for Lp: filament breaking (Lp > 5 Øbrin)

39 Pascal TIXADOR

Cryostabilization

The exchanges with the coolant have been neglected(adiabatic conditions)

Coolant: important and favorable part

0,001

0,01

0,1

1

10

10 100

Cp (

J/c

m3/K

)

T (K)

Cuivre

Hélium

NbTiTc

He : enthalpy tankR I2 < Wλ Sexc

Stekly cond.

40 Pascal TIXADOR

Exhanges with He

0

0,5

1

1,5

2

1 2 3 4 5 6

Cp (

J/c

m3/K

)

T (K)

!"

Teb

He

1 atm

Cp (NbTi, 4 K) = 0,005 J/cm

3/K

0

1

2

3

4

5

6

0 1 2 3 4 5

Cri

tica

l hea

t fl

ux (

W/c

m2)

T (K)

T!

He II1 atm

(180 °)

(90 °)

(0 °)

(Angle of inclination)

He I

41 Pascal TIXADOR

Conclusion : multifilament composite

SC embedded in a matrix with high electrical andthermal conductivity Increases MPZ and limit temperature rise (quench)

SC under the form of fine filaments Avoid flux jump

A very efficient cooling if possible (cryostabil.) An operation not to close the critical surf. Reduction of the perturbation on the SC Very good mechanics and electromagnetic shields

Stabilization achieved by :

42 Pascal TIXADOR

Multifilament composite

Fine SC filaments(tens of µm or lower)

Intrinsic stabilization

LMPZProtection (quench)Cooling and shielding

AC loss reduction

Stabilizing matrix (Cu)

Possible resistive barriers(CuNi)

43 Pascal TIXADOR

Multifilament composite - examples

44 Pascal TIXADOR

Multifilament composite - example

45 Pascal TIXADOR

Heat

treatments

SC composite elaboration

Twisting

46 Pascal TIXADOR

Alstom MSA processPROCEDE « SINGLE STACKING »

DESCENTE MONOtréfilage

étirage

Mise en hexasdébitage

BILLETTE MONOFILAMENTAIRE

MONTAGE MONO

HIP extrusionmontagedécapage Soudage

DESCENTE MULTI

ETAMAGE

tréfilage torsadage Calibrage final

TTH

étirage

TTH final

CABLAGE / TTH

BILLETTE MULTIFILAMENTAIRE

MONTAGE MULTI

47 Pascal TIXADOR

Billet

Furu

kawa

Ele

ctri

c co

mpa

ny

48 Pascal TIXADOR

Billet

Photos Alstom

49 Pascal TIXADOR

Drawing

Photo Alstom

50 Pascal TIXADOR

SC cables

Reduction on strand length (1/N) Current redistribution - higher stability Reduction of series turns (winding) Reduction of coil inductance

High currents (10 -200 kA) Large current supply and current leads

Strand current < 1000 A==> necessity for a multi strand cable

51 Pascal TIXADOR

SC cable examples

52 Pascal TIXADOR

Rutherford cables

Used for particule accelerator magnet coils

Flat two layer, slightlykeystoned cable with afew tens of strands,

twisted together.

53 Pascal TIXADOR

Cables in conduct (CICC)

Very high current cables used for fusion magnets

Cryostable cables

A large number of twistedSC strands inside a

metallic jacket wherehelium flows.

Large capacity to acceptlosses

Nb3Sn CICC

54 Pascal TIXADOR

Cable embedded in Aluminum

Cables for indirect cooling magnets(detector magnets)

Large Al section for stabilization

Cryocourse 2011Grenoble Septembre 2011


IV. AC losses

2 Pascal TIXADOR

Losses in SC (under critical surface)

Time constant electromagnetic environment No or very little losses

Depend on electromagnetic environment(magnetic field or current)

Time varying electromagnetic environment Losses, AC losses

HTS with low “n” value : resistive losses under Ic

3 Pascal TIXADOR

AC losses

Time varying electromagnetic environment

B: external field or self field

==> Electric field

==> Losses E Jc - AC losses

Curl E = - ∂B/∂ t Maxwell-Faraday law

4 Pascal TIXADOR

AC loss consequences (1/2)

SC operation Energetic cost Wmin

Qf

To - Tc

Tc

1ηf

=

0,1

1

10

100

1 10 100

Carn

ot

Inp

ut

Po

wer

Tc (K)

4 K : 74

77 K : 2.9

(Tc = 300 K)

5 Pascal TIXADOR

AC loss consequences (2/2)

Investment cryocooler cost

< 25 $/W> 30 % carnot< 12 W/W

Objective

100 - 200 $/W15-20 % carnot18-24 W/W

Now

Investment costRunning cost

65 K cryocooler costs

6 Pascal TIXADOR

Self field losses 1/2

Self field: field created by the transport currentThe conductor being alone or with little other conductors

Cable, single layer windings …

One expression: Norris formula

!

Pl

cp =µo f I c

2

"f (i) W /m[ ] i =

Imax

I c

#

$ %

&

' (

!

f (i) = 1" i( ) ln 1" i( ) + 2 " i( )i

2

!

f (i) = 1" i( ) ln 1" i( ) + 1+ i( ) ln 1+ i( ) " i2

Elliptical section

Rectangular section

7 Pascal TIXADOR

Self field losses 2/2

Reduction of self field losses:

Reduced conductor section Low operating factor

0,0001

0,001

0,01

0,1

1

0 0,2 0,4 0,6 0,8 1

Ellipse

Rectangle

Fit (0.4 i4)

f (i

)

i (Imax

/Ic)

!

Pl

cp =µo f I c

2

"f (i) W /m[ ] i =

Imax

I c

#

$ %

&

' (

8 Pascal TIXADOR

Hysteresis losses

Losses in superconducting twisted filaments

Hp = Jc Øf / πM = 2/3π Jc Øf

M = -2/3π Jc Øf

Hmax

M

H

He

9 Pascal TIXADOR

Hysteresis losses

M = 2/3π Jc Øf Hp

M = -2/3π Jc Øf

Hmax

-Hmax

M

H

10 Pascal TIXADOR

Hysteresis losses

Dissipated energy : cycle area

!

Wh

= µoM dH" J /m

3[ ]

M = 2/3π Jc Øf Hp

M = -2/3π Jc Øf

Hmax

-Hmax

M

H

11 Pascal TIXADOR

Hysteresis losses

Dissipated energy : cycle area

!

Wh

= µoM dH" J /m

3[ ]

M = 2/3π Jc Øf Hp

M = -2/3π Jc Øf

Hmax

-Hmax

W ≈ µo 2 Hmax x 2 Mr = µo 8/3π Hmax Jc Øf

!

Wh =8

3"Jc Øf Bmax J /m3[ ]

!

Ph = f Wh =8

3"Jc Øf f Bmax W /m3[ ]

M

H

12 Pascal TIXADOR

Hysteresis losses

!

Wh =8

3"Jc Øf Bmax J /m3[ ]

!

Ph = f Wh =8

3"Jc Øf f Bmax W /m3[ ]

Be

ØfFully

penetration

13 Pascal TIXADOR

Resistive

parts

Coupling losses (1/2)

Losses in the matrix by coupling currentinduced between SC filaments

B (transverse field)

Superconducting

filaments

Lp/2

! Induced currents

Pcc α Lp2 (dB/dt)2 / ρt

14 Pascal TIXADOR

Coupling losses 2/2 Non twisted filaments• Little coupling losses

o low resistivity favourable

Hysteresis loss reduction

Lc⊗ Be

Ic

Twisted filaments• High coupling losses

o high resistivity favourable

15 Pascal TIXADOR

Summary: AC loss reduction

Self field losses Conductor section reduction Low operating factor

Hysteresis losses (remanent field) Transverse field reduction Small SC twisted filaments

Coupling current losses (if twisted) High transverse resistivity matrix Short twist pitch (strand Ø)

16 Pascal TIXADOR

Conclusion: AC losses

AC loss accurate calculation Complex and hard task except in simple geometries

Numerical computation Useful tool but rapidly computing time problems

AC losses: an very important quantityo Thermal load for cryocoolero Interest itself of the SC device



V. Quench

2 Pascal TIXADOR

Quench-transition: loss of SC state

Origins Mechanical perturbations Weak zone (strand, cable) Non equilibrated current distribution Rapid current variation (loading …) Cooling fluid lack ...

A magnet is designed to avoid its quenchbut it can always occur

3 Pascal TIXADOR

Quench

To avoid quench Rigorous mechanical design

Good cooling conditions: HeII, cryostabilization

Important safety margins

4 Pascal TIXADOR

Quench

Equation in adiabatic conditions :

NbTi @ 4 KJc = 2000 A/mm2

(dT/dt)to ≈ 300 K/µs 103

104

105

106

107

108

109

0 0,2 0,4 0,6 0,8 1

(dT

/dt)

qu

ench

(K

/s)

Cu matrix

CuNi matrix

Ssc

/ Stot

!

S l cpdT

dt= R I

2= " j

2S l

!

dT

dt=" j

2

cp

5 Pascal TIXADOR

Quench

Known Strand

Calculation of the hot spot temperature

Hot spotcriterion

!

dT

dt= "n (T )

J (t)2

cp (T )

!

J (t)2dt =

cp (T )

"n (T )dT=>

!

J (t)2dt

0

"

# =cp (T )

$n (T )dT

To

Tmax

# = F (Tmax )

6 Pascal TIXADOR

Quench

1011

1012

1013

1014

1015

1016

1017

1018

1019

0 50 100 150 200 250 300 350 400

J2

sc (

t) d

t

Tmax

(K)

100 % Sc

30 % Sc,70 % CuNi

30 % Sc,70 % Cu

!0 0

"

F (

Tm

ax)

=

7 Pascal TIXADOR

Quench

Maximum temperature

In general, the magnet isdesigned not to overstep

80 K

0

1

2

3

4

5

0 100 200 300 400

!l/

l =

(

l(T

) -l

o )

/ l

o (

mm

/m)

Temperature (K)

Inox

Cu

Brass

Al

8 Pascal TIXADOR

Protection

Power supply

(current

source)

SC coil

inductance L

Rd: isolation - Rd Io = Vmax < 2 kV

Hypothesis: no propagation ==> J = Jo Exp(-t/τ)

!

F (Tmax ) = Jo2 Wmag

Vmax Io+ tdet

"

# $

%

& '

!

Vmax = Rd Io ; Wmag =1

2L Io

2

9 Pascal TIXADOR

Protection

!

F (Tmax ) = Jo2 Wmag

Vmax Io+ tdet

"

# $

%

& '

Wilson

10 Pascal TIXADOR

Protection

Quench detection as soon as possible

Switching off the power supply

Triggering heater to distribute energy

11 Pascal TIXADOR

Detection circuit 1/2

Bridge typeEquilibration at low current

12 Pascal TIXADOR

Detection circuit 2/2

V

kM

V = k R I + k L dI/dt - M dI/dt

k / kL = M ==> V = kRI



VI. SC conventionalmaterials

2 Pascal TIXADOR

NbTi & Nb3Sn: critical parameters

CostNbTi: 0.8-2 €/kA/mNb3Sn: 8-10 €/kA/m

Winding complex (“wind & react”)

23.2 T25.5 T10.4 K18 KNb3Sn

11 T14 T4.2 K9.5 KNbTi

µoHc2 (4.2 K)µoHc2 (1.8 K)Tc (11T)Tc (0T)

3 Pascal TIXADOR

NbTi & Nb3Sn : critical characteristics

0

2000

4000

6000

8000

4 6 8 10 12 14 16 18 20

Nb3Sn - 4,2 K

Nb3Sn "avancé" - 4,2 K

NbTi - 4,2 K

NbTi - 1,8 K

Induction magnétique (T)

Jcn

on

Cu (

MA

/m2)

4 Pascal TIXADOR

NbTi

Most widely SC used 2000 tons/y (NbTi strand)

Low cost ductile material

Ti content : 45-50 % wt Optimum in BC2

Very mature material

Little advances now

0

2000

4000

6000

8000

10000

12000

14000

0 2 4 6 8 10 12 14

T = 4.2 K

T = 1.8 K

Jc (A/mm

2) NbTi

B (T)

5 Pascal TIXADOR

NbTi wire example: LHC strands

Internal layer External layer

Ø strand 1.065 mm 0.825 mm

Ø filaments 7 µm 6 µm

Nomber of filaments 8900 6500

Ratio Cu/Non Cu 1.6 1.9

Twist pitch 25 mm 25 mm

Critical current strand 515 A (10 T, 1.9 K) 380 A (9 T, 1.9 K)

Strand number of the cable 28 36

Critical current cable 13750 A (10 T, 1.9 K) 12950 A (9 T, 1.9 K)

6 Pascal TIXADOR

LHC strand

Alstom strand

7 Pascal TIXADOR

Nb3Sn, A 15 material (15 tons/y)

Tc (0 T) = 18 K Tc (11T) = 10.4 K

µoHc2 (1.8 K) = 25.5 T µoHc2 (4.2 K) = 23 T

Jc (4 K, 10 T) ≈ 1200 A/mm2 Jc (4 K, 16 T) ≈ 300 A/mm2

==> High magnetic field material

Nb3Sn difficulties: strain sensitive, very brittle

“wind and react” technique

Winding when non brittle (Nb + Sn)And after reaction Nb + Sn => Nb3Sn

8 Pascal TIXADOR

Nb3Sn manufacturing

Four main methods of producing Nb3Sn wires Bronze Internal tin Modified Jelly Roll Powder in Tube (PIT)

Brittleness of Nb3Sn

Formed in situ at final stage

9 Pascal TIXADOR

Internal tin Nb3Sn wire

Strand developed for ITER Ø = 0.765 mm Jc = 635 A/mm2 - 12 T @ 4,2 K Heat treatment: 19 days

10 Pascal TIXADOR

Advances in Nb3Sn wires

3000 A/mm2 @ 12T, 4 K in Nb3Sn strands

Courtesy A. Devred

11 Pascal TIXADOR

Advances in Nb3Sn wires



VIII. High Tcsuperconductors

2 Pascal TIXADOR

HTS specificities

Relevant field for HTS:irreversibility field H*, not Hc2

HTSmaterials:

-YBaCuO

3 Pascal TIXADOR

HTS specificities

BaO

Y

CuO2

CuO

YBa2Cu3O7

CuO2

High anisotropy

caxis

abplan

C. Bougerol - CNRS-LCD. Dimos et al., Physical Review Letter, Vol. 61, 1988)

Orientationimportance

0,01

0,1

1

0 10 20 30 40Jc(i

nte

rgra

in)/

Jc(i

ntr

ag

rain

)

(!)Angle between grains (°)

Joint de grain

a2

!

" c

Grain 2 Grain 1

a1

Ca

4 Pascal TIXADOR

HTS

Ceramic type materials Very sensitive to default (G.B.)

Sintered

Textured

Epitaxial 1 10 100 1000 104

105

Jc (A/mm2)

Epitaxial film

Textured tape (OPIT)

Textured bulk

Sintered bulk

YBaCuOBi

Bi

Jc (77 K, 0T)

5 Pascal TIXADOR

Texturation

Sintered Textured

6 Pascal TIXADOR

Powder In Tube Bi wire

First generation ofHTS wires

Bi-2212 or Bi-2223 Km length EAS, Sumitomo, ...

1

10

100

1000

0 2 4 6 8 10

Je (A/mm

2)

B (T)

35 K

20 K

77 K B // axe c

Je (77 K, 0T) ≈ 100 A/mm2

7 Pascal TIXADOR

1G: PIT Bi wires

8 Pascal TIXADOR

Powder In Tube Bi wire

0,1

1

10

100

0 0,5 1 1,5 2

Je (A/mm

2)

B (T)

B // ab

B // c

T = 77 K

Bi-2223 OPIT

Magnet design should decreasethe transverse component

9 Pascal TIXADOR

Longitudinal and transverse fields

10 Pascal TIXADOR

PIT elaboration technique

ASC

11 Pascal TIXADOR

Bi PIT

Low J under field @ 77 K Ac losses High cost 300 €/kA/m (50 €/km/m)

Complex, far from limits Increasing SC ratio Alloys, resistive barriers Anisotropy reduction

0

250

500

750

1000

1990 1992 1994 1996 1998 2000

0

250

500

750

1000

Jc (A/mm2) ASC OPIT

77 K, 0 TEch. court

12 Pascal TIXADOR

Bi PIT: niche application high field

10

100

1000

10000

0 10 20 30 40

Jc (M

A/m

2)

Magnetic flux density (T)

Nb3Sn

1.8 K

Nb3Sn 4.2 K

NbTi

1.8 K

NbTi

4.2 K

Bi-2212 (RW) 4.2 K

13 Pascal TIXADOR

Coated conductors

2nd generation of HTS wire Y compound 100 m length

Great hopes Moderate cost High J under field @ 77 K

Large R & D programs

14 Pascal TIXADOR

Coated conductors

10

100

1000

10000

0 2 4 6 8 10 12 14

Ic (A/cm) CC @ 20 KIc (A/cm) CC @ 50 KIc (A/cm) CC @ 77 KIc (A/cm) PIT @ 20 KIc (A/cm) PIT @ 50 KIc (A/cm) PIT @ 77 K

Ic (A

/cm-w)


CC - 20 K

PIT - 20 K

PIT - 50 KCC - 50 K

CC - 77 KPIT - 77 K

0

500

1000

1500

0

1000

2000

3000

0 5 10 15

SuperPower YBCO tape(4 mm x 0.095 mm)

Ic (A) J

e (MA/m

2)

B (T)

4 K (Blg

)

20 K (Blg

)

40 K (Blg

)

4 K (Btr)

15 Pascal TIXADOR

Coated conductors - two main techniques

16 Pascal TIXADOR

RABiTS technique

Rolling-Assisted Biaxially Textured Substrate

Hot-rolling operationsand annealing

17 Pascal TIXADOR

IBAD technique

Metallic subtrate (SS) (some tens of µm)

YSZ layer withbiaxial texture

Buffer layer(CeO2, ...)

Ion Beam Assisted Deposition

100-150 A/cm tens of meter

18 Pascal TIXADOR

Superconducting materials

1G

2G

PIT BiSrCaCuOBi-2212 & Bi-2223

Coated conductorYBaCuO

10

100

1000

10000

100000

0 5 10 15 20 25 30

Jc (M

A/m

2)


20 K

20 K

50 K

50 K

77 K

77 K

Nb3Sn @ 4 K

NbTi @ 4 & 1,8 K

======= HTS =======

======= LTS =======

NbTi Nb3Sn

19 Pascal TIXADOR

HTC materials summary

Cost, cost

PIT: niche applications

CC: large hopes

20 Pascal TIXADOR

HTS current leads for the LHC

60082060-1202104

60002981300064

Current rating (A)Number

HTS

1720 electrical circuits, total current 1.7 MA

3286 current leads using Bi-2223 multi-filamentary tape

21 Pascal TIXADOR

HTC applications

First application : HTC current leads

Second application : HTC high field insert

22 Pascal TIXADOR

HTS insert Bi-2212 versus YBaCuO

High current cable Thermal treatment Cost

Thin tape (4 x 0.1 mm2) Lengths Large field anisotropy

Mechanical performances (100 MPa) Defect free lengths Niche conductor

Conductor of future Performances Jc & mechanics (700 MPa)

Round isotropic wire (Ø = 0.8 mm) High current cable (Rutherford) Bending radius (W & R)

YBaCuO (coated conductor)Bi-2212 (round wire)

23 Pascal TIXADOR

HTS insert Bi-2212 versus YBaCuO

YBCO Blg

YBCO Btr

Blg

Btr

Courtesy J. Fleiter

van der Laan

24 Pascal TIXADOR

MgB2

Superconductivity under 39 K discoveredin 2001 by J. Akimitsu (Tokyo)

Material known since 1953

Material used in chemist

Non expensive material

25 Pascal TIXADOR

MgB2

Light (2.4) & little resistive ( ρ(40 K) = 4 nΩm)

Very brittle material (A15)

µoHc2 (0 K) ≈ 15 T ; µoH* (4,2 T) > 14 T

26 Pascal TIXADOR

Critical current density (MgB2 filaments)

5K

20 K

µo He (T)

1000

100

1

Jc (MA/m2)

P.C. Canfield et al.

95

1



VIII.SC MAGNETS

Pascal TIXADOR2

SC strand-cable choice 1/2

Superconductor - NbTi - Nb3Sn - HTS Field level Cryogenics (4 K - 1.8 K - 30 K)

Conductor - assembled - CICC … Mechanical stresses Cooling technique

Pascal TIXADOR3

SC strand-cable choice 2/2

Filament diameter Stability Hysteresis losses Permanent currents (remanent field) Operating mode (continuous, pulsed)

Matrix Protection Coupling losses Cryostabilization

Pascal TIXADOR4

Constant current operation

ich

IscIps

Powersupply

Heater

SCcoil

SC shunt with thermal (or magnetic) control

→ Ultra constant current→ No power supply in normal operation→ No current lead losses (current leads removed)

(cold discharge resistances for protection)

Pascal TIXADOR5

Electromagnetic design - example

Need for 5 T in a bore of Ø 60 mm - h = 100 mmNo special requirements

5 T ==> Simpliest solution :NbTi @ 4.2 K (Helium bath)

Small coil : single strand

Pascal TIXADOR6

Value of current ?

Section flexibility (winding difficulties) number of turns

Power supply Current lead Realization Losses (prop. to the current)

Pascal TIXADOR7

Alstom wire (0.8 mm)24 NbTi filaments

0

100

200

300

400

500

0 2 4 6 8I c

(A

)B (T)

4,2 K0,1 µV/cm

5 Tfl

Ic = 190 Afl

Ie = 100 A

Pascal TIXADOR8

Coil design

Bo = 5 T ; I = 100 AAfter some iterations :

!

Bo =µo Ns I

h2 +D2

Pascal TIXADOR9

Field distribution

FLUX2D®

code

Bmax = 5.45 T

Bo = 5.1 T

Pascal TIXADOR10

Load line

0

50

100

150

200

250

0 2 4 6 8

Ic

B (T)

Load line(highest field )

120 A6.5 T

Operatingpoint

100 A ; 5.4 T

Criticalcharacteristic

Pascal TIXADOR11

Training

0

0,2

0,4

0,6

0,8

1

0 5 10 15 20 25 30

I qu

ench

/Ic (

sho

rt s

amp

le)

Test number

Pascal TIXADOR12

Cooled magnets

Possibility to extract losses by coolingfluid

Possible operation even with perturbations SC state recovery

Very stable magnets butlarge and expensive magnets

Pascal TIXADOR13

Cryostable magnets

Steckly criterion High matrix/SC ratio Low using factor Io/Ic

Large cooling surfaces Efficient cooling He I, 4.2 K - 1 atm He II, 1.8 K - 1 atm (Claudet bath)

Pascal TIXADOR14

Non cooled magnets

Little possibility to extract losses Reduction of the perturbations Very stable conductor Fine filaments, high Cu/SC ratio, low Io/Ic

Very good mechanical design Rigorous holding, shrinkage, impregnation

Protection from varying fields Electromagnetic shields

Pascal TIXADOR15

Field quality

Geometry Magnetic circuit magnetization SC filament magnetization Coupling losses Current non equilibrated distribution

Pascal TIXADOR16

Mechanics

Viriel theorem => very simple relationbetween magnetic energy and magnet mass

Wmag = (Mt - Mc) σu /d

Fundamental for SC magnets

Steel 30 kJ/kg ; Carbon fibers 150 kJ/Kg (ultimate data)

Classical value ≈ 10 kJ/kg (Record 13.4 kJ/kg)

Applied superconductivity P. Tixador - CRYOCOURSE...

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