Carmine SENATORE

Superconductivity and its applications

Lecture 1

Département de Physique de la Matière QuantiqueUniversité de Genève

Scope & Summary

• Phenomenology

• An introduction to electrodynamics of superconductors

• The Ginzburg-Landau theory

• Interactions in the vortex line system, focused on pinning phenomena, critical state and thermal effects on vortex dynamics

• An overview of the superconducting materials, addressing also the properties of superconducting wires and cables

• Superconductor Technology: basic design and operation issues of a superconducting device

Discovery of Superconductivity in 1911

Ability to carry a current without dissipation

• Transport of energy

• Generation of high magnetic fields

Loss-less currents cannot exceed the critical current Ic

1000+ superconducting compounds, very few for practical use

temperature

resi

stiv

ity

Tc

0

Drawbacks:

Superconductors Today

Medical Imaging and

NMR spectroscopy

Superconductors Today

Medical Imaging and

NMR spectroscopy

Superconductivity and LHC

Higgs boson

Superconductors Today

Superconductivity and LHC

Higgs boson

1200 dipole magnets

400 quadrupole magnets

Along the 27 Km of LHC

1200+ tonnes of NbTi @ 1.9K

Superconductors Today

Superconductivity and LHC

Uniform field (dipole)

x

y z

(a)

x

y z

(b) Gradient field (quadrupole)

Bending the beam Focusing the beam

The FCC playground

LHC27 km, 8.33 T

14 TeV (c.o.m.)1300 tons NbTi

FCC-hh80 km, 20 T

100 TeV (c.o.m.)9000 tons LTS2000 tons HTS

FCC-hh100 km, 16 T

100 TeV (c.o.m.)6000 tons Nb3Sn

3000 tons NbTi

HE-LHC27 km, 20 T

33 TeV (c.o.m.)3000 tons LTS700 tons HTS

Geneva

PS

SPS

LHC

Courtesy of L. Bottura (CERN)

The idea of a Future Circular Collider @ 100 TeV

Superconductors Today

Medical Imaging and

NMR spectroscopy

Superconductivity and LHC

Higgs boson

High speed trains

by magnetic levitation

Superconductors Today

High speed trains

by magnetic levitation

The line between Tokyo and Osaka (550 Km) is under construction

Superconductors Tomorrow

Power distribution, generation and storage

20% from renewable sources by 2020superconducting cables

fault current limiters

energy density of the

magnetic field

BE

21

2

New medical applications:

Compact accelerators for

hadron therapy

A big step to get there…

Superconductors HistoryNbTi

Nb3Sn

MgB2

Bi2223

Bi2212

1900 1940 1980 1985 1990 1995 2000 2005 2010 20150

10

20

30

40

50

100

150

200

PbMo6S

8

H2S @ 140 GPa

AEFeAs

LaFeAsO

LaFePO

FeSe-1 layer

HgBaCaCuO @ 30 GPa

Night on

the Moon

Surface of Pluto

Liquid nitrogen

Liquid neon

Liquid hydrogen

Liquid helium

FeSeTe

SmFeAsO

HgTlBaCaCuO

HgBaCaCuO

TlBaCaCuO

BiSrCaCuO

LaBaCuO

YBaCuO

YC6

CaC6

CNT

diamondCNT

K3C

60

RbCsC60

CeCoIn5UPd

2Al

3CeCu2Si

2UPt

3

MgB2

BKBONb3Ge

V3Si

Nb3Sn

NbN

NbTiNbPb

Hg

Tem

per

atu

re [

K]

Year Y123

Superconductors Pre-History

A great physics problem in 1900:

What is the limit of electrical resistivity at the absolute zero ?

… electrons flowing through a conductor would come to a complete halt or, in other words, metal resistivity will become infinity at absolute zero.

W. Thomson (Lord Kelvin)

"There is nothing new to be discovered in physics now. All that remains is more and more precise measurement”

“I have not the smallest molecule of faith in aerial navigation other than ballooning or of expectation of good results from any of the trials we hear of”

“X-rays are an hoax”

temperature

resi

stiv

ity

Superconductors Early History

… thus the mercury at 4.2 K has entered a new state, which, owing to its particular electrical properties, can be called the state of superconductivity…

H. Kamerlingh-Onnes (1911)

1913

Onnes in 1913 conceived a 10 T magnet

What he pointed out:

• The impossibility of doing this with Cu cooled by liquid air (as expensive as a warship)

• The possibility of doing it with superconductor (1000 A/mm2 with a Hg wire, 460 A/mm2 with a Pb wire)

A « little » problem!

• Resistance developed at 0.8 A, not 20 A• 48 years had to go by before the path to high field

superconducting magnets was cleared

Superconductors Early History

The great silence: 1914-1961

Abolish Ohm’s law !

J E holds also for superconductors

0

, J is finite E = 0J

BE

c t

1From the Maxwell equation

BE B const.

t

0 0

B = constant

T < Tc

H = 0

T < Tc

H 0

T > Tc

H 0

T < Tc

H 0

This would imply that superconductivity is not a thermodynamic state !!

Some ingredients are missing...

The Meissner–Ochsenfeld effect - B = 0 !

T < Tc

H = 0

T < Tc

H 0

T > Tc

H 0

T < Tc

H 0

Superconductor = Perfect Conductor + Perfect Diamagnetism

Superconducting Phase Diagram

temperature

ma

gn

etic

fi

eld

Tc0

Hc(0)

c c

c

TH T H

T

2

0 1S

N

Type-I and Type-II superconductors

H

-4πM

Hc0 H < Hc

Type-IHc 10-3 – 10-2 T

H

-4πM

Hc20 Hc1H < Hc1 Hc1 <H < Hc2

Type-IIHc2 10 – 102 T

-4πM = H - B

Thermodynamics of the superconducting state

Legendre transformation Legendre transformationU(S,V,B) F(T,V,B) G(T,P,H)

dG VdP SdT BdH

1

4

The differential of the Gibbs free energy is

Thermodynamics of the superconducting state

1st case: T = T’ , normal state , field sweep from 0 to H*

H

N N

HG T H G T BdH

**2

0

1( ', *) ( ',0)

4 8

2nd case: T = T” , superconducting state , field sweep from 0 to H*< Hc

S SG T H G T( ", *) ( ",0) 0

At H = Hc S c N cG (T ,H ) G (T ,H ) cN

HG (T , )

2

08

and thus S NG (T , ) G (T , )0 0 cH

2

8

Entropy: ΔS @ H = 0 and T < Tc

P ,H

GS

T

N S N SS S G GT

cHd

dT

2

8c

c

dHH

dT

1

4

S NS S cc c

c

dHTH T H

T dT

2

0 1 0

Specific heat: Δc @ Tc

P ,H

Sc T

T

S N S Nc c T S ST

cc

dHdT H

dT dT

1

4

c cc

dH d HTH

dT dT

2 2

24

c

c cS N T

T dHc c

dT

2

4At T = Tc

If it is a superconductor, then…

temperature

resi

stiv

ity

Tc

0

1

T < Tc

H < Hc

2 3

Phenomenological theories: The London Theory

dv e vE v h

dt m c

1

S Sv v x ,y ,z ,t S S

S S

dv v(v ) v

dt t

SS S S

vv v v

t

21

2

SS S S S

v e ev v v E v h

t m mc

21

2

SS S S

v e ev E v v h

t m mc

21

2

Drude model

SS

dv eE v h

dt m c

1London model

Phenomenological theories: The London Theory

S

eQ v h

mc

SQ v Qt

Sh , v Q 0 0 0If at t = 0 Qt

0

SS S S

v e ev E v v h

t m mc

21

2and define

S S

ev E v Q

t m

Rewrite with Q + Rotor

S S

e hv v Q

t m c t

1With the help of Maxwell

SS

v ev E

t m

210

2S

ev h

mc 0

London equations

S

ev h

mc 0 S

S

v ev E

t m

210

2

S S Sj n ev

S

S

m hj

n e c

2

Sv eE

t m

0

S

S

mj E

t n e

2

The supercurrent density is defined as

see F. London, Superfluids (1961), pp. 57-60

S

hj

c

1st London equation

Sj Et

2nd London equation

London equations

S

hj

c h j

c

4

ch h

2

4

c

h h h

22

4

Lh h 2 2 0

h

z0

insulator superconductor

H L

z

h(z) He

andCombine

*

L *S

c m c

n e

2 2

24 4with

penetration depth

Bibliography

Applications & Historical background Rogalla & Kes100 Years of Superconductivity

Phenomenology Fosshein & SudbøSuperconductivity: Physics and ApplicationsChapter 1

London Equations LondonSuperfluids – Macroscopic Theory of SuperconductivityChapter B