superconductivity and its applications - unige · 2018-12-17 · applications & historical...
Post on 22-May-2020
3 Views
Preview:
TRANSCRIPT
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
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
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
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
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
top related