Transcript Principali applicazioni industriali della Superconduttivit&#224

Engineering of electromagnetic systems
for controlled thermonuclear fusion
Scuola di Dottorato in
Ingegneria Industriale
Università degli Studi di Bologna
22,24 giugno 2009
INDEX
Introduction to controlled thermonuclear fusion
 Superconductivity
 NbTi e Nb3Sn superconducting cables
 ITER (International Tokamak Experimental Reactor) experiment
 Wendelstein experiment

2
Introduction to
Controlled Thermonuclear Fusion
Fission and Fusion nuclear reactions
4
Fusion reactions
With neutron emission (activation of materials)
2
1
D  31T  24He ( 3.5 MeV )  01n ( 14.1 MeV )
2
1
D D
2
1
3
2
He ( 0.82 MeV )  01n ( 2.4 MeV )
3
1
T
(
1
MeV
)

1
1 H ( 3 MeV )
Without neutron emission
2
1
D  23He  24He ( 3.7 MeV )  11H ( 14.7 MeV )
1
1
H  115B  3 24He ( 8.7 MeV )
5
Fusion reactions
In order for the fusion reaction to take place, the kinetic energy of the
reacting nuclei must be high enough to overcome the repulsive force due
to their positive electric charge.
Potential Energy
potenziale
 0.28 Z1 Z2 MeV
Z1 Z2 e2 / (4  0 r)
R0  5 10-15  nuclear radius
Distance ( r )
Potential energy vs. distance between nuclei
6
Thermonuclear fusion
The higher is the temperature of the the nuclear fuel (a gas mixture of
deuterium and tritium for the D + T reaction), the higher is the kinetic
energy of the nuclei.
f(E)
Maxwell velocity distribution
E
3
2
 mv 
 m 
 ;
f v   n 
 exp 
 2kT 
 2kT 
2
f E   n
2

3
2
 1 
 E 
E   exp 

 kT 
 kT 
k = Boltzmann constant = 1.3805 10-23 J K-1
7
Thermonuclear fusion
10-22
<v> (m3 s-1)
10-23
D-T
R  n1 n2 E12  v12
R = reaction rate
 = cross section
D-D
10-24
10-25
10-26
1


10
100
1000
T (keV)
The D -T gas mixture should reach a temperature higher than 1
keV = 11 600 000 K.
The gas is in the plasma state: fully ionized but macroscopically
neutral (for distances larger than the Debye length).
8
Plasma confinement
The plasma can be confined by means of:

High magnetic fields (magnetic confinement)
Due to the high value of the required magnetic field the winding
producing it must be realized with superconducting materials.

High power LASER pulse (inertial confinement)
9
Magnetic Confinement
An electric charged particle (q = electric charge) moving in a uniform
magnetic field region, follows an helical trajectory around a field line.
 The velocity component parallel to the field (vp) is constant.
 In the plane orthogonal to the field the motion is of the uniform circular
type with a radius rL which is called Larmor radius and an angular
velocity () which is called cyclotron frequency.
B
B
q<0
dvp
m
0
dt
dv
 q v  B  vn   rL
dt
q vn B  m  2 rL
q>0
v p  costante
qB
 
m
m vn
rL 
qB
Particles are completely
confined in the directions
normal to the field but no
confinement is present in
the direction parallel to
the field
10
Magnetic confinement
A magnetic field with closed toroidal field line can be utilized.
q<0
B
B larger
B smaller
B
E
q>0
The magnetic field is larger in the inner region than in the outer one.
As a consequence a charge separation takes place which produces a
vertical electric field.
11
Magnetic confinement

Due to the electric field a drift velocity of the particles vD in the
radial direction is present which is independent from the charge
of the particle and produces a motion of the entire plasma
E p  0  v p  cos t .
q
 Ep
v  v n ,0  v D
dt
m
 n
dv n q
EB
 E n  v n  B 
vD 
dt
m
B2
dv p
m
dv
 q E  v  B  
dt
In order to confine the plasma one more component of the magnetic
field is necessary, normal to the toroidal one. Thus should be
simultaneously present:
A toroidal magnetic field
A poloidal magnetic field
And the field lines should be of helical type
12
Magnetic confinement
The poloidal magnetic field can be generated by:
 A toroidal plasma current (TOKAMAK TOroidalnaya KAmera and
MAgnitnaya Katushka (toroidal chamber and magnetic coil) )
 External windings (STELLARATOR)
13
TOKAMAK - STELLARATOR
TOKAMAK
STELLARATOR
14
TOKAMAK
z
p  J  B
Central solenoid =
primary winding of a
transformer
Equilibrium equation
plasma =
secondary winding
of a transformer
z
B
r
p
The plasma is the secondary
winding of a transformer; the
primary winding of the
transformer is the central
solenoid external coil.
B
r
Radial profiles of pressure (p),
toroidal magnetic flux density (B) and
poloidal magnetic flux density (B)
15
TOKAMAK
16
TOKAMAK
17
STELLARATOR
Winding system to produce poloidal magnetic field
18
Reactor
 Ignition is reached when the
energy produced by the fusion
reactions and transported by the
charged particles which are
confined in the plasma equals
the energy which is lost by the
plasma due to thermal
conduction and radiation.
6
3
7
3
Li  01n  31T  24He ( 4.8MeV )
Li  01n  31T  24He  01n (2.5MeV )
Natural Litium is a mixture of
Litium-6 (7.4 %) and Litium-7
(92.6 % )
At ignition, the energy which is
transported by the neutrons,
which are not confined in the
plasma, can be used to produce
heat and then electric energy by
means of a standard turbine
plant.
19
Reactor: plasma energy balance
dE
 POH  P  Paux  PL
dt
E   3 k n T dV
E = Plasma energy (n = density of D and T nuclei)
POH = Power loss due to Joule effect
POH    p j dV
P = Power generation due to fusion
reactions: the fraction which is released to
the plasma is that transported by alfa
particles which are confined in the plasma
2
p
Vp
Vp
P  Q E  n 2 v dV
Vp
PL = Power loss due to heat conduction, convection and
radiation (E = energy confinement time)
PL 
E
E
Paux = Power input by additional heating system
At ignition:
POH  Paux  P  PL
dE
0
dt
20
Reactor
21
Reactor
Research and development ………..
22
International Thermonuclear Experimental Reactor
ITER
The goal is:

To demonstrate the scientific and technological
feasibility of electric energy production by means of
controlled thermonuclear fusion: ignition conditions
should be reached and the energy produced by fusion
reaction should be much larger than that utilized to
heat the plasma
23
International Thermonuclear Experimental Reactor
ITER
Fusion power : 500 MW
Q(
Fusion energy
Input energy
) : 10
Average neutronic flux :0.57 MW/m2
Maior radius : 6.2 m
Minor radius : 2.0 m
Plasma current : 15 MA
Magnetc flux density on axis : 5.3 T
Plasma volume (m3): 837 m3
24
ITER superconducting magnets
 18 coils to generate toroidal
field: stored magnetic energy 41
GJ, maximum field 11.8 T,
centripetal force on each coil
403 MN, vertical force on half
coil 205 MN, discharge time 11
s.
 6 coils to generate poloidal and
field and the field for plasma
stability: maximum field 5.8 T.
 1 central solenoid
 Total weight of the system: 10130 t
 The cost of the SC coil system is about 30% of the total cost of the machine
25
ITER
26
ITER
27

“Normal” conductors (copper, aluminum, ..) can not be utilized to
generate the magnetic field necessary for the plasma confinement
due to the excessive joule power loss

Superconducting magnets need to be utilized.
28
Superconductivity
Superconductivity history
1911
Kamerlingh-Onnes finds transition from normal
state to superconducting state of a mercury
sample at 4.19 K
1957 Bardeen, Cooper e Schrieffer state a microscopic
theory of susperconductivity (BCS theory)
1973 Superconductivity of Nb3Ge at 23.2 K
1986 Bednorz and Mueller find superconductive state
in La2-xBaxCuO4 at 30 K
1987 Superconductivity of Y-Ba-Cu-O (YBCO) at 93 K
1988 Superconductivity of Bi-Sr-Ca-Cu-O (BSCCO) at
125 K
2001 Superconductivity of MgB2 at 40 K
30
Properties of superconducting materials

Type I superconductors

Low transition temperature Type II superconductors

High transition temperature Type II superconductors

Losses in transient regime
31
Type I superconductors
At temperatures lower than the critical one the electrical resistivity is nil
(< 10-21 m)
32
Type I superconductors
The superconducting state is a new phase of the material
Heat capacity vs.
temperature
Thermal conductivity vs.
temperature
33
Type I superconductors
 Perfect diamagnetism (Meissner effect): the magnetic flux density
inside a type I superconducting material is nil.
 (T ) 
 = penetration length
R
 (0)
T 
1   
 Tc 
4
1.2
Hext
H/Hext
1.0
0.8
H
 rR 
 exp

H ext
  
0.6
0.4
0.2
0.0
0
0.2
0.4
0.6
0.8
1
1.2
r/R
Superconducting screen currents (supercurrents) are presents which
flow in a shell, with thickness of about the penetration length, near the
surface of the sample.
34
Type I superconductors
From a macroscopic point of view the phenomenon can be modeled
with a volume magnetization of the superconducting material.
B
M
M=0
(normal state)
B = 0 H
(normal state)
Hc
H
Hc
H
B=0
(superconducting state)
M = -H
(superconducting state)
Magnetization characteristics
35
Type I superconductors
A type I superconductor is not only a perfect conductor
Zero field cooling
Perfect conductor
Superconductor
Field cooling
Perfect conductor
Superconductor
36
Type I superconductors
 The superconducting state is destroyed when magnetic flux
density becomes larger than a critical value Bc (critical field)
 The superconducting state is destroyed when current density
becomes larger than a critical value Jc (critical current density)
Bc  Bc 0
Jc 
 T
1  
  Tc
Bc T 
0 T 



2



when
when
J 0
Bext  0
37
Type I superconductors
The critical surface defines all the possible operating condition for the
superconducting state to be present
J
Jc0
Jc
B
Bc0
B
T
Tc0
T
38
Type I superconductors
Type I superconductors are not useful for applications:

Due to the fact that current density is confined in a small shell
near the surface, transport current is too low for applications.

Critical magnetic field is too low.
Elem.
Al
Tc0
(K)
1.18
Bc0 Elem.
(mT)
10.5 Zr
Tc0
(K)
0.61
Ti
V
0.40
5.40
5.6 Nb
141.0 Mo
9.25 206.0 Hg()
0.92 9.6 Hg()
4.15
3.9
41.1
33.9
Zn
0.85
7.8
7.20
80.3
5.4
Tc
Bc0 Elem.
(mT)
4.7 Cd
141.0 Pb
Tc0
Bc0
(K) (mT)
0.51 2.8
7
39
BCS theory
The BCS theory (proposed in 1957 by Bardeen, Cooper e Schriffer)
state a quantistic and microscopic model of the superconducting state
in the metallic material.

Couples of “super-electrons” can move in the material without
loss due to collisions with the crystal lattice by means of a
binding force connected with vibration of the crystal lattice
(phonon).

The energy of the couples of “super-electrons” is lower than the
energy of the fundamental state of a single electron. The energy
reduction is proportional to the critical temperature of the
material.

The binding force between two “super-electrons” vanishes at
distances larger than the “coherence length”
40
Type II superconductors
When coherence length () is lower than the penetration length ()
magnetic field can penetrate in the superconducting material
ns
B

normal material

type I superconductor material
0
x
ns
B

normal material

type II superconducting material
0
x
41
Type II superconductors
Material
Cd
Al
Pb
Nb
Nb-Ti
Nb3Sn
YBa2Cu3O7
Tc (K)
0.56
1.18
7.20
9.25
9.5
18
89
 (nm)
760
550
82
32
4
3
1.8
 (nm)
110
40
39
50
300
65
170
42
Type II superconductors

When Hext < Hc1 (lower critical field) Type II
superconductor undergoes Meissner effects
as type I superconductor

When Hc1 < Hext < Hc2 (upper critical field)
magnetic
field
penetrates
into
the
superconducting material (mixed state)

When H > Hc2 superconducting state is
destroyed
R
Hext
43
Type II superconductors
H
H
Type I
Hc0
Type II
Hc0
Hc(T)
Hc2(T)
Mixed state
B=0
Meissner effect
Hc1(T)
B=0
Meissner effect
T
T
Magnetic phase diagram
44
Type II superconductors
In type II superconductors, in the mixed state, magnetic field is
concentrated in normal region (fluxoids) with the size of the coherence
length, surrounded by currents (vortexes) flowing in the
superconducting region of the material.
 The magnetic flux connected to
each fluxoid is equal to:
0 = h/2e = 2.0678 10-15 Wb
 When the upper critical field is
reached the fluxoids occupy all the
volume of the material
45
Type II superconductors
First image of Vortex lattice, 1967
Bitter Decoration
Pb-4at%In rod, 1.1K, 195G
U. Essmann and H. Trauble
Max-Planck Institute, Stuttgart
Physics Letters 24A, 526 (1967)
Abrikosov lattice in MgB2, 2003
Bitter Decoration
MgB2 crystal, 200G
L. Ya. Vinnikov et al.
Institute of Solid State Physics, Chernogolovka
Phys. Rev. B 67, 092512 (2003)
http://www.fys.uio.no/super/vortex/
46
Type II superconductors
Vortex structure can be modeled from a macroscopic point of view by
means of a volume magnetization.
Magnetization characteristics
47
Macroscopic model
From a macroscopic point of view, when average values of electromagnetic
quantities over volume with size larger than the coherence length and the
penetration length, the following usual Maxwell equations can be
considered
1
1


H
h
x
dV
;
B

bx  dV


V V
V V
E
1
V
 ex  dV
H  J
;
J
V
;
B
E  
t
1
V
;
 jx  dV
V
B
H
M
0
 Vortex can not be modeled by means of the the current density J in this
approach.
 Each superconducting material is characterized by electrical E = E(J)
and magnetic M = M(H) properties
 Most of the models considers M = 0
48
Type II superconductors
NbTi - T = 4.2 K, B = 5 T
2.0E-04
1.8E-04
E (V/m)
1.6E-04
1.4E-04
1.2E-04
1.0E-04
8.0E-05
6.0E-05
4.0E-05
2.0E-05
0.0E+00
0.0E+00
5.0E+08
1.0E+09
1.5E+09
2.0E+09
2.5E+09
J (A/m^2)
 From a macroscopic point of view, in a type II superconductor, in the
mixed state, when a transport current density is flowing, an electric field
is present and a Joule dissipation of electric energy into heat occurs.
49
Type II superconductors
 Joule dissipation (electric field) is due to
movement of vortexes.
E  n v 0
 Two forces are applied to the vortexes:
 Lorentz force FL is directed normally to the
directions either of the magnetic field and of
the transport current density
 “pinning” force Fp opposes to any movement
of the vortexes and is connected to the lattice
imperfections
I
Fp
FL
50
Type II superconductors
 When temperature is much lower than the critical one, fluxoid motion
is very slow (“Flux creep” region) and the electric field is negligible
NbTi - T = 4.2 K, B = 5 T
1.6E-04
1.4E-04
E (V/m)
 When temperature
overcomes the critical one
fluxoid motion is fast and
electric field is large (“Flux
flow” region)
2.0E-04
1.8E-04
1.2E-04
flux flow
1.0E-04
8.0E-05
6.0E-05
flux creep
4.0E-05
2.0E-05
0.0E+00
0.0E+00
5.0E+08
1.0E+09
1.5E+09
2.0E+09
2.5E+09
J (A/m^2)
51
Type II superconductors
 The critical current density (Jc) is defined as the current density
corresponding to the critical value of the electric field (Ec)
Two different values for the
critical electric field are
utilized
 Ec = 10 –4 V/m
 Ec = 10
–5
V/m
NbTi - T = 4.2 K, B = 5 T
E (V/m)
The value of the critical
current density depends on
the choice for the value of
the critical electric field.
Ec
2.0E-05
1.5E-05
1.0E-05
5.0E-06
0.0E+00
0.0E+00
5.0E+08
1.0E+09
1.5E+09
J (A/m^2)
2.0E+09
2.5E+09
Jc
52
200
164 K
Hg-1223
150
High-TC
Temperature, TC (K)
High temperature superconductors
100
50
La-214
Hg
Bednorz and Mueller
IBM Zuerich, 1986
0
1900
1920
Low-TC
1940
1960
Year
V3Si
1980
2000
53
High temperature superconductors (HTSC)
 The critical temperature is feasible for operation with liquid nitrogen
 Large upper critical field




Brittle, low ductility and malleability
Strong anisotropy
Long and costly manufacturing process
Low value of the critical current density (2 104 A/cm2 at 77K, in
direct current regime, without external field, against 105 A/cm2 at
4.2K for metallic superconductors)
 Jc is strongly dependent on strain
54
Typical structure of ceramic superconductors
Perovskite ABX3
YBCO YBa2Cu3O6
YBCO YBa2Cu3O7
55
BSCCO
BSCCO Bi2Sr2Can-1CunOy
Conducting layers
Cu O
Non-conducting layers
56
Anisotropy
BSCCO-2223 Jc vs. applied magnetic field
The field is parallel
to CU-O planes
The field is normal
to CU-O planes
57
Magnesium boride
J. Akimitsu, Symp. on Transition Metal Oxides, Sendai, Jan 2001
Tc40 K
MgB2
58
Magnesium boride
Main characteristics of MgB2:
 High machinability (wires can be easily manufactured)
 Well known manufacturing technology
 Low cost
 Critical temperature feasible for operation with liquid hydrogen
 Low electrical properties at high value of the magnetic field
59
Type II superconductors
 Presently, in the devices for
controlled thermonuclear
fusion, the more utilized
materials are NbTi and Nb3Sn
 HTS materials are utilized in
the current leads of the coils
60
Cryogenics
efficiency :
Qc

W
COP = Coefficient of Performance :
W 1
COP 

Qc 
Heat rejection
to ambient
( Qh )
Fluid expansion
to reduce
temperature
QHX
Carnot
Work done on
process fluid
(W)
Power input
COPideal 
Heat absorption
( Qc )
COPreal
SC load at Tc
Tc

Th  Tc
1
Carnot
COPideal

(0.1  0.3)
61
Cryogenics
OPERATING
TEMPERATURE
CARNOT
COP (Watt
Input per
Watt Lifted)
273 K
200 K
150 K
100 K
77 K
50 K
40 K
30 K
0.11
0.52
1.01
2.03
2.94
5.06
6.58
9.10
"TYPICAL" COP FOR
>100 WATT HEAT LOADS
(Watt Input at 300 K
per
Watt Lifted at Top)
~ 0.4
~2
~4
~ 8-10
~ 12-20
~ 25-35
~ 35-50
~ 50-75
Treject = 303 K
62
Losses in transient regime
When a supercondutor is immersed in a time dependent magnetic field
(due to external coils or to a transport current flowing in the
superconductor itself), due to the fluxoids motion, electric power is
dissipated into heat in the superconducting material.
63
Losses in transient regime
Infinite slab in an
alternate magnetic field
parallel to the main
surfaces of the slab
Ba t  BM sin t 
Magnetic field penetrates into the superconducting slab starting from
the outer surface. A current density equal to the critical current density
of the material flows in the region occupied by the magnetic field
(critical state model).
Q = Energy loss per cycle per unit volume
64
Losses in transient regime
Bp = minimum magnetic flux density
change which fully penetrates into the slab
BM
p
 Bp  0 J c a
0 J c
If magnetic field does not fully penetrates into the slab

BM
1
Bp
BM
BM
p
p
x
x
x
p
x
p
- BM

t
2
1
Q
a
t
t0 
2


t0


t
2
3
t
2

2BM2  2BM2
E y x, t J y x, t  dx 



0 3
0
ap
a
65
Losses in transient regime
If magnetic field fully penetrates into the slab
t
Bp

2
t
3
2

BM
1
Bp
t
- BM+2Bp
2

x
x
x
BM
BM
BM- 2Bp
x
x
x
- BM
1
Q
a
t0 
2
 a

t0
2BM2
0 E y x, t J y x, t  dx  0
1
2  2BM2
   3 2    


0
The lower is the slab thickness the larger is  and the lower are the
losses
66
“flux jump” instability
T = T0 + T
 Bz
  0 J c T 
x
BM
T = T0
 T 
J c T  J c 0 1  
  Tc 
Qs
x
In a first approximation :
Q 
Qs 
0 J c T0 2 a 2
T
0 J c T0 2 a 2
T   C T
3Tc  T0 
3Tc  T0 
0 J c T0 2 a 2
Ceff  C 
3  Tc  T0 
2
  T 
 1  
   Tc 
1
4 2



J c T  J c T0 
Tc  T
Tc  T0
Q = Energy loss per unit volume corresponding
to a change T of the temperature
Energy balance (adiabatic case)
Effective heat capacity is lower
than the real one
67
“flux jump” instability
0 J c T0 2 a 2
Ceff  C 
3  Tc  T0 
When Ceff = 0, at a small heat input
corresponds a large increase of the
temperature
The smaller is the depth a of the slab the more stable is the
superconductor
Typical values for NbTi:
Jc = 1.5  109 A m-2
 = 6.2  103 kg m-3
a < 115 m
C = 0.89 J kg-1 K-1
Tc = 6.5 K (B = 6 T)
68
NBTi e Nb3Sn Cables
Superconducting cables
Rutherford cable
CICC
70
Cable in Conduit Conductor (CICC)
The most utilized cable in the winding of the devices for the controlled
thermonuclear fusion is of the multi-filamentary, multi-stage type,
cooled by liquid helium which is forced to flow in the channel where
the SC strands are jacketed (cable-in-conduit conductor - CICC).
Typical multi-filamentary, multistage structure
 N. of cabling stages: 5
 N. of Strands: 1350
 Cabling pattern: 33556
 Twist pitches (mm):
80, 140, 190, 300, 440
71
Strand
Each strand is made of a lot of superconducting wires (more
than one thousand, with a diameter lower than 10 m), twisted
and immersed in a matrix of normal material (typically copper)
The strand structure is necessary :
 To prevent flux-jump instability
 To reduce hysteresis losses
 To reduce power dissipation during
quench (transition to normal state of the
superconductor in the strand)
72
Strand modelling
n
In superconductor
In copper
E
J
J 
E  Ec  s  sign  J s  k
 Jc 
E  m J m k
J s As  J m Am  I
I

As
Am 

 k
J   Js
 Jm
As  Am 
 As  Am
From previous equation the elctrical
characteristics E-J of the strand is obtained
E  EJ 
Experimental strand characterization is made by measuring its critical
current ( Ic) and its current sharing temperature (Tcs)
73
Critical current measurement
V
+
A
L
I t    t
I
E t  
V t 
L
E  E I 
At the critical current the value of the electric field equals
the critical value (Ec).
Ec  E I c 
The critical value of the electric field is not fixed; typical values are:
Ec = 10-5 V/m, Ec = 10-4 V/m
Ic
J

c
At the critical conditions is Jm << Js thus:
As
74
Current sharing temperature measurement
V
T(t)
+
A
L
T t    t
I
E t  
V t 
L
E  ET 
The temperature correspondig to the critical value of the electric
field is the measured current sharing temperature (Tcs)
Ec  ETcs 
75
Current distribution
 The cable critical current / current sharing temperature
measurements are similar to the strand measurements.
 Non-uniform distribution of the current among the strands of the
cable reduce the value of the critical current / current sharing
temperature
A non-uniform distribution of the current among the strands of the
cable is due to:

Non-uniform contacts of the strands at terminations of the cable
and at joints between two cable-segments.

Electro-motive forces due to transient magnetic field.
76
Terminations / joints
In terminations/joints not all the strands touch the current
exchange surface; thus current distribution can not be uniform
77
Current distribution
Current can redistribute among the strands along the cable, because
the strands are not insulated and touch each other into the cable.
The lower is the transversal contact resistance per unit length
between the strands, the higher is the current redistribution.

The lower is the transversal resistance per unit length between
the strands, the more uniform is the current distribution
but ..

The lower is the transversal resistance per unit length between the
strands, the larger are the losses due to coupling currents
circulating among the strands
78
NbTi strand
NbTi is a metallic alloy with good mechanical properties; it is easy to
process by conventional extrusion and drawing techniques.
Given its superconducting properties, it is well suited for the production
of fields in the 2 to10 T range and requires liquid-helium cooling.
79
NbTi strand
A Cu-stabilized, NbTi multifilament composite wire is fabricated in three
main steps:
 production of NbTi alloy ingot (typically 80 cm hight and 20 cm diameter)
 production, extrusion and drawing of mono-filament billet.
 production, extrusion and drawing of multi-filament billet.
Cold extrusion
Thermal treatement
1 mm
80
NbTi strand
The electrical characteristics of aNbTi strand
can be modeled by means of the Bottura scaling

C

J c  B, T   0 1  t 1.7  b  1  b 
B
q
I 
n I c   1   c 
 I0 
T
B
t
; b
Bc 2 T   Bc 20 1  t1.7 
Tc 0
Bc 2 T 
Bc20 (T)
15.07
Tc0 (K)
8.99
C0 (A T m-2)
4.78011011

1.96

2.1

2.12
I0 (A)
0.846
q
0.5925
81
Nb3Sn Strand
Nb3Sn is an intermetallic compound; it is formed by thermal
diffusion of Sn in Nb (Sn consentration should be in the range 18
% - 25 %). The process requires high temperatures (about 700
°C). It is well suited for the production of fields in the 10- 21T
range
 Nb3Sn is brittle and difficult to machinery. To overcome these
problems the “wind and react” technique can be used. The coil is
realized with the strand before Nb3Sn formation, then the
thermal process takes place for the entire coil.
Some of the main process which are utilized to manufacture
Nb3Sn are the followings:
 Bronze process,
 Internal Sn process,
 Power-in-Tube process.
82
Nb3Sn Strand
83
Nb3Sn strand
During cool down process from the reaction temperature (about 700
°C) to operating temperature (about 4.2 K), due to the different value
of the thermal expansion coefficients of the materials in the strand
(Nb3Sn, Cu), a strain (thermal strain) is generated in the materials:
Nb3Sn is compressed (SC  - 0.27 %).
T = 700 °C
T = 4.2 K
LCu
Cu
Nb3Sn
L0
LSC
Cu
 Cu 
L  LCu
LCu
 SC 
L  LSC
LSC
Nb3Sn
L
L0
84
Nb3Sn strand
The Nb3Sn electrical characteristic is strain sensitive ( is the uni-axial
strain):
Js


E  Ec 



J
T
,
B
,

 c

n T , B ,  
sign  J s  k
Durham scaling

T    T 0 1  c2  c3  c4
*
c
*
c
2
3


t
1
4 w
B T ,    B 0,01  c2  c3  c4
*
c2
*
c2

2
3
A   A0 1  c2  c3  c4
2

3

J c T , B,    A  Tc*   1  t 2
1 t 
b

Tc*  
B
Bc*2 T ,  

u
4 w
 B T ,  
2
4
T
*
c2
m 3
b p 1 1  b 
q
nT , B,    1  rT ,  J c T , B,  
s
85
Nb3Sn strand
86
Experimental tests towards ITER
To test the design of the ITER machine experimental activities
have been performed / are performed on small size test
systems
 Tests of short cable segments and joints/terminations (TFMCFSJS, CSMC-FSJS, PF-FSJS, PFIS) at CRPP Losanna –
Switzerland
 Tests on model coils:
 TFMC (Toroidal Field Model Coil) at FZK – Karlsruhe –
Germany - 2001
 CSMC (Central Solenoid Model Coil) at JAERI - Naka – Japan
- 2000
 PFCI (Poloidal Field Conductor Insert) presso JAERI - Naka –
Japan – just concluded
87
SULTAN Test Facility
(Switzerland)
88
Sudden quench in NbTi cable
WIC-130909
20
20
18
18
Voltage (LV2122) (micro-Volt)
Voltage (LV2122) (micro-Volt)
WIC-130905
16
14
12
10
8
6
4
2
0
-2
20
22
24
current (kA)
26
28
16
14
12
10
8
6
4
2
0
-2
25
27
29
31
33
35
current (kA)
At a large value of the current, the quench of the cable occurs and it
is not possible to measure the critical current.
 Sudden quench shows that the current redistribution among the
strands of the cable is too low.
89
Sudden quench in NbTi cable

When current was lower than 45 kA (PFISnw) and 38 kA (PFISw),
it is not possible to measure a critical current and/or a current
sharing temperature, but only a quench current

The value of the quench current is significantly lower than the
estimation of the critical current supposing uniform current
distribution.
90
Degradation of the characteristics of Nb3Sn cable
The critical current of the Nb3Sn cables tested in the SULTAN facility
is significantly lower of the critical current measured in the
characterization of the strand at the same operating condition
(temperature, field).
The current-sharing temperature of the Nb3Sn cables tested in the
SULTAN facility is significantly lower of the current-sharing temperature
measured in the characterization of the strand at the same operating
condition (field, current).
91
Degradation of the characteristics of Nb3Sn cable
Cross sectio of TFI, in
the most stressed region
Cross sectio of TFI, in
the lesst stressed region
A possible mechanism for the degradation of the characteristics of
Nb3Sn cable is the strain pattern which is present in the strand at
operation in the cable due to the bending action of the Lorentz force.
Each strand is maintained in its position by the forces from the other
strands at points whose distance is about 5-10 mm, depending on the
twist pitch.
92
Degradation of the characteristics of Nb3Sn cable
The experiments performed in Japan and
The Netherland on a single strand
confirm a strong reduction of electrical
properties due to bending effects.
93
Future developments
 Nb3Al use: properties are
not strain sensitive
 HTS use: critical field
extremely high
94