engineering of electromagnetic systems for controlled thermonuclear fusion scuola di dottorato in...
Post on 15-Jan-2016
222 views
TRANSCRIPT
![Page 1: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/1.jpg)
Engineering of electromagnetic systemsfor controlled thermonuclear fusion
Scuola di Dottorato inIngegneria Industriale
Università degli Studi di Bologna
22,24 giugno 2009
![Page 2: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/2.jpg)
2
INDEX
Introduction to controlled thermonuclear fusion Superconductivity NbTi e Nb3Sn superconducting cables ITER (International Tokamak Experimental Reactor) experiment Wendelstein experiment
![Page 3: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/3.jpg)
Introduction toControlled Thermonuclear Fusion
![Page 4: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/4.jpg)
4
Fission and Fusion nuclear reactions
![Page 5: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/5.jpg)
5
Fusion reactions
)MeV.(n)MeV.(HeTD 11453 10
42
31
21
)MeV(H)MeV(T
)MeV.(n)MeV.(HeDD
31
4282011
31
10
322
121
)MeV.(H)MeV.(HeHeD 71473 11
42
32
21
)MeV.(HeBH 783 42
115
11
With neutron emission (activation of materials)
Without neutron emission
![Page 6: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/6.jpg)
6
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.
Distance ( r )
Potential Energy potenziale
R0 5 10-15 nuclear radius
Z1 Z2 e2 / (4 0 r)
0.28 Z1 Z2 MeV
Potential energy vs. distance between nuclei
![Page 7: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/7.jpg)
7
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.
E
f(E)
Maxwell velocity distribution
kT
Eexp
kTEnEf;
kT
mvexp
kT
mnf
2
322
3
12
22 v
k = Boltzmann constant = 1.3805 10-23 J K-1
![Page 8: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/8.jpg)
8
Thermonuclear fusion
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).
R = reaction rate = cross section
10 1 100 1000 10-26
10-25
10-24
10-23
10-22
<v> (m3 s-1)
T (keV)
D - D D - T
121221 vEnnR
![Page 9: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/9.jpg)
9
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)
![Page 10: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/10.jpg)
10
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 q < 0
Bq
vmr
m
Bqtetancosv
rmBvq
rvdt
dv
qdt
dm
nL
p
Ln
Ln
p
2
0
Bvv
Particles are completely confined in the directions normal to the field but no confinement is present in the direction parallel to the field
![Page 11: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/11.jpg)
11
Magnetic confinement
A magnetic field with closed toroidal field line can be utilized.
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.
B
B larger
q < 0
q > 0
B smaller
E B
![Page 12: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/12.jpg)
12
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
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:
2
0
0
B
.tcos
m
q
dt
dm
q
dt
d
qdt
dm
D
D,nn
pp
nnn
p
p
BEv
vvvvE
BvEv
Ev
BvEv
A toroidal magnetic field
A poloidal magnetic field
And the field lines should be of helical type
![Page 13: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/13.jpg)
13
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)
![Page 14: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/14.jpg)
14
TOKAMAK - STELLARATOR
TOKAMAK STELLARATOR
![Page 15: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/15.jpg)
15
TOKAMAK
BJ p
Radial profiles of pressure (p),toroidal magnetic flux density (B) and
poloidal magnetic flux density (B)
Equilibrium equation
The plasma is the secondary winding of a transformer; the primary winding of the transformer is the central solenoid external coil.
z
r
Central solenoid =primary winding of a transformer
plasma =secondary winding of a transformer z
p
B
Br
![Page 16: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/16.jpg)
16
TOKAMAK
![Page 17: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/17.jpg)
17
TOKAMAK
![Page 18: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/18.jpg)
18
STELLARATOR
Winding system to produce poloidal magnetic field
![Page 19: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/19.jpg)
19
Reactor
)MeV.(HeTnLi 8442
31
10
63
)5.2(10
42
31
10
73 MeVnHeTnLi
Natural Litium is a mixture of Litium-6 (7.4 %) and Litium-7 (92.6 % )
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.
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.
![Page 20: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/20.jpg)
20
Reactor: plasma energy balance
LauxOH PPPPdt
dE
E = Plasma energy (n = density of D and T nuclei)
POH = Power loss due to Joule effect
pV
dVTnkE 3
pV
ppOH dVjP 2
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
pV
dVvnEQP 2
PL = Power loss due to heat conduction, convection and radiation (E = energy confinement time) E
L
EP
LauxOH PPPP At ignition: 0dt
dE
Paux = Power input by additional heating system
![Page 21: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/21.jpg)
21
Reactor
![Page 22: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/22.jpg)
22
Reactor
Research and development ………..
![Page 23: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/23.jpg)
23
International Thermonuclear Experimental Reactor ITER
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
The goal is:
![Page 24: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/24.jpg)
24
Fusion power : 500 MW
Q ( ) : 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
International Thermonuclear Experimental Reactor ITER
energyInput
energyFusion
![Page 25: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/25.jpg)
25
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
![Page 26: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/26.jpg)
26
ITER
![Page 27: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/27.jpg)
27
ITER
![Page 28: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/28.jpg)
28
“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.
![Page 29: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/29.jpg)
Superconductivity
![Page 30: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/30.jpg)
30
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
![Page 31: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/31.jpg)
31
Properties of superconducting materials
Type I superconductors
Low transition temperature Type II superconductors
High transition temperature Type II superconductors
Losses in transient regime
![Page 32: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/32.jpg)
32
Type I superconductors
At temperatures lower than the critical one the electrical resistivity is nil (< 10-21 m)
![Page 33: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/33.jpg)
33
Type I superconductors
The superconducting state is a new phase of the material
Thermal conductivity vs. temperature
Heat capacity vs. temperature
![Page 34: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/34.jpg)
34
Type I superconductors
Hext
R
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1 1.2
r/R
H/H
ext
Rr
H
H
ext
exp
Perfect diamagnetism (Meissner effect): the magnetic flux density inside a type I superconducting material is nil.
Superconducting screen currents (supercurrents) are presents which flow in a shell, with thickness of about the penetration length, near the surface of the sample.
4
1
)0()(
cT
TT
= penetration length
![Page 35: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/35.jpg)
35
Type I superconductors
Magnetization characteristics
H
B
Hc
B = 0(superconducting state)
B = 0 H(normal state)
H
M
Hc
M = -H(superconducting state)
M = 0(normal state)
From a macroscopic point of view the phenomenon can be modeled with a volume magnetization of the superconducting material.
![Page 36: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/36.jpg)
36
Type I superconductors
A type I superconductor is not only a perfect conductor
Zero field cooling
Perfect conductor Superconductor
Field cooling
Perfect conductor Superconductor
![Page 37: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/37.jpg)
37
Type I superconductors
The superconducting state is destroyed when magnetic flux density becomes larger than a critical value Bc (critical field)
012
0
Jwhen
T
TBB
ccc
The superconducting state is destroyed when current density becomes larger than a critical value Jc (critical current density)
0
0
extc
c BwhenT
TBJ
![Page 38: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/38.jpg)
38
Type I superconductors
The critical surface defines all the possible operating condition for the superconducting state to be present
T
J
B
Bc0
Tc0
B T
Jc
Jc0
![Page 39: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/39.jpg)
39
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. Tc0
(K)Bc0
(mT)Elem. Tc0
(K)Bc0
(mT)Elem. Tc0
(K)Bc0
(mT)
Al 1.18 10.5 Zr 0.61 4.7 Cd 0.517
2.8
Ti 0.40 5.6 Nb 9.25 206.0 Hg() 4.15 41.1
V 5.40 141.0 Mo 0.92 9.6 Hg() 3.9 33.9
Zn 0.85 5.4 Tc 7.8 141.0 Pb 7.20 80.3
![Page 40: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/40.jpg)
40
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”
![Page 41: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/41.jpg)
41
Type II superconductors
When coherence length () is lower than the penetration length () magnetic field can penetrate in the superconducting material
x
normal material type I superconductor material
B ns
0
x
normal material type II superconducting material
B ns
0
![Page 42: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/42.jpg)
42
Type II superconductors
Material Tc (K) (nm) (nm)
Cd 0.56 760 110
Al 1.18 550 40
Pb 7.20 82 39
Nb 9.25 32 50
Nb-Ti 9.5 4 300
Nb3Sn 18 3 65
YBa2Cu3O7 89 1.8 170
![Page 43: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/43.jpg)
43
Type II superconductors
Hext
R
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
![Page 44: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/44.jpg)
44
Magnetic phase diagram
Type II superconductors
T
Hc0
Hc2(T)
Mixed state
T
Type II
B = 0Meissner effect
Hc1(T)
H
Hc0
Hc(T)
B = 0Meissner effect
Type IH
![Page 45: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/45.jpg)
45
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
![Page 46: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/46.jpg)
46
Abrikosov lattice in MgB2, 2003
Bitter DecorationMgB2 crystal, 200G
First image of Vortex lattice, 1967
Bitter DecorationPb-4at%In rod, 1.1K, 195G
U. Essmann and H. TraubleMax-Planck Institute, Stuttgart Physics Letters 24A, 526 (1967)
L. Ya. Vinnikov et al.Institute of Solid State Physics, ChernogolovkaPhys. Rev. B 67, 092512 (2003)
http://www.fys.uio.no/super/vortex/
Type II superconductors
![Page 47: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/47.jpg)
47
Magnetization characteristics
Type II superconductors
Vortex structure can be modeled from a macroscopic point of view by means of a volume magnetization.
![Page 48: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/48.jpg)
48
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
MB
HB
EJH
0
;;t
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
dVV
dVV
dVV
dVV
VV
VV
xjJxeE
xbBxhH
1;
1
1;
1
![Page 49: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/49.jpg)
49
Type II superconductors
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.
I
x E
NbTi - T = 4.2 K, B = 5 T
0.0E+00
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
1.2E-04
1.4E-04
1.6E-04
1.8E-04
2.0E-04
0.0E+00 5.0E+08 1.0E+09 1.5E+09 2.0E+09 2.5E+09
J (A/m^2)
E (
V/m
)
![Page 50: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/50.jpg)
50
Type II superconductors
Joule dissipation (electric field) is due to movement of vortexes.
Two forces are applied to the vortexes:
I
FL
Fp
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
0 vE n
![Page 51: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/51.jpg)
51
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
When temperature overcomes the critical one fluxoid motion is fast and electric field is large (“Flux flow” region)
NbTi - T = 4.2 K, B = 5 T
0.0E+00
2.0E-05
4.0E-05
6.0E-05
8.0E-05
1.0E-04
1.2E-04
1.4E-04
1.6E-04
1.8E-04
2.0E-04
0.0E+00 5.0E+08 1.0E+09 1.5E+09 2.0E+09 2.5E+09
J (A/m^2)
E (
V/m
)flux creep
flux flow
![Page 52: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/52.jpg)
52
Type II superconductors
The critical current density (Jc) is defined as the current density corresponding to the critical value of the electric field (Ec)
The value of the critical current density depends on the choice for the value of the critical electric field.
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
0.0E+00
5.0E-06
1.0E-05
1.5E-05
2.0E-05
0.0E+00 5.0E+08 1.0E+09 1.5E+09 2.0E+09 2.5E+09
J (A/m^2)
E (
V/m
)Ec
Jc
![Page 53: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/53.jpg)
53
High temperature superconductors
Bednorz and MuellerIBM Zuerich, 1986
1900 1920 1940 1960 1980 2000 0
50
100
150
200
Tem
per
atu
re,
TC
(K)
Year
Low-TC
Hig
h-T
C
164 K
La-214
Hg-1223
Hg V3Si
![Page 54: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/54.jpg)
54
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
![Page 55: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/55.jpg)
55
Typical structure of ceramic superconductors
YBCO YBa2Cu3O6 YBCO YBa2Cu3O7
Perovskite ABX3
![Page 56: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/56.jpg)
56
BSCCO
BSCCO Bi2Sr2Can-1CunOy
Conducting layersCu O
Non-conducting layers
![Page 57: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/57.jpg)
57
Anisotropy
BSCCO-2223 Jc vs. applied magnetic field
The field is parallel to CU-O planes
The field is normalto CU-O planes
![Page 58: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/58.jpg)
58
Magnesium boride
Tc40 K
MgB2
J. Akimitsu, Symp. on Transition Metal Oxides, Sendai, Jan 2001
![Page 59: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/59.jpg)
59
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
![Page 60: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/60.jpg)
60
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
![Page 61: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/61.jpg)
61
Cryogenics
Heat rejection to ambient
( Qh )
Heat absorption( Qc )
Fluid expansionto reduce
temperature
Work done onprocess fluid
( W ) Power input
QHX
SC load at Tc
ch
cCarnot TT
T
Carnotideal
1COP
)3.01.0(
COPCOP ideal
real
efficiency : COP = Coefficient of Performance : W
Qc
1W
COP cQ
![Page 62: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/62.jpg)
62
Cryogenics
OPERATING TEMPERATURE
CARNOT COP (Watt Input per
Watt Lifted)
"TYPICAL" COP FOR >100 WATT HEAT LOADS
(Watt Input at 300 K per
Watt Lifted at Top) 273 K 0.11 ~ 0.4
200 K 0.52 ~ 2 150 K 1.01 ~ 4 100 K 2.03 ~ 8-10 77 K 2.94 ~ 12-20 50 K 5.06 ~ 25-35 40 K 6.58 ~ 35-50 30 K 9.10 ~ 50-75
Treject = 303 K
![Page 63: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/63.jpg)
63
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.
![Page 64: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/64.jpg)
64
Losses in transient regime
Infinite slab in an alternate magnetic field parallel to the main surfaces of the slab
2a
x
z
y Ba
tBtB Ma sin
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
![Page 65: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/65.jpg)
65
Losses in transient regime
x
BM
p
2t
x
BM
p
t
x
- BM
p
3
2t
x
p
2
t
0
2
0
22
2
3
2,,
10
0
MM
t
t
a
pa
yy
BBdxtxJtxE
aQ
aJBJ
Bp cp
c
M0
0
Bp = minimum magnetic flux density change which fully penetrates into the slab
1p
M
B
BIf magnetic field does not fully penetrates into the slab
![Page 66: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/66.jpg)
66
Losses in transient regime
x
Bp
2t
2
3t
2
t
x
BM
x
BM- 2Bp
x
- BM
x
- BM+2Bp
x
BM
If magnetic field fully penetrates into the slab
0
2
20
22
0
2
3
212,,
10
0
MM
t
t
a
yy
BBdxtxJtxE
aQ
1p
M
B
B
The lower is the slab thickness the larger is and the lower are the losses
![Page 67: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/67.jpg)
67
“flux jump” instability
Q = Energy loss per unit volume corresponding to a change T of the temperature
T
TT
aTJQ
c
c
0
2200
3
Effective heat capacity is lower than the real one
TJx
Bc
z0
x
BM T = T0 +
T
T = T0 Qs
2
142
110
cccc T
T
T
TJTJ
In a first approximation : 0
0 TT
TTTJTJ
c
ccc
TCT
TT
aTJQ
c
cs
0
2200
3Energy balance (adiabatic case)
0
2200
3 TT
aTJCC
c
ceff
![Page 68: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/68.jpg)
68
“flux jump” instability
When Ceff = 0, at a small heat input corresponds a large increase of the temperature
0
2200
3 TT
aTJCC
c
ceff
Typical values for NbTi:
Jc = 1.5 109 A m-2
= 6.2 103 kg m-3
C = 0.89 J kg-1 K-1
Tc = 6.5 K (B = 6 T)
The smaller is the depth a of the slab the more stable is the superconductor
a < 115 m
![Page 69: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/69.jpg)
NBTi e Nb3Sn Cables
![Page 70: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/70.jpg)
70
Superconducting cables
CICCRutherford cable
![Page 71: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/71.jpg)
71
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, multi-stage structure
N. of cabling stages: 5
N. of Strands: 1350
Cabling pattern: 33556
Twist pitches (mm):
80, 140, 190, 300, 440
![Page 72: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/72.jpg)
72
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)
![Page 73: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/73.jpg)
73
Strand modelling
I
E J
kE s
n
c
sc Jsign
J
JE
In superconductor
kE mm JIn copper
IAJAJ mmss
kJ
ms
mm
ms
ss AA
AJ
AA
AJ
Experimental strand characterization is made by measuring its critical current ( Ic) and its current sharing temperature (Tcs)
From previous equation the elctrical characteristics E-J of the strand is obtained
JEE
![Page 74: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/74.jpg)
74
Critical current measurement
I
V
L
A
+
The critical value of the electric field is not fixed; typical values are: Ec = 10-5 V/m, Ec = 10-4 V/m
ttI L
tVtE
At the critical current the value of the electric field equals the critical value (Ec).
s
cc A
IJ At the critical conditions is Jm << Js thus:
cc IEE
IEE
![Page 75: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/75.jpg)
75
Current sharing temperature measurement
I
V
L
A
+ T(t)
ttT L
tVtE
The temperature correspondig to the critical value of the electric field is the measured current sharing temperature (Tcs)
csc TEE
TEE
![Page 76: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/76.jpg)
76
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.
![Page 77: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/77.jpg)
77
Terminations / joints
In terminations/joints not all the strands touch the current exchange surface; thus current distribution can not be uniform
![Page 78: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/78.jpg)
78
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
![Page 79: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/79.jpg)
79
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.
![Page 80: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/80.jpg)
80
NbTi strand
1 mm
Cold extrusion
Thermal treatement
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.
![Page 81: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/81.jpg)
81
NbTi strand
TB
Bb
T
Tt
cc 20
;
bbt
B
CTBJc 11, 7.10
7.1202 1 tBTB cc
Bc20 (T) 15.07
Tc0 (K) 8.99
C0 (A T m-2) 4.78011011
1.96
2.1
2.12
I0 (A) 0.846
q 0.5925
q
cc I
IIn
0
1
The electrical characteristics of aNbTi strand can be modeled by means of the Bottura scaling
![Page 82: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/82.jpg)
82
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
Some of the main process which are utilized to manufacture Nb3Sn are the followings:
Bronze process,
Internal Sn process,
Power-in-Tube process.
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.
![Page 83: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/83.jpg)
83
Nb3Sn Strand
![Page 84: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/84.jpg)
84
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 %).
L0
Cu Cu
Nb3Sn
LCu
LSC
L0
Cu Cu
Nb3Sn
L
Cu
CuCu L
LL
SC
SCSC L
LL
T = 700 °C T = 4.2 K
![Page 85: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/85.jpg)
85
Nb3Sn strand
The Nb3Sn electrical characteristic is strain sensitive ( is the uni-axial strain):
kE s
BTn
c
sc Jsign
BTJ
JE
,,
,,
Durham scaling
wcc cccTT
14
43
32
2** 10 *
cT
Tt
tcccBTB cc 110,0, 44
33
22
*2
*2 ,*
2 TB
Bb
c
w
u
cccAA 44
33
2210
qpm
ccc bbTBtTABTJ 1,1,, 13*
2
22*
sc BTJTrBTn ,,,1,,
![Page 86: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/86.jpg)
86
Nb3Sn strand
![Page 87: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/87.jpg)
87
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 (TFMC-
FSJS, 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
![Page 88: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/88.jpg)
88
SULTAN Test Facility (Switzerland)
![Page 89: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/89.jpg)
89
Sudden quench in NbTi cable
WIC-130905
-2
0
2
4
6
8
10
12
14
16
18
20
25 27 29 31 33 35
current (kA)
Vo
ltag
e (L
V21
22)
(mic
ro-V
olt
)
WIC-130909
-2
0
2
4
6
8
10
12
14
16
18
20
20 22 24 26 28
current (kA)
Vo
ltag
e (L
V21
22)
(mic
ro-V
olt
)
Sudden quench shows that the current redistribution among the strands of the cable is too low.
At a large value of the current, the quench of the cable occurs and it is not possible to measure the critical current.
![Page 90: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/90.jpg)
90
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.
Sudden quench in NbTi cable
![Page 91: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/91.jpg)
91
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).
![Page 92: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/92.jpg)
92
Degradation of the characteristics of Nb3Sn cable
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.
Cross sectio of TFI, in the most stressed region
Cross sectio of TFI, in the lesst stressed region
![Page 93: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/93.jpg)
93
The experiments performed in Japan and The Netherland on a single strand confirm a strong reduction of electrical properties due to bending effects.
Degradation of the characteristics of Nb3Sn cable
![Page 94: Engineering of electromagnetic systems for controlled thermonuclear fusion Scuola di Dottorato in Ingegneria Industriale Università degli Studi di Bologna](https://reader033.vdocument.in/reader033/viewer/2022051316/56649d485503460f94a2456d/html5/thumbnails/94.jpg)
94
Future developments
Nb3Al use: properties are not strain sensitive
HTS use: critical field extremely high