Engineering of electromagnetic systems for controlled thermonuclear fusion

1
Engineering of electromagnetic systemsfor
controlled thermonuclear fusion
Scuola di Dottorato in Ingegneria
Industriale Università degli Studi di Bologna
22,24 giugno 2009
2
INDEX

• Introduction to controlled thermonuclear fusion
• Superconductivity
• NbTi e Nb3Sn superconducting cables
• ITER (International Tokamak Experimental
  Reactor) experiment
• Wendelstein experiment

3
Introduction toControlled Thermonuclear Fusion
4
Fission and Fusion nuclear reactions
5
Fusion reactions
With neutron emission (activation of materials)
Without neutron emission
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.
Potential energy vs. distance between nuclei
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.
Maxwell velocity distribution
k Boltzmann constant 1.3805 10-23 J K-1
8
Thermonuclear fusion
R reaction rate ? cross section

• 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).

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)

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.

Particles are completely confined in the
directions normal to the field but no confinement
is present in the direction parallel to the field
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.

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

• A toroidal magnetic field
• A poloidal magnetic field

And the field lines should be of helical type
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)

14
TOKAMAK - STELLARATOR
TOKAMAK
STELLARATOR
15
TOKAMAK
Equilibrium equation

• The plasma is the secondary winding of a
  transformer the primary winding of the
  transformer is the central solenoid external coil.

Radial profiles of pressure (p), toroidal
magnetic flux density (B?) and poloidal magnetic
flux density (B?)
16
TOKAMAK
17
TOKAMAK
18
STELLARATOR
Winding system to produce poloidal magnetic field
19
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.

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.
Natural Litium is a mixture of Litium-6 (7.4 )
and Litium-7 (92.6 )
20
Reactor plasma energy balance
E Plasma energy (n density of D and T nuclei)
POH Power loss due to Joule effect
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
PL Power loss due to heat conduction,
convection and radiation (?E energy confinement
time)
Paux Power input by additional heating system
At ignition
21
Reactor
22
Reactor
Research and development ..
23
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

24
International Thermonuclear Experimental Reactor
ITER
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
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

26
ITER
27
ITER
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.

29
Superconductivity
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
31
Properties of superconducting materials

• Type I superconductors
• Low transition temperature Type II
  superconductors
• High transition temperature Type II
  superconductors
• Losses in transient regime

32
Type I superconductors
At temperatures lower than the critical one the
electrical resistivity is nil (lt 10-21 ?m)
33
Type I superconductors
The superconducting state is a new phase of the
material
Thermal conductivity vs. temperature
Heat capacity vs. temperature
34
Type I superconductors

• Perfect diamagnetism (Meissner effect) the
  magnetic flux density inside a type I
  superconducting material is nil.

? penetration length
Superconducting screen currents (supercurrents)
are presents which flow in a shell, with
thickness of about the penetration length, near
the surface of the sample.
35
Type I superconductors
From a macroscopic point of view the phenomenon
can be modeled with a volume magnetization of the
superconducting material.
Magnetization characteristics
36
Type I superconductors
A type I superconductor is not only a perfect
conductor
Field cooling
Zero field cooling
Perfect conductor
Superconductor
Perfect conductor
Superconductor
37
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)

38
Type I superconductors
The critical surface defines all the possible
operating condition for the superconducting state
to be present
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
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

41
Type II superconductors
When coherence length (?) is lower than the
penetration length (?) magnetic field can
penetrate in the superconducting material
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
43
Type II superconductors

• When Hext lt Hc1 (lower critical field) Type II
  superconductor undergoes Meissner effects as type
  I superconductor
• When Hc1 lt Hext lt Hc2 (upper critical field)
  magnetic field penetrates into the
  superconducting material (mixed state)
• When H gt Hc2 superconducting state is destroyed

44
Type II superconductors
Hc0
T
Magnetic phase diagram
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

46
Type II superconductors
First image of Vortex lattice, 1967
Bitter DecorationPb-4atIn rod, 1.1K, 195G
U. Essmann and H. TraubleMax-Planck Institute,
Stuttgart Physics Letters 24A, 526 (1967)
Abrikosov lattice in MgB2, 2003
Bitter DecorationMgB2 crystal, 200G
L. Ya. Vinnikov et al.Institute of Solid State
Physics, ChernogolovkaPhys. Rev. B 67, 092512
(2003)
http//www.fys.uio.no/super/vortex/
47
Type II superconductors
Vortex structure can be modeled from a
macroscopic point of view by means of a volume
magnetization.
Magnetization characteristics
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

• 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

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.

50
Type II superconductors

• Joule dissipation (electric field) is due to
  movement of vortexes.
• 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

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)

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

53
High temperature superconductors
200
150
Temperature, TC (K)
100
50

Low-TC
Hg
V3Si
0
1900
1920
1940
1960
1980
2000
Year
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

55
Typical structure of ceramic superconductors

Perovskite ABX3
YBCO YBa2Cu3O6
YBCO YBa2Cu3O7
56
BSCCO
BSCCO Bi2Sr2Can-1CunOy
Conducting layers Cu O
Non-conducting layers
57
Anisotropy
BSCCO-2223 Jc vs. applied magnetic field
The field is normal to CU-O planes
The field is parallel to CU-O planes
58
Magnesium boride
J. Akimitsu, Symp. on Transition Metal Oxides,
Sendai, Jan 2001
Tc?40 K
MgB2
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

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

61
Cryogenics
COP Coefficient of Performance
efficiency
62
Cryogenics
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.

64
Losses in transient regime
Infinite slab in an alternate magnetic field
parallel to the main surfaces of the slab

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
65
Losses in transient regime
Bp minimum magnetic flux density change which
fully penetrates into the slab
If magnetic field does not fully penetrates into
the slab
66
Losses in transient regime
If magnetic field fully penetrates into the slab
The lower is the slab thickness the larger is b
and the lower are the losses
67
flux jump instability

In a first approximation
DQ Energy loss per unit volume corresponding to
a change DT of the temperature
Energy balance (adiabatic case)
Effective heat capacity is lower than the real one
68
flux jump instability
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 C 0.89 J kg-1 K-1 Tc 6.5 K
(B 6 T)
a lt 115 ?m
69
NBTi e Nb3Sn Cables
70
Superconducting cables
CICC
Rutherford cable
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 3?3?5?5?6
• Twist pitches (mm)
• 80, 140, 190, 300, 440

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)

73
Strand modelling
In superconductor
In copper
From previous equation the elctrical
characteristics E-J of the strand is obtained
Experimental strand characterization is made by
measuring its critical current ( Ic) and its
current sharing temperature (Tcs)
74
Critical current measurement
At the critical current the value of the electric
field equals the critical value (Ec).

• The critical value of the electric field is not
  fixed typical values are Ec 10-5 V/m, Ec
  10-4 V/m

• At the critical conditions is Jm ltlt Js thus

75
Current sharing temperature measurement
The temperature correspondig to the critical
value of the electric field is the measured
current sharing temperature (Tcs)
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.

77
Terminations / joints
In terminations/joints not all the strands touch
the current exchange surface thus current
distribution can not be uniform
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

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.
80
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.

81
NbTi strand
The electrical characteristics of aNbTi strand
can be modeled by means of the Bottura scaling
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
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

• 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.

83
Nb3Sn Strand
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 ).
T 4.2 K
T 700 C
85
Nb3Sn strand
The Nb3Sn electrical characteristic is strain
sensitive (? is the uni-axial strain)
Durham scaling
86
Nb3Sn strand
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

88
SULTAN Test Facility (Switzerland)
89
Sudden quench in NbTi cable
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.

90
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.

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).

92
Degradation of the characteristics of Nb3Sn cable
Cross sectio of TFI, in the lesst stressed region
Cross sectio of TFI, in the most 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.
93
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.
94
Future developments

• Nb3Al use properties are not strain sensitive
• HTS use critical field extremely high