Superconducting magnets for
Accelerators
Martin N Wilson (Rutherford Lab ⇒ Oxford Instruments ⇒ CERN ⇒ consultant)
Outline
• why bother with superconductivity?
• properties of superconductors: critical
field, temperature & current density
• magnetic fields and how to create them
• load lines, training and how to cure it
• screening currents and the critical state
model
• fine filaments, composite wires & cables
• magnetization, field errors & ac losses
• quenching and protection
• hardware
• where to get more info
Martin Wilson Lecture 1 slide 1
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Superconducting magnets for Accelerators
Who needs superconductivity anyway?
Abolish Ohm’s Law!
• no power consumption
(although do need refrigeration power)
• ampere turns are cheap, so don’t need iron ⇒ higher fields
(although often use it for shielding)
• high current density ⇒ compact windings, high gradients
Consequences
q
• lower power bills
• higher magnetic fields mean reduced bend radius
⇒ smaller rings
⇒ reduced capital cost
⇒ new technical possibilities
(eg muon collider)
• higher quadrupole gradients
⇒ higher luminosity
Martin Wilson Lecture 1 slide 2
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
The critical surface of niobium titanium
• Niobium titanium NbTi is the standard
‘work horse’ of the superconducting magnet
business
Jc
• it is a ductile alloy
θc
Bc2
Current density (kA.mm-2)
• picture shows the critical surface, which is
the boundary between superconductivity and
normal resistivity in 3 dimensional space
• superconductivity prevails everywhere
below the surface, resistance everywhere
above it
• we define an upper critical field Bc2 (at zero
temperature and current) and critical
temperature θc (at zero field and current)
which are characteristic of the alloyy
composition
• critical current density Jc(B,θ) depends on
processing
Martin Wilson Lecture 1 slide 3
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Critical curreent density A.m
mm-2
The critical line at 4.2K
• because magnets usually work in
boiling liquid helium, the critical
surface is often represented by a curve
of current versus field at 4.2K
104
Nb3Sn
103
NbTi
• but it is brittle intermetallic compound
with poor mechanical properties
• note
t that
th t both
b th the
th field
fi ld andd currentt
density of both superconductors are
way above the capability of
conventional electromagnets
102
10
• niobium tin Nb3Sn has a much higher
performance in terms of critical
current field and temperature than
NbTi
Conventional
iron yoke
electromagnets
Magnetic
g
field (Tesla)
(
)
Martin Wilson Lecture 1 slide 4
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Critical field & temperature of metallic
superconductors
Note: of all the
metallic
superconductors,
only
l NbTi is
i
ductile.
All the rest are
brittle
intermetallic
compounds
Martin Wilson Lecture 1 slide 5
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Critical field & temperature of metallic
superconductors
30
crritical field Bc2 T .
To date, all
superconducting
accelerators have
used NbTi.
20
Nb3Sn
Of the
intermetallics,
only Nb3Sn has
NbTi
10
found significant
use in magnets
0
0
Martin Wilson Lecture 1 slide 6
5
10
temperature K
15
20
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature
superconductors
1987 Bednortz
and Muller
250
High critical
temperature also
brings
g high
g
critical field
crittical field Bc2 T .
200
YBCO
150
Yttrium Barium
Copper Oxide
YBa2Cu3O7
100
50
Nb3Sn
S
NbTi
0
0
20
Martin Wilson Lecture 1 slide 7
40
60
temperature K
80
100
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature superconductors
250
Unfortunately we
only get
superconducting
current carrying
below the
irreversibility field
critical field Bc2 T .
200
YBCO
150
Yttrium Barium
Copper Oxide
YBa2Cu3O7
100
50
irreversibility
y line
Nb3Sn
NbTi
0
0
Martin Wilson Lecture 1 slide 8
20
40
60
temperature K
80
100
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature superconductors
40
YBCO
irreversibility
field
YBCO
critical field B c2 T .
c
30
Nb3Sn
Yttrium Barium
Copper Oxide
YBa2Cu3O7
20
10
NbTi
0
0
Martin Wilson Lecture 1 slide 9
20
40
60
temperature K
80
100
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature superconductors
40
YBCO
irreversibility
field
YBCO
critiical field Bc
c2 T .
30
More recently
magnesium
diboride MgB2
offers moderately
high temperature
in a simpler
cheaper material
MgB2
20
Nb3Sn
10
0
NbTi
0
Martin Wilson Lecture 1 slide 10
20
40
60
temperature K
80
100
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature superconductors
40
YBCO
irreversibility
field
YBCO
crritical field B
Bc2 T .
30
MgB2
But MgB2
20
Nb3Sn
also has an
irreversibility
field
MgB2
irreversibilty
field
10
0
NbTi
0
Martin Wilson Lecture 1 slide 11
20
40
60
temperature K
80
100
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
High temperature superconductors
So here’s
h ’ the
h
parameter
space
p
for
future
magnets
40
YBCO
irreversibility
field
critic
cal field Bc2 T .
30
Nb3Sn
20
MgB2
irreversibilty
field
10
NbTi
0
0
20
Martin Wilson Lecture 1 slide 12
40
60
temperature K
80
100
Critical
current
density Jc
depends on
skilful
processing of
the material
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Filamentary composite wires
• for reasons that will be described
later, superconducting materials
are always used in combination
with a good normal conductor
such as copper
• to ensure intimate mixing
between the two, the
superconductor is made in the
form of fine filaments embedded
in a matrix of copper
• typical
t i l dimensions
di
i
are:
• wire diameter = 0.3 - 1.0mm
• filament diameter = 5 - 50μm
• for electromagnetic reasons, the
composite wires are twisted so
that the filaments look like a rope
Martin Wilson Lecture 1 slide 13
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Fields and ways to create them:
conventional
• iron yoke reduces magnetic reluctance
⇒ reduces ampere turns required
⇒ reduces power consumption
• iron
i
guides
id andd shapes
h
the
h field
fi ld
I
I
B
1.6
T
B
H
-100A/m
100A/m
100A/m
-1.6T
1 6T
Martin Wilson Lecture 1 slide 14
IIron electromagnet
l t
t
– for accelerator, HEP experiment
transformer, motor, generator, etc
BUT iiron saturates
t
t att ~ 2T
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Fields and ways to create them: superconducting
dipoles
simplest winding
uses racetrack
coils
'saddle' coils make
better field
shapes
• some iron - but field shape is set
mainly by the winding
• used when the long dimension is
transverse to the field, eg accelerator
magnets
g
• known as dipole magnets (because
the iron version has 2 poles)
special winding cross
sections for good
uniformity
I
I
I
B
Martin Wilson Lecture 1 slide 15
LHC has
'up' & 'down'
dipoles side by side
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Dipole field from overlapping
cylinders
Ampere'ss law for the field inside a cylinder carrying uniform current density
Ampere
2
B.ds
=
2π
rB
=
μ
I
=
μ
π
r
J
o
o
∫
B=
μ o Jr
J
B
B
2
• two cylinders with opposite currents
• push them together
• where they overlap, currents cancel out
• zero current ⇒ the aperture
JJJ
J
• fields in the aperture:
B
B
B − μ Jt
μo J
(− r1cosθ1 + r2cosθ2 ) = o
By =
2
2
μJ
Bx = o (− r1sinθθ1 + r2 sinθθ2 ) = 0
2
• thus the two overlapping cylinders
give a perfect dipole field
Martin Wilson Lecture 1 slide 16
By =
B
r1
θ1
t
t
B
BB r2
B
θ2
t
− μo J e t
2
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Dipole
Magnets
• made from
superconducting
cable
• winding must have
the right cross section
• also need to shape the
endd turns
t
I
I
I
B
Martin Wilson Lecture 1 slide 17
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Fields and ways to create them: superconducting
quadrupoles
• gradient fields produce focussing
• quadrupole windings
I
I
Bx = ky
Martin Wilson Lecture 1 slide 18
By = kx
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Critical line and
magnet load lines
800
7
Engineering
g Current den
nsity (A/mm2)
6
1000
Engineering Cuurrent
dennsity Amm-2
800
600
400
200
2
2
4
*
6
10
8
600
superconducting
*
400
magnet
aperture
field
quench
200
magnet
peak field
0
4
0
6
2
4
6
Field (T)
8
8
10
12
14
16
Martin Wilson Lecture 1 slide 19
resistive
we expect the magnet to go resistive
'quench' where the peak field load line
crosses the critical current line ∗
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
10
‘Training’ of magnets
field
quench
10.0
time
• when the current ((and
field) of a magnet is
ramped up for the first
time, it usually ‘quenches’
(goes resistive)) at less
(g
than the expected current
• at the next try it does
better
• known
k
as training
t i i
Martin Wilson Lecture 1 slide 20
field acheived .
9.5
9.0
8.5
stainless steel collars
stainless steel collars
aluminium collars
operating field
8.0
0
5
10
15
20
25
quench number
30
35
40
Training of LHC short prototype dipoles (from A.
A Siemko)
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
45
Causes of training:
((1)) low specific
p f heat
102
Specifiic Heat Joules / kg / K
102
• the specific heat of all substances
falls with temperature
10
• at 4.2K, it is ~2,000 times less
than at room temperature
1
• a given release of energy within
the winding thus produce a
temperature rise 2,000 times
greater than at room temperature
300K
10-1
• th
the smallest
ll t energy release
l
can
therefore produce catastrophic
effects
4.2K
10-2
1
Martin Wilson Lecture 1 slide 21
10
temperature K 100
1000
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Causes of training: (2) conductor motion
• Big electromagnetic forces in magnets
F
• Bursting force in LHC dipoles = 320 tonne/m
• Conductors are pushed by the electromagnetic forces.
• Frictional heating if they move
B
work done per unit length of conductor if it is pushed a
distance δz
J
W = F.δ z = B.I.δ z
frictional heating per unit volume
Q=B
B.J.
J δz
typical numbers for NbTi:
B = 5T Jeng = 5 x
108 A.m-2
so if δ = 10 μm
then Q = 2.5 x 104 J.m-3
Starting from 4.2K
4 2K θfinal = 7.5K
7 5K
Martin Wilson Lecture 1 slide 22
can you
engineer a
winding to
better than
10 μm?
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Causes of training: (3) resin cracking
• try to stop wire movement by impregnating the winding with epoxy resin
• the resin contracts much more than the metal - so it goes into tension
• it also become brittle at low temperature.
brittleness + tension ⇒ cracking ⇒ energy release
Calculate the stain energy induced in resin by differential
thermal contraction
l
let:
σ = tensile
il stress
Y=Y
Young’s
’ modulus
d l
ε = differential strain ν = Poisson’s ratio
thermal contraction of Cu ~ 3×10-3
(room to 4K)
thermal contraction of resin ~ 11×10-3
so ε = (11 – 3) x 10-3
typically Y = 7 x 109 Pa
strain energy
σ2
n = 1/3
Yε 2
Q1 =
=
2Y
2
Q1 = 2.5 x 105 J.m-3
if released adiabatically, raises temperature to
Martin Wilson Lecture 1 slide 23
(uniaxial strain)
θfinal
fi l = 16K
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
How to reduce training?
1) Reduce the disturbances occurring in the magnet winding
• make the winding fit together exactly to reduce movement of conductors under field forces
• pre-compress the winding to reduce movement under field forces
• if using resin, minimize the volume and choose a crack resistant type
• match thermal contractions, eg fill epoxy with mineral or glass fibre
most accelerator magnets are insulated using a Kapton film with a thin adhesive coating
2) Make
M k the
th conductor
d t able
bl tto withstand
ith t d di
disturbances
t b
without
ith t quenching
hi
K
800
600
400
200
• increase the
minimum
quench
energy
gy
2
2
4
4
6
8
Martin Wilson Lecture 1 slide 24
Fi
*
el
d
T
6
8
10
Eng Curren
nt density (Amm
m-2)
re
ddensity kAmm-2
te
e
mp
u
rat
Engineering Curreent
• increase the
temperature
margin
800
NbTi at 6T
600
400
operate
* quench
200
margin
0
0
2
4
Temperature (K)
6
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Minimum quench energy MQE
large MQE
⇒ more stable conductor
⇒ less training
open insulation
Porous metal
ALS 83 bare
bare wire
10000
MQE μJ
• MQE is the smallest energy input
which quenches the conductor.
• measure it by injecting short
(100μs) heat pulses at a point on
the conductor.
100000
1000
for a large MQE we need:
• large
l
temperature
t
t
margin
i
• large thermal conductivity – need
copper
100
• small resistivity
resisti it – need copper
• large specific heat – difficult
• good cooling – winding porous to
liquid helium coolant
Martin Wilson Lecture 1 slide 25
10
0.4
0.5
0.6
0.7
I / Ic
0.8
0.9
1.0
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Persistent screening currents
• when a superconductor is subjected to a
changing magnetic field, screening currents
are induced to flow
• screening currents are in addition to the
transport current, which
hi h comes from
f
the
h
power supply
• they are like eddy currents but, because
there is no resistance,, they
y don't decayy
• usual model is a superconducting slab in a
changing magnetic field By
• assume it's infinitely long in the z and y
directions - simplifies
p
to a 1 dim problem
p
• dB/dt induces an electric field E which
causes screening currents to flow at critical
current density Jc
• known as the critical state model or Bean
model
J
d infinitee slab
s b geometry,
geo e y,
• in thee 1 dim
Maxwell's equation says
∂B y
J
B
x
Martin Wilson Lecture 1 slide 26
∂x
= −μ o J z = μ o J c
• so uniform Jc means a constant field
gradient inside the superconductor
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
The flux penetration process
plot field profile across the slab
B
fully penetrated
fi ld increasing
field
i
i from
f
zero
everywhere current density is ± Jc or zero
(C
(Critical
l SState or B
Bean model)
d l)
field decreasing through zero
Martin Wilson Lecture 1 slide 27
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Magnetization of the Superconductor
When viewed from outside the sample,
the persistent currents produce a
magnetic moment.
ffor cylindrical
li d i l filaments
fil
the
h inner
i
current boundary
b
d
is roughly elliptical (controversial)
define a magnetization (magnetic
moment per unit volume)
J
J
M =∑
V
I .A
V
NB units of H
J
B
for a fully penetrated slab
B
when fully penetrated, the magnetization is
d
a
J a
1
M = ∫ J c x dx = c
a0
4
Martin Wilson Lecture 1 slide 28
M=
2
Jc d f
3π
where df = filament diameter
Note: M is
i here
h defined
d fi d per unit
i volume
l
off NbTi
b i filament
fil
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Magnetization of NbTi
M
Bext
Martin Wilson Lecture 1 slide 29
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
recap
M=
Coupling between
filaments
2
Jc d f
3π
• reduce M by making fine filaments
• for ease of handling, filaments are
embedded
b dd d in
i a copper matrix
i
• fortunately the coupling currents
may be reduced by twisting the wire
• coupling currents behave like
eddy
dd currents
t andd produce
d
an
additional magnetization
dB 1 ⎡ pw ⎤
Me =
dt ρt ⎢⎣ 2π ⎥⎦
• but in changing fields, the filaments are
magnetically coupled
• screening currents go up the left filaments
and return down the right
Martin Wilson Lecture 1 slide 30
2
where ρt = resistivity across the copper
and pw = wire twist pitch
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Coupling ⇒ rate dependent
magnetization
recap: magnetization
i i has
h two components:
Mag
gnetization
• persistent current in the filaments
Mf =
External field
Me
Mf
2
Jc( B )d f
3π
Mf depends on B
• and eddy current coupling
between the filaments
dB 1 ⎡ pw ⎤
Me =
dt ρt ⎢⎣ 2π ⎥⎦
2
Me depends
d
d on dB/dt
dB/d
Note Mf defined per unit volume
of NbTi filament
and Me per unit volume of wire
Martin Wilson Lecture 1 slide 31
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Magnetization and field errors
Magnetization is important in accelerators because it produces field error.
error The effect is worst
at injection because
- ΔB/B is greatest
- magnetization, ie ΔB is greatest at low field
skew qu
uadrupole error
300
6 mT/sec
13 mT/seec
19 mT/sec
200
skew
quadrupole
error in
i
Nb3Sn dipole
which has
exceptionally
l
large
coupling
magnetization
(University of
T
Twente)
t )
100
0
-100
-200
-300
0
Martin Wilson Lecture 1 slide 32
1
2
Field B ((T))
3
4
5
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Synchrotron
injection
don't inject here!
• synchrotrons
inject at low
field, ramp to
high field and
then down again
B
t
• note how quickly
the magnetization
changes when we
start the ramp up
ΔM
B
ΔM
much
h better
b tt here!
h !
Martin Wilson Lecture 1 slide 33
• much less
magnetization
g
change if we
ramp down to
zero and then
upp to injection
j
B
t
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Why cables?
• for g
good trackingg we connect synchrotron
y
magnets in series
• if stored energy is E, rise time t and operating
current I , the charging voltage is
E=
1 2
LI
2
V=
L I 2E
=
t
It
• for a given magnet size and field the stored
energy E is fixed
• so to keep a reasonable voltage V we need
high current
the RHIC tunnel
• a composite wire of fine filaments typically has 5,000 to 10,000 filaments, so it carries 250A to 500A
• for 5 to 10kA, we need 20 to 40 wires in pparallel - a cable
Martin Wilson Lecture 1 slide 34
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Rutherford
cable
• fully transposed - every
strand changes places with
every other
• cable insulated by wrapping
2 or 3 layers
l
off Kapton
K
roller die
puller
ll
finished
cable
• gaps may be left to allow
penetration of liquid
helium
• outer layer is treated with
an adhesive layer for
bonding to adjacent turns.
Martin Wilson Lecture 1 slide 35
superconducting
wires
i
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Coupling in Rutherford cables
• To enable current sharing, we keep some electrical contact between strands of the cable
crossover resistance Rc
Ra
Rc
adjacent resistance Ra
• Changing transverse fields induce coupling currents
via the crossover resistance Rc
Martin Wilson Lecture 1 slide 36
B&
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Cable coupling adds more
magnetization
Mag
gnetization
filament magnetization Mf depends on B
External field
Mtc
t
Me
coupling
between
filaments Me
depends on dB/dt
Mf
coupling
between wires
in cable depends on dB/dt
Martin Wilson Lecture 1 slide 37
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
AC losses
For a magnet material, work done
by magnetic field
dW = μo HdM
Mag
gnetization
around a closed loop
External field
W = ∫ μ o HdM
loop comes back to
same place
- field energy is same
- so work done is ac
loss in material
within filaments
between filaments
b t
between
wires
i
Martin Wilson Lecture 1 slide 38
ac loss is area of hysteresis loop
W = ∫ μ o HdM = ∫ μo MdH
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Quenching: magnetic stored energy
Magnetic energy density
B2
E=
2μ o
LHC dipole magnet (twin apertures)
at 5T E = 107 Joule.m
l -33
at 10T E = 4x107 Joule.m-33
E = ½ LI 2 L = 0.12H I = 11.5kA E = 7.8 x 106 Joules
the magnet weighs 26 tonnes
so the magnetic stored energy is
equivalent to the kinetic energy of:26 tonnes travellingg at 88km/hr
coils weigh 830 kg
equivalent to the kinetic energy of:830kg travelling at 495km/hr
Martin Wilson Lecture 1 slide 39
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
The quench
process
• resistive region starts somewhere
in the winding at a point
- this is the problem!
• it grows by thermal conduction
• stored energy ½LI2 of the magnet
is dissipated as heat
• greatest integrated heat
dissipation is at point where the
quench starts
• internal voltages much greater
than terminal voltage ( = Vcs
current supply)
• maximum temperature may be
calculated from the current decay
time via the U(θ) function
(adiabatic approximation)
Martin Wilson Lecture 1 slide 40
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
The temperature rise function U(θ)
or the 'fuse
fuse blowing'
blowing calculation
(adiabatic approximation)
1.6E+17
∫
∞
o
θm
J 2 (T ) dT = ∫
θo
γ C (θ )
dθ
ρ (θ )
-4
1.2E+17
2
J(T) = overall current density,
T = time,
ρ(θ) = overall resistivity,
γ = density, θ = temperature,
C(θ) = specific heat,
TQ= quench decay time.
U( ) (A sm )
U
J 2 (T ) ρ (θ )dT = γ C (θ )dθ
8.0E+16
4.0E+16
= U (θ m )
J o2TQ = U (θ m )
GSI 001 dipole winding
pure copper
p
pp
0.0E+00
0
• GSI 001 dipole winding is
pp , 22% NbTi,,
50% copper,
16% Kapton and 3% stainless steel
Martin Wilson Lecture 1 slide 41
100
200
300
temp (K)
400
500
• NB always use overall current density
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
8000
Measured current decay after a
quench
currentt (A)
6000
4000
2000
0
0.0
0.2
time (s)
0.4
0.6
0.8
Dipole GSI001 measured at Brookhaven National Laboratory
Martin Wilson Lecture 1 slide 42
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Calculating the temperature rise from the current
decay curve
U(θ) (calculated)
6 E+16
6.E+16
4.E+16
4.E+16
2.E+16
2.E+16
0.E+00
0.E+00
2
U(θ) (A sm
-4)
6 E+16
6.E+16
2
inte
egral (J dt)
∫ J 2 dt
d (measured)
(
d)
0.0
Martin Wilson Lecture 1 slide 43
0.2
time ((s))
0.4
0.60
200
temp (K)
400
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Growth of the resistive zone
the quench starts at a point and then grows
in three dimensions via the combined
effects
ff t off Joule
J l heating
h ti andd
thermal conduction
*
Martin Wilson Lecture 1 slide 44
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Quench propagation velocity
• resistive zone starts at a point and spreads along
the conductor and transverse to it
• the force driving it forward is the heat generation
in the resistive zone,, together
g
with heat
conduction along the wire
1
⎫2
J ⎧ ρk
=
⎨
⎬
γ C ⎩θ t − θ 0 ⎭
θt
distance
αv
superconducting
xt
αv
v
1
2
Typical values
Martin Wilson Lecture 1 slide 45
temperature
where: J = engineering current density, γ = density, C = specific heat,
ρ = resistivity, k = thermal conductivity, θt = transition temperature
Transverse to the conductor
vtrans ⎧⎪ ktrans ⎫⎪
α=
=⎨
⎬
vlong ⎪⎩ klong ⎪⎭
v
θo
Along the conductor
vlong
resistive
vad = 5 - 200 mss-1
α = 0.01 − 0.03
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Computation of resistance growth and current
decay
v δt
start resistive zone 1
*
αvdt
in time δt zone 1 grows v.dt longitudinally and α.v.dt transversely
temperature off zone grows by
b δθ1 = J2 ρ(θ
(θ1)δτ
δ / γ C(θ1)
resistivity of zone 1 is ρ(θ1)
calculate resistance and hence current decay δI = R / L.δt
in time δt add zone n:
v δt longitudinal and α.v.
v.
v δt transverse
v δt
αvdt
temperature of each zone grows by δθ1 = J2ρ(θ1)δt /γC(θ1) δθ2 = J2ρ(θ2)δt /γC(θ2) δθn = J2ρ(θ1)dt /γC(θn)
resistivity
i ti it off eachh zone is
i ρ(θ
(θ1) ρ(θ
(θ2) ρ(θ
(θn) resistance
it
r1= ρ(θ
(θ1) ∗ fg1 (geom
(
factor)
f
) r2= ρ(θ
(θ2) * fg2 rn= ρ(θ
(θn) * fgn
calculate total resistance R = ∑ r1+ r2 + rn.. and hence current decay δI = (I R /L)δt
when I ⇒ 0 stop
Martin Wilson Lecture 1 slide 46
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Methods of quench protection:
1) External dump resistor
2) Quench back heater
method most
commonly used
in accelerator
magnets 9
•
detect the quench electronically
• detect the quench electronically
•
power a heater in thermal contact with the winding
• open an external circuit breaker
•
this quenches other regions of the magnet,
magnet forcing
the normal zone to grow more rapidly
⇒ higher resistance
⇒ shorter decay time
⇒ lower temperature rise at the hot spot
• force the current to decay through
the resistor
Martin Wilson Lecture 1 slide 47
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Winding an LHC dipole
photo courtesy of Babcock Noell
Martin Wilson Lecture 1 slide 48
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Curing press
Martin Wilson Lecture 1 slide 49
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Collars
How to make an external structure that
• fits tightly round the coil
• presses it into an accurate shape
• has low ac losses
• can be mass produced cheaply
• ???
• Answer make collars by precision stamping of
stainless steel or aluminium alloy plate a few
mm thick
- inherited from conventional magnet laminations
invert alternate pairs so that they interlock
Martin Wilson Lecture 1 slide 50
press collars over coil from above and below
push steel rods through holes to lock in position
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Collars and
end plate
(LHC
dipole)
Martin Wilson Lecture 1 slide 51
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Adding the iron
stainless
shell
iron
laminations
• iron
laminations
are added around
the collared coil
• they are forced into place, again using the
collaring press
• remember however that pure iron
becomes brittle at low temperature
• the tensile forces are therefore taken by a
stainless steel shell which is welded
around the iron, while still in the press
• this stainless shell can also serve as the
helium vessel
Martin Wilson Lecture 1 slide 52
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Dipole inside its stainless shell
Martin Wilson Lecture 1 slide 53
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Complete magnet in
cryostat
Martin Wilson Lecture 1 slide 54
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Make a lot of Magnets and install in the
tunnel
Martin Wilson Lecture 1 slide 55
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Concluding remarks
• superconductivity offers higher magnetic fields and field gradients
gradients, with less energy dissipation
• NbTi is the most common superconducting material and has been used in all accelerators to date
• superconducting magnets do not use iron to shape the field
field, so must use special winding shapes
• magnets don’t reach their expected current/field first time but show training
- control training by reducing movement, attention to contraction and increasing MQE
• persistent screening currents produce magnetization of the superconductor which causes field
errors and ac loss – need fine ~ 5μm filaments
• accelerators need high currents,
currents so must use many wires in parallel – a cable
• coupling between filament in wire and between wires in cable increases magnetization
• magnets store large inductive energy which is released at quench as heating – must protect
• magnet manufacturing techniques have been developed to ensure accurate winding shape and
minimize conductor movement
customer support: m-wilson@dsl.pipex.com
Martin Wilson Lecture 1 slide 56
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Some useful references
Superconducting Magnets
Mess P Schmuser,
Schmuser
• Superconducting Accelerator Magnets: KH Mess,
S Wolf., pub World Scientific, (1996) ISBN 981-02-2790-6
• High Field Superconducting Magnets: FM Asner, pub Oxford
University Press (1999) ISBN 0 19 851764 5
• Case Studies in Superconducting Magnets: Y Iwasa, pub
Pl
Plenum
Press,
P
New
N York
Y k (1994),
(1994) ISBN 00-306-44881-5.
306 44881
• Superconducting Magnets: MN Wilson, pub Oxford University
Press (1983) ISBN 0-019-854805-2
• Proc Applied Superconductivity Conference: pub as IEEE Trans
Applied Superconductivity,
Superconductivity Mar 93 to 99
99, and as IEEE Trans
Magnetics Mar 75 to 91
• Handbook of Applied Superconductivity ed B Seeber, pub UK
Institute Physics 1998
• JUAS lectures on superconducting magnets (and all accelerator
t i ) http://juas.in2p3.fr
topics)
htt //j
i 2 3f
• 'Superconducting Accelerator Magnets' DVD available from mjball
@ comcast.net
Superconducting Materials
• Superconductor Science and Technology, published monthly by
Institute of Physics (UK).
• Superconductivity of metals and Cuprates, JR Waldram, Institute
of Physics Publishing (1996) ISBN 0 85274 337 8
Science, A
• High Temperature Superconductors: Processing and Science
Bourdillon and NX Tan Bourdillon, Academic Press, ISBN 0 12
117680 0
Martin Wilson Lecture 1 slide 57
Materials Mechanical
Clark
• Materials at Low Temperature: Ed RP Reed & AF Clark,
pub Am. Soc. Metals 1983. ISBN 0-87170-146-4
• Handbook on Materials for Superconducting Machinery
pub Batelle Columbus Laboratories 1977.
• Nonmetallic materials and composites at low
temperatures: Ed AF Clark, RP Reed, G Hartwig pub
Plenum
• Nonmetallic materials and composites at low
temperatures 2, Ed G Hartwig, D Evans, pub Plenum
1982
• Austenitic Steels at low temperatures Editors R.P.Reed
and T.Horiuchi, pub Plenum1983
Cryogenics
Cryogenics Van Sciver SW
SW, pub Plenum 86
• Helium Cryogenics,
ISBN 0-0306-42335-9
• Cryogenic Engineering, Hands BA, pub Academic
Press 86 ISBN 0-012-322991-X
• Cryogenics: published monthly by Butterworths
• Cryogenie: Ses Applications en Supraconductivite, pub
IIR 177 Boulevard Malesherbes F5017 Paris France
• Handbook of Cryogenic Engineering, ed JG Weisand,
Taylor & Francis 1998 ISBN 1-56032-332-9
• Cryogenic
C
i Systems,
S t
RF Barron,
B
Oxford
O f d Science
S i
Publications ISBN 0-19-503567-4
Superconducting Magnets for Accelerators CAS Frascati Oct
2008
Materials data web sites and software
www.cryogenics.nist.gov
www
cryogenics nist gov (free) thermal
conductivity, specific heat, and thermal
expansion of solids, have been empirically
fitted and the equation parameters
www.cpia.jhu.edu (charged) plots and
automated data-look-up using the NIST
equations
www.cryodata.com
www
cryodata com (charged) cryogenic
properties of about 100 materials.
www.jahm.com (charged) temperature
dependent properties of about 1000
materials, many at cryogenic temperatures).
www.matweb.com (free) room-temperature
data for 10 to 20 properties of about 24,000
materials
thanks to Jack Ekin of NIST for this information
materialdatabase.magnet.fsu.edu (free)
structural materials at low temperature
Martin Wilson Lecture 1 slide 58
www.nist.gov/chemistry/fluid/ costs $200 runs as dll from
E l calculates
Excel,
l l t th
thermosphyiscal
h i l properties
ti off flfluids
id ffrom
the triple point upwards
Software Products from www.cryodata.com
GASPAK
properties of pure fluids from the triple point to high
temperatures.
HEPAK
properties of helium including superfluid above 0.8 K, up to
1500 K
K.
STEAMPAK
properties of water from the triple point to 2000 K and 200
MPa.
METALPAK CPPACK
METALPAK,
CPPACK, EXPAK
reference properties of metals and other solids, 1 - 300 K.
CRYOCOMP
properties and thermal design calculations for solid
materials, 1 - 300 K.
SUPERMAGNET
four unique engineering design codes for superconducting
magnet systems.
KRYOM
numerical modelling calculations on radiation-shielded
cryogenic enclosures.
Superconducting Magnets for Accelerators CAS Frascati Oct
2008