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1/41
Super
conduct
ing M
agnet
s fo
r Fusion
Applica
tion
Lu
isa
Ch
iesa
(Luis
a.C
hie
sa@
tuft
s.ed
u)
Oct
ob
er 8
, 20
09
Acc
eler
ator
Physi
cs a
nd T
echn
olo
gy S
emin
ars,
FN
AL
2/41
Outline
In
troduct
ion
S
uper
conduct
ivit
y a
nd i
ts a
ppli
cati
ons
H
igh e
ner
gy p
hysi
cs
F
usi
on
M
echan
ical
beh
avio
r of
cable
in c
onduit
conduct
ors
C
oncl
usi
ons
3/41
What is superconductivity?
A m
ater
ial
is s
aid
to
be
sup
erco
nd
uct
ive
if i
t h
as t
he
abil
ity o
f co
nd
uct
ing
ele
ctri
city
WIT
HO
UT
the
loss
of
ener
gy…
bas
ical
ly y
ou
car
ry c
urr
ent
for
FR
EE
!
In 1
908
H. K
amer
lin
gh
Onn
es
succ
essf
ull
y l
iqu
ifie
d
hel
ium
.
In 1
911
he
studie
d
the
low
tem
per
ature
resi
stiv
ity o
f m
ercu
ry
and…
He
go
t th
e N
ob
el
pri
ce i
n 1
91
3 f
or
it.
In 1
957
th
e B
CS
th
eory
was
dev
elop
ed a
nd
expla
ined
su
per
con
duct
ivit
y t
hro
ug
h a
mac
rosc
op
ic
coll
ecti
ve
qu
antu
m m
ech
anic
eff
ect.
Her
e’s
a
SIM
PL
IFIE
D
expla
nat
ion…
Req
uir
emen
t is
to
hav
e
LOW TEMPERATURES
4/41
What does BCS theory get you?
No
bel
pri
ce i
n p
hy
sics
19
72
Bar
dee
nC
oo
per
Sch
rief
fer
In 1
98
6 B
edn
orz
an
d M
ull
er d
isco
ver
ed superconductivity at high temperatures
in
layer
ed m
ater
ials
co
mp
risi
ng
co
pp
er o
xid
e p
lan
es a
nd
…
…th
ey g
ot
the
No
bel
pri
ce f
or
it i
n 1
98
7.
No
bel
pri
ce i
n p
hy
sics
19
87
Bed
no
rzM
ull
er
5/41
Type of superconductors
Th
ere
are
two
typ
es o
f su
per
con
du
ctin
g m
ater
ials
:
Type II
(co
mp
osi
te m
ater
ials
):
mix
ed s
tate
an
d a
llo
w p
arti
al p
enet
rati
on
Type I
(pu
re m
etal
s):
per
fect
dia
mag
net
ism
Perfect Diamagnetism
Diamagnetism
6/41
Critical Field
field
Bc2
Bc1
Tc
temperature
NO
RM
AL
ST
AT
E
MIX
ED
ST
AT
E
ME
ISS
NE
R (
type
I)(T
yp
e I)
Type I
sup
erco
nd
uct
or
wit
hst
and
ver
y
low
mag
net
ic f
ield
(<
0.1
T).
An
ele
ctri
c cu
rren
t in
a w
ire
crea
tes
mag
net
ic f
ield
. S
up
erco
nd
uct
ors
are
wel
l su
ited
fo
r m
akin
g s
tro
ng
el
ectr
om
agn
ets
(no
lo
ss a
nd
hig
h c
urr
ents
).B
UT
if
an “
exte
rnal
”fi
eld
ap
pli
ed t
o a
sin
gle
str
and
is
too
hig
h, it
wil
l ca
use
th
etr
ansi
tio
n f
rom
su
per
con
du
ctin
g t
o r
esis
tiv
e st
ate.
Pra
ctic
al m
ater
ials
fo
r el
ectr
om
agn
ets
are
on
ly Type II
sup
erco
nd
uct
ors
(cr
itic
al f
ield
up
to
30
T).
Examples:
Pb
V Ta
Hg
Sn
In Ti
Zn
Examples:
NbT
iM
gB
2
Nb
3S
nH
TS
(Y
BC
O, B
SS
CO
)
Nb
3A
l
V3G
a
Nb
3G
a
Ga
Nb
Zn
7/41
J, B, T
A s
up
erco
nd
uct
or
is c
har
acte
rize
d b
y a
cri
tica
l
curr
ent
I c(o
r cu
rren
t d
ensi
ty J
c),
a c
riti
cal
fiel
d
Bc,
a c
riti
cal
tem
per
atu
re T
c.
Dep
end
ing
on
th
e cr
itic
al t
emp
erat
ure
sup
erco
nd
uct
ors
are
def
ined
as
Lo
w T
emp
erat
ure
Su
per
con
du
cto
r (L
TS
)
Hig
h T
emp
erat
ure
Su
per
con
du
cto
r (H
TS
)
10
100
1000
10000
05
10
15
20
25
30
35
40
45
Applied Field (T)
JE(A/mm²)
YBCO Insert Tape (B|| Tape Plane)
YBCO Insert Tape (B
⊥ ⊥⊥⊥Tape Plane)
MgB219Fil 24% Fill (HyperTech)
2212 OI-ST 28%
Ceram
ic Filaments
NbTi LHC Production 38%
SC (4.2K)
Nb3Sn RRP Internal Sn (OI-ST)
Nb3Sn High Sn Bronze Cu:Non-Cu 0.3
YBCO B|| Tape Plane
YBCO B
YBCO B
⊥ ⊥⊥⊥⊥ ⊥⊥⊥Tape Plane
Tape Plane
2212
RRP Nb
RRP Nb33Sn
Sn
Bronze
Bronze
Nb
Nb33Sn
Sn
MgB2Nb
Nb-- TiTi
SuperPower tape
SuperPower tape
used in record
used in record
breaking NHMFL
breaking NHMFL
insert coil 2007
insert coil 2007
18+1 MgB
18+1 MgB22/Nb/Cu/Monel
/Nb/Cu/Monel
Courtesy M. Tomsic, 2007
Courtesy M. Tomsic, 2007
427 filam
ent st
rand w
ith
Ag a
lloy
oute
r sh
eath
test
ed a
t N
HM
FL
Maximal J Efor
entire LHC Nb-Ti
strand production
(–)CERN-
T.Boutboul '07,
and (--)<5T data
from Boutboul et al.
MT-19, IEEE-
TASC’06)
Complied from
Complied from
ASC'02 and
ASC'02 and
ICMC'03 papers
ICMC'03 papers
(J. Parrell OI
(J. Parrell OI --ST)
ST)
4543 filament High Sn
4543 filament High Sn
Bronze
Bronze-- 16wt.%Sn
16wt.%Sn--
0.3wt%Ti (M
iyazaki
0.3wt%Ti (M
iyazaki --
MT18
MT18-- IEEE
IEEE’’ 04)
04)
10
100
1000
10000
05
10
15
20
25
30
35
40
45
Applied Field (T)
JE(A/mm²)
YBCO Insert Tape (B|| Tape Plane)
YBCO Insert Tape (B
⊥ ⊥⊥⊥Tape Plane)
MgB219Fil 24% Fill (HyperTech)
2212 OI-ST 28%
Ceram
ic Filaments
NbTi LHC Production 38%
SC (4.2K)
Nb3Sn RRP Internal Sn (OI-ST)
Nb3Sn High Sn Bronze Cu:Non-Cu 0.3
YBCO B|| Tape Plane
YBCO B
YBCO B
⊥ ⊥⊥⊥⊥ ⊥⊥⊥Tape Plane
Tape Plane
2212
RRP Nb
RRP Nb33Sn
Sn
Bronze
Bronze
Nb
Nb33Sn
Sn
MgB2Nb
Nb-- TiTi
SuperPower tape
SuperPower tape
used in record
used in record
breaking NHMFL
breaking NHMFL
insert coil 2007
insert coil 2007
18+1 MgB
18+1 MgB22/Nb/Cu/Monel
/Nb/Cu/Monel
Courtesy M. Tomsic, 2007
Courtesy M. Tomsic, 2007
427 filam
ent st
rand w
ith
Ag a
lloy
oute
r sh
eath
test
ed a
t N
HM
FL
Maximal J Efor
entire LHC Nb-Ti
strand production
(–)CERN-
T.Boutboul '07,
and (--)<5T data
from Boutboul et al.
MT-19, IEEE-
TASC’06)
Complied from
Complied from
ASC'02 and
ASC'02 and
ICMC'03 papers
ICMC'03 papers
(J. Parrell OI
(J. Parrell OI --ST)
ST)
4543 filament High Sn
4543 filament High Sn
Bronze
Bronze-- 16wt.%Sn
16wt.%Sn--
0.3wt%Ti (M
iyazaki
0.3wt%Ti (M
iyazaki --
MT18
MT18-- IEEE
IEEE’’ 04)
04)
8/41
Materials suitable for magnets
Man
y m
ater
ials
are
su
per
con
du
ctiv
e b
ut
on
ly f
ew o
f th
em a
re r
ead
y t
o b
e u
sed
in
su
per
con
du
ctin
g
mag
net
s.
Nb
3S
n(a
fter
hea
t tr
eatm
ent
bec
om
es B
RIT
TL
E a
nd
sen
siti
ve
to s
trai
n)
crit
ical
tem
per
atu
re
18
.2 K
crit
ical
fie
ld2
4.5
T (
@ 4
.2 K
)
Nb
Ti
crit
ical
tem
per
atu
re
9.1
K
crit
ical
fie
ld1
0.5
T (
@ 4
.2 K
)
9/41
High Tem
perature Superconductors
Hig
h T
emp
erat
ure
Su
per
con
du
cto
rs a
re m
ater
ials
of
inte
rest
bec
ause
th
ey c
an o
per
ate
at
hig
her
tem
per
atu
re (
liq
uid
nit
rog
en v
s. l
iqu
id h
eliu
m).
4.1
mm
0.2
2 m
m
First Generation (1G) HTS wire
Multi-Filamentary Composite
(Co
mm
erci
ally
avai
lab
le)
Super
Pow
er
Second Generation (2G) HTS wire
Coated Conductor Composite
(Co
mm
erci
ally
avai
lab
le A
MS
C, S
up
erp
ow
er)
Su
bst
rate
50
µm
Cop
per
Sta
bil
izer
20
µm
Sil
ver
Over
layer
2 µ
m
(RE
)BC
O H
TS
1 µ
m
Bu
ffer
sta
ck ~
0.2
µm
10/41
Energy Applications
Su
per
con
du
ctin
g M
agn
etic
En
erg
y S
tora
ge
(SM
ES
)F
usi
on
En
erg
y
Su
per
con
du
ctin
g P
ow
er T
ran
smis
sio
n C
able
s“S
up
er-c
able
”H
yd
rog
en-E
lect
rici
ty t
ran
spo
rt
Copper
str
and 1
0A
/mm
2
Super
condu
ctor
600
-120
0A
/mm
2
11/41
Other Applications
Mag
net
ic R
eso
nan
ce I
mag
ing
(M
RI)
Hig
h E
ner
gy
Ph
ysi
cs
Mag
net
ic L
evit
atio
n
12/41
High Energy Physics-LHC
Th
e L
arg
e H
adro
nC
oll
ider
(L
HC
) is
a 2
7-k
ilo
met
er c
ircu
lar
coll
ider
in
wh
ich
hig
h-e
ner
gy p
roto
ns
in tw
o co
un
ter-
rota
tin
g b
eam
s w
ill
be
smas
hed
to
get
her
in
se
arch
o
f H
igg
s b
oso
ns
and n
ew
par
ticl
es p
red
icte
d b
y s
up
er-s
ym
met
ry.
Th
e b
eam
s ar
e ac
cele
rate
d a
nd
kep
t ci
rcu
lati
ng
usi
ng
sup
erco
nd
uct
ing
mag
net
s.
Wh
y s
up
erco
nd
uct
ing
?
Usi
ng
co
pp
er m
agn
ets
we
wo
uld
nee
d >1000 M
W
Wit
h s
up
erco
nd
uct
ing
mag
net
s “o
nly
”120 M
W
(cry
og
enic
27
.5 M
W,
exp
erim
ents
22
MW
)
13/41
How strong is strong?
1.9
K s
up
erco
nd
uct
ing
dip
ole
s p
rod
uci
ng
a f
ield
of
8.3
T -
curr
ent
11
85
0 A
.
Th
e m
ach
ine
has
ro
ug
hly
~5
00
0 m
agn
ets
Mai
n m
agn
et c
om
po
nen
ts a
re b
end
ing
mag
net
s (D
IPO
LE
S, 1
23
2 t
ota
l,1
4.3
m l
on
g, 3
5 t
on
in
wei
gh
t)
Qu
adru
po
les
are
use
d t
o f
ocu
s th
e b
eam
in
th
e in
tera
ctio
n r
egio
ns
Sto
red
mag
net
ic e
ner
gy i
s ~
1.3
GJ
per
sec
tor
(8 s
ecto
rs, to
tal
ener
gy s
tore
d 1
1 G
J).
“The
com
bin
ed s
tran
ds
of
the
super
conduct
ing c
able
s fo
r th
e m
achin
e w
ould
go a
round t
he
equ
ator
6.8
tim
es.
If y
ou a
dd a
ll t
he
fila
men
ts o
f th
e st
rands
toget
her
th
ey w
ould
str
etch
to t
he
sun a
nd b
ack 5
tim
es w
ith e
nough l
eft
over
for
a fe
w t
rips
to t
he
moon.”
Ruth
erfo
rd c
able
Nb
Ti
Sup
erco
nd
uct
ing s
tran
dS
up
erco
nd
uct
ing f
ilam
ents
Win
dR
eact
Ep
ox
y i
mp
reg
nat
ion a
nd
in
stru
men
tati
on
14/41
Cooling of magnets
0.6 m
6 cm
0.6 m
6 cm
LH
C d
ipo
le c
ross
sec
tio
n
LH
C m
agn
ets
are
Nb
Ti
and
co
ole
d w
ith
su
per
flu
idh
eliu
m a
t 1
.9 K
(b
elo
w 2
.17
K p
art
of
the
flu
id h
as
“zer
o”
vis
cosi
ty).
Th
e ca
ble
s ar
e em
bed
ded
in
ep
ox
y e
lim
inat
ing
lo
cal
coo
lan
t (a
dia
bat
ic w
ind
ing
)
Win
din
g i
s a
sin
gle
mo
no
lith
ic e
nti
ty (
imp
rov
e m
echan
ical
sta
bil
ity
).
Th
e w
ind
ing
is
glo
bal
ly c
oo
led
by f
orc
ed-f
low
cry
og
en (
vs.
fu
sio
n m
agn
ets)
.
Cry
og
en f
orc
ed t
hro
ug
h p
ipe
15/41
Main M
agnets
Mag
net
s ar
e d
esig
ned
to
rea
ch a
n i
dea
l si
ng
le m
ult
ipo
le(d
ipo
le, q
uad
rup
ole
and
so
on
)
to a
vo
id s
pre
adin
g o
f b
eam
.
In r
eal
life
we
hav
e to
dea
l w
ith
har
mo
nic
s an
d w
e w
ant
them
to
be
smal
l (0
.01
% d
evia
tio
n
fro
m i
dea
l fi
eld
) o
r co
rrec
t th
em w
ith
geo
met
ry c
han
ges
.
Dip
ole
to
ben
d t
he
bea
mQ
uad
rup
ole
to f
ocu
s th
e b
eam
at
the
inte
ract
ion
reg
ion
16/41
CMS detector
Cab
les
use
d i
n C
MS
so
len
oid
(cr
yo
stab
le)
CM
S d
etec
tor
Co
ndu
cto
r n
eed
s to
ab
sorb
a l
ot
of
hea
t an
d p
rod
uce
s lo
wer
fie
ld
(~4
-5T
) so
les
s su
per
con
du
ctin
g
stra
nd
s ar
e u
sed
in
alu
min
um
stab
iliz
er (
loca
l co
ola
nt)
.
Alu
min
um
all
oy r
einfo
rcem
ent
Alu
min
um
sta
bil
izer
17/41
Pla
sma
self
-hea
tin
g
Tri
tiu
m
rep
len
ish
men
t
Li
Electricity,
Hydrogen
What about fusion?
Fu
sio
n a
nd
pla
sma
ph
ysi
cs a
re a
t th
e co
re o
f n
atu
re’s
mo
st i
ntr
igu
ing
sel
f d
riv
en s
yst
ems.
Ex
amp
les?
Th
e su
n c
on
fin
es h
ot
pla
sma
(gra
vit
atio
nal
an
d m
agn
etic
co
nfi
nem
ents
).
Pro
du
cin
g p
ow
er u
sin
g f
usi
on
rea
ctio
ns
has
bee
n t
he
gre
at p
rom
ise
of
the
last
50 years…
How m
any m
ore do we have to wait?
18/41
Like charges rep
el each
other
Pro
ble
m 1
: P
arti
cles
mu
st h
ave
eno
ug
h e
ner
gy
to
ov
erco
me
the
cou
lom
b b
arri
er.
Th
eref
ore
: v
ery
ho
t (1
00
Million
Deg
rees
) P
lasm
a
Pro
ble
m 2
: In
ph
ysi
cs t
erm
s: σCoul>> σfusion
Th
erm
al d
istr
ibu
tio
n
Problem: Coulomb Barrier
Fo
r fu
sio
n w
e n
eed
to
get
a. e
no
ug
h particles
at a
b. h
igh
en
ou
gh
temperature
c. f
or
a lo
ng
en
ou
gh
tim
eto
fu
se.
Fu
sio
n r
equ
ires
T = 15 keV
(10
0 M
illi
on
deg
rees
).
Fu
sio
n r
equ
ires
n = 1020m
-3(1
Mil
lio
n t
imes
les
s d
ense
th
an a
ir).
Th
is m
ean
s w
e n
eed
τ τττ= 1 –10 sec
pτ τττ>8 atm-sec
Confinement
19/41
Ho
t p
lasm
as l
ike
to s
pre
ad o
ut.
H
ow
can
th
ey b
e co
nfi
ned
? W
e ca
n’t
pu
t it
in
a c
on
tain
er b
ut…
•G
rav
itat
ion
al C
on
fin
emen
t:
Sta
rs d
o i
t th
is w
ay s
o w
e n
eed
sta
r-si
ze p
lasm
a.
•In
erti
al c
on
fin
emen
t:
Get
en
ou
gh
fu
sio
n f
uel
ho
t en
ou
gh
an
d c
lose
en
ou
gh
to
get
her
th
at
the
reac
tio
n i
s d
on
e b
efo
re i
t h
as t
ime
to s
pre
ad o
ut.
•M
agn
etic
Co
nfi
nem
ent:
Th
e le
adin
g s
chem
e fo
r en
erg
y p
rod
uct
ion
. T
ake
adv
anta
ge
of
char
ged
par
ticl
es t
end
ency
to
cli
ng
to
mag
net
ic f
ield
lin
es.
How do we confine very hot particles
20/41
Rec
all cyclotron orbits
a. G
oo
d c
on
fin
emen
t p
erp
end
icu
lar
to B c
ircu
lar
orb
its
per
pen
dic
ula
r to
th
e fi
eld
wit
h
gyro
-rad
ius
r l=
v⊥/Ω
, w
her
e Ω
=q
B/m
c
b. N
o c
on
fin
emen
t p
aral
lel
to B
Un
ifo
rm F
ield
Incomplete confinem
ent!
Magnetic confinem
ent
The Answ
er:
"D
onuts. Is
ther
e anyt
hin
g they
can't d
o?"
-Hom
er Sim
pso
n
Tokamak:
Th
e m
ost
su
cces
sfu
l co
nfi
gu
rati
on
to
dat
e.
Spherical Torus:
So
me
adv
anta
ges
ov
er t
ok
amak
bu
t
less
dev
elo
ped
.
Stellarator:
Mo
re s
tab
le, b
ut
has
no
t d
emo
nst
rate
d
con
fin
emen
t o
f a
tok
amak
.
Dipole:
Pro
mis
ing
bu
t tr
ick
y
21/41
We
nee
d t
o c
on
tain
a h
igh
tem
per
atu
re,
T,
hig
h d
ensi
ty,
n, p
lasm
a fo
r a
lon
g e
no
ugh
tim
e, τ
,to
ach
iev
e ig
nit
ion
(P
ow
erout>
> P
ow
erin
)W
hy
is
it s
o d
iffi
cult
to
ach
iev
e in
th
e la
b?
It w
ork
s la
rge
scal
e…
We
on
ly n
eed
τ ∼
1-1
0 s
bu
t τ
incr
ease
s w
ith
th
e si
ze o
f th
e m
ach
ine
($$
$)
and
…
“C
onfinin
g p
lasm
a is like
hold
ing jello
with rubber
bands”
Fu
sio
n p
ow
er d
ensi
ty i
n s
un
~ 3
00
W/m
3,
In a
bu
rnin
g p
lasm
a ex
per
imen
t ~
10
MW
/m3
Ph
ysi
cs(e
qu
ilib
riu
m,
stab
ilit
y,
tran
spo
rt)
and
en
gin
eeri
ng c
hal
len
ges
What do we need to m
ake fusion power?
22/41
•W
ater
-co
ole
d c
op
per
to
kam
ak
•W
orl
d’s
lar
ges
t fu
sio
n d
evic
e
Existing experim
ents: Joint European Torus
23/41
JET, PPPL, MIT
MIT
-Alc
ato
r
PP
PL
-TF
TR
24/41
KS
TA
R T
okam
ak
•T
oro
idal
Fie
ld C
oil
s -
Nb
3S
n C
ICC
wit
h I
nco
loy A
llo
y 9
08
Jac
ket
35
.2 k
A
7.2
T (
max
fie
ld)
•C
entr
al S
ole
no
id -
Nb
3S
n C
ICC
wit
h
Inco
loy
All
oy 9
08
Jac
ket
25
kA
•P
olo
idal
Fie
ld C
oil
s -
Nb
Ti
CIC
C w
ith
mo
dif
ied
31
6L
N J
ack
et
•2
0 t
on
s o
f N
b3S
n i
s la
rges
t p
rod
uct
ion
run
sin
ce I
TE
R E
DA
Mo
del
Co
ils
Why not superconducting then?
EA
ST
Tokam
ak
•M
agn
ets
are
Nb
Ti
CIC
C w
ith
SS
Jac
ket
•O
per
atin
g t
emp
erat
ure
is
3.8
K
•T
F 1
4.3
kA
at
5.8
T (
max
fie
ld)
•C
S p
lasm
a in
itia
tio
n c
ycl
e 1
4.5
kA
4
.3 T
(max
fie
ld)
•F
ast
dis
char
ge
at 6
.8 T
/s
25/41
In a
ste
llar
ato
rw
e u
se a
sin
gle
co
il s
yst
em w
ith
no
lo
ng
itu
din
al n
et-c
urr
ent
in t
he
pla
sma
and
hen
ce
wit
ho
ut
a tr
ansf
orm
er (
con
tin
uo
us
op
erat
ion
an
d i
nh
eren
t st
abil
ity
).
Alternative design Stellarator
26/41
The future promise…IT
ER
Div
erto
r
54
cas
sett
es
Cen
tral
Sole
noid
Nb
3S
n, 6
mo
dule
s
To
roid
al F
ield
Co
il
Nb
3S
n, 18
, w
edg
ed
Polo
idal
Fie
ld C
oil
Nb
-Ti,
6
Bla
nk
et M
odule
440
m
od
ule
s
Vac
uu
m V
esse
l
9 s
ecto
rs
Cry
ost
at
24
m h
igh
x 2
8 m
dia
.
Port
Plu
g (
IC H
eati
ng)
6 h
eati
ng
3 t
est
bla
nk
ets
To
rus
Cry
opu
mp
8 u
nit
s
Fu
sio
n P
ow
er:
500
MW
Pla
sma
Vo
lum
e: 8
40
m3
Q ≥
10
Pla
sma
Indu
ctiv
e B
urn
Tim
e ≥
400
s
No
min
al P
lasm
a C
urr
ent:
15
MA
To
roid
alfi
eld
5.3
T
Typ
ical
Tem
per
ature
: 2
0 k
eV
Typ
ical
Den
sity
: 10
20
m-3
Ind
ia
27/41
ITER coil assem
bly
Nu
mb
er o
f T
F c
oil
s 1
8
Mag
net
ic e
ner
gy i
n T
F c
oil
(G
J)4
1
Op
erat
ing
cu
rren
t (k
A)
68
Max
imu
m f
ield
(T
)1
1.8
Cen
teri
ng
fo
rce
per
TF
co
il (
MN
)4
03
Ver
tica
l fo
rce
per
hal
f T
F c
oil
(M
N)
20
5
ITE
R t
echnic
al b
asis
Nu
mb
er o
f C
S m
od
ule
s 6
Mag
net
ic e
ner
gy i
n C
S c
oil
(G
J)2
1
Op
erat
ing
cu
rren
t (k
A)
41
.8/4
6
Max
imu
m f
ield
(T
)1
3.5
/12
.8
28/41
Cable-In-C
onduit-C
onductor
Fu
sio
n m
agn
ets
are cryostable
mag
net
s ch
arac
teri
zed
by t
he
pre
sen
ce o
f lo
cal
or
“nea
r-lo
cal”
coo
lin
g
(vs.
HE
P m
agn
ets)
. C
able
d s
tran
ds
of
sup
erco
nd
uct
or
enca
sed
in
aco
nd
uit
(C
ICC
), w
hic
h p
rov
ides
mec
han
ical
str
eng
th(R×J×
B)
larg
e an
d t
hro
ug
h w
hic
h s
ing
le-p
has
e cr
yo
gen
(g
ener
ally
hel
ium
) is
forc
ed t
o p
rov
ide
coo
lin
g t
o t
he
sup
erco
nd
uct
or.
Th
e ca
ble
s ar
e w
ou
nd
in
sta
ges
(fo
r ex
amp
le 3
x3
x4
x5
x6
).
Per
form
ance
of
Nb3
Sn
cab
le i
s cr
uci
al t
o r
each
des
ired
plasm
a current
and
tim
e o
f plasm
a burn.
Cri
tica
l ef
fect
s th
at c
ou
ld r
edu
ce p
erfo
rman
ce:
AC
lo
sses
an
d m
echanical effects
.
45
mm
Co
oli
ng
ch
ann
el a
nd
vo
id f
ract
ion
~3
0%
Fo
rced
sin
gle
-ph
ase
cryo
gen
Co
nd
uit
29/41
Mechanical Effects
d
Nb
3S
n s
up
erco
nd
uct
or
per
form
ance
is very sensitive
to s
trai
ns
(vs.
Nb
Ti
use
d i
n H
EP
).
Var
iou
s st
rain
s ap
pea
r in
a m
agn
et:
-A
xia
l T
her
mal
mis
mat
ch a
nd
ho
op
fo
rce
-B
end
ing
Th
erm
al m
ism
atch
an
d L
ore
ntz
fo
rce
-T
ran
sver
seL
ore
ntz
fo
rce
B
I
F
N.
Mit
chel
l, F
usi
on E
ng.
and
Des
ign,
Vo
l. 6
6–6
8, p
. 97
1–9
93,
200
3.
30/41
TFMC-C
SMC and Bending M
odel
d
N.
Mit
chel
l, F
usi
on E
ng.
and
Des
ign,
Vo
l. 6
6–6
8, p
. 97
1–9
93,
200
3.
ITE
R m
od
el c
oil
tes
t re
sult
s sh
ow
ed unexpected degradation
in 2
00
0-2
00
3:
50
% T
FM
C
35
% C
SI,
TF
I
25
% C
SM
C
A bending
mo
del
to
ex
pla
in t
he
deg
rad
atio
n h
as b
een
pro
po
sed
by N
. M
itch
ell:
N.
Mar
tovet
sky,
Ph
ysi
caC
40
1 (
20
04
) 2
2–
27.
Ben
din
g i
s w
her
e m
ost
of
the
exp
erim
enta
l w
ork
fo
cuse
d i
n t
he
pas
t fe
w y
ears
.
Transverse load
effe
ct i
s co
nsi
der
ed s
eco
nd
ary.
31/41
Single Strand Experiments
D.
Ugli
etti
et a
l.,I
EE
ET
ransa
ctio
ns
on
Ap
pli
ed S
up
erco
nd
uct
ivit
y,
v.1
3,
n2
,
June
20
03
, p
35
44
-35
47
.
EMPIR
ICAL
scal
ing
law
s ex
ist
to
esti
mat
e th
e d
egra
dat
ion
cau
sed
by t
he
axia
l st
rain
.
Un
cert
ain
ty e
xis
ts i
n t
he
real
ax
ial
stra
in c
on
dit
ion
of
a st
ran
d i
n a
cab
le
and
th
is e
ffec
t al
on
e d
oes
no
t ex
pla
in
the
beh
avio
r o
f a
full
siz
e ca
ble
.(I
TE
R d
esig
n v
alues
-0.7
% f
or
stee
l ja
cket
, -0
.3%
for
Inco
loy
All
oy 9
08
®.)
Un
i-ax
ial
stra
in d
epen
den
ce.
A.
Nij
huis
et a
l.,
Sup
erco
nd
. S
ci.
Tec
hno
l. 1
8,
20
05
, p.
S27
3-S
28
3.
Bea
ms
(sam
ple
ho
lder
)
Sup
erco
nd
uct
ing w
ires
Ro
tati
on a
xes
Ro
tati
on a
rms
Fix
ed e
nd
s
Cu j
oin
ts
D.
L.
Har
ris,
M.S
. in
Mec
han
ical
En
gin
eeri
ng,
Mas
sach
use
tts
Inst
itute
of
Tec
hno
log
y,
U.S
.A.
20
05.
A.
All
egri
tti,
Univ
ersi
ty o
f B
olo
gna,
Dep
artm
ent
of
Mec
han
ical
En
gin
eeri
ng,
Ital
y,
20
06
.
Ben
din
g e
ffec
t.T
ran
sver
se l
oad
eff
ect.
A.
Nij
huis
et a
l.,
Sup
erco
nd
.
Sci
. T
echno
l. 1
9,
20
06
,
p.
108
9–1
096
.
B.
See
ber
et a
l.,
Sup
erco
nd
. S
ci.
Tec
hno
l.
20
, 20
07,
p. S
184
–S
18
8.
32/41
Transverse load of sub-cable samples
Use
sp
lit
sup
erco
nd
uct
ing
mag
net
fac
ilit
y a
t N
HM
FL
:
30
x70
mm
rad
ial
acce
ss p
ort
15
0 m
m a
xia
l b
ore
(u
nif
orm
hig
h f
ield
reg
ion
)
Hai
rpin
typ
e o
f ca
ble
-I
+ I
xB
To
sim
ula
te s
ame
load
ing
con
dit
ion
s as
IT
ER
cab
le w
e n
eed
to a
pp
ly e
xte
rnal
mec
han
ical
lo
ad
(ap
pli
ed w
ith
a m
ov
ing
wed
ge)
.
To
in
sure
pre
ssu
re u
nif
orm
ity i
t is
nec
essa
ry t
o u
se a
“te
eth
”-li
ke
wed
ge.
Sam
e st
ruct
ure
can
be
use
d f
or
single strand, triplet and
45-strand samples.
Var
iou
s ca
ble
tes
ts w
ith
min
or
sam
ple
ho
lder
mo
dif
icat
ion
s.
33/41
Hairpin Sample
S
amp
le i
nse
rted
wit
h
its
ho
lder
and
wed
ge
insi
de
the
single
pie
ce c
ase
Co
pp
er c
han
nel
of
the
curr
ent
lead
s w
her
e th
e
sam
ple
is
sold
ered
Res
tin
g p
osi
tio
nF
Ex
ten
som
eter
Mo
vin
g
pie
ce
Ap
ply
ing
lo
ad
34/41
Typical Measurements
Cri
tica
l cu
rren
t m
easu
rem
ents
are
per
form
ed a
t4.2 K
and
fixed
field
.
Sta
nd
ard
cri
tica
l cu
rren
t cr
iter
ia o
fE
c1=
10
µV
/m,
Ec2
=1
00
µV
/m h
ave
bee
n
use
d t
o e
val
uat
e cr
itic
al c
urr
ent.
Vol
tage
Tap
Sig
nal
@ 1
5 T
-5.0
E-0
6
0.0
E+
00
5.0
E-0
6
1.0
E-0
5
1.5
E-0
5
2.0
E-0
5
2.5
E-0
5
3.0
E-0
5
3.5
E-0
5
050
01
00
01
500
200
0
Cur
ren
t (A
)
Voltage (V)
10
0 µ
V/m
10
µV
/m
35/41
Some Results
0.0
0
0.2
0
0.4
0
0.6
0
0.8
0
1.0
0
1.2
0
02
04
06
08
010
01
20
Nominal Pressure (MPa)
I/Ic-zeroload
10 microV/m
45
str
and
s
3 s
tran
ds
Sin
gle
str
and
•S
ing
le s
tran
d a
nd
3-s
tran
d c
able
rea
ched
th
e ex
pec
ted
cri
tica
l cu
rren
t.
•T
he
45
-str
and
sam
ple
sh
ow
ed a
23
% i
nit
ial
deg
rad
atio
n.
•A
ll s
amp
les
sho
wed
a s
ign
ific
ant
chan
ge
in c
riti
cal
curr
ent
as a
fun
ctio
n o
f th
e n
om
inal
pre
ssu
re.
•D
egra
dat
ion
dat
a o
f si
ng
le s
tran
d a
nd
3-s
tran
d s
amp
les
can
no
t b
e ex
pla
ined
wit
h e
xis
tin
g b
end
ing
mo
del
s b
ecau
se t
hey
do
no
t h
ave
sig
nif
ican
t b
end
ing
, in
dic
atin
g L
ore
ntz
lo
ad c
an e
ffec
t th
e b
ehav
ior
of
sup
erco
nd
uct
ors
.
36/41
Contact M
echanics and M
odel
Wit
h t
ho
se d
ata
con
tact
mec
han
ics
was
use
d t
o e
val
uat
e th
e ef
fect
of
loca
l p
ress
ure
bet
wee
n
stra
nd
s an
d i
t w
as p
oss
ible
to
rep
rod
uce
th
e re
sult
s o
f th
e 4
5-s
tran
d c
able
usi
ng
th
e 3
-str
and
dat
a.
A n
ew m
od
elw
as p
rop
ose
d t
o e
val
uat
e th
e d
egra
dat
ion
cau
sed
by
th
e tr
ansv
erse
Lo
ren
tz l
oad
effe
ct o
n f
ull
siz
e ca
ble
san
d s
ug
ges
tio
ns
on
th
e ca
ble
des
ign
wer
e m
ade.
Her
e’s
a si
mp
lifi
ed e
xp
lan
atio
n o
f th
e m
od
el…
Ap
pli
ed
Forc
e F
c
2η
2ξ
2a
E1 E2
Ap
pli
ed
Forc
e F
c
2η
2ξ
2a
E1 E2
In o
ur
exp
erim
ent
we
app
lied
a k
no
wn
to
tal
mec
han
ical
load
so
in
ord
er t
o e
stim
ate
Fc
we
nee
d t
he
nu
mb
er o
f co
nta
ct p
oin
ts i
n a
cab
le
-1.5-1
-0.50
0.51
1.5
050
100
150
200
250
300
350
400
450
500
Tra
nsv
erse
lo
ad
Tw
ist
pit
ch
A
B
C
A
B
C
C
C
C
C
C
B
B
B
B
B
A
A
A
A
A
54
53
54
25
43
15
43
2N
Nk
Nk
kN
kk
kN
kk
kk
NT
+⋅
+⋅
⋅+
⋅⋅
⋅+
⋅⋅
⋅⋅
=
Th
e total contact points
per
un
it l
eng
th f
or
a ca
ble
wit
h n
um
ber
of
stra
nd
Ns=k 1·k2·k3·k4·k5
(kin
um
ber
of
bun
dle
s, N
in
um
ber
of
conta
cts
in a
sta
ge)
37/41
Model results
0.0
0.2
0.4
0.6
0.8
1.0
1.2
015
030
045
060
0750
900
Effective C
ontact Pressure (M
Pa)
3-st
rand
Fitt
ing
Normalized Critical Current3-strand data
0
0.2
0.4
0.6
0.81
1.2
020
04
00
600
80
0
Force (kN/m
)
Normalized Critical Current
45-s
tran
d e
xperi
men
tal
un
twis
ted
twis
ted
“can we predict the behavior of a cable from its smallest stage
behavior (3-strand sample)?”
Mec
han
ical
Forc
eA
ccu
mu
lati
ng
Ele
ctro
mag
net
ic
(Lore
ntz
) F
orc
e
Hig
hes
t
pre
ssure
are
as
i
B
Fi
Acc
um
ula
ting
forc
e
dis
trib
uti
on
Un
iform
forc
e
dis
trib
uti
on
38/41
Model Results
Current Distribution in Cable
0
20
40
60
80
100
120
140
-20
-10
010
20
y (mm)
Current (A)
Un
twis
ted
Tw
iste
d
Contact Pressure Distribution
in C
able
0
200
400
600
800
1000
-20
-10
010
20
y (mm)
Contact Pressure
(MPa)
Untw
iste
d
Tw
iste
d
Fu
ll s
ize
cab
le 3x4x4x4x6
(11
52
str
and
s).
Th
e m
od
el r
esu
lts
sho
w t
hat
fo
r a
full
siz
e ca
ble
wit
h t
he
ori
gin
al c
able
pat
tern
pro
po
sed
fo
r th
e
TF
co
il i
n I
TE
R (
cab
lin
g p
atte
rn 3x
4x4x4x6
an
d
twis
t p
itch
es
65
, 9
0,
15
0,
27
0,
43
0
mm
),
the
Lo
ren
tz
load
co
uld
af
fect
fo
r u
p
to
20
%
of
deg
rad
atio
n a
t o
per
atio
n c
urr
ent
of
68
kA
.
Ax
ial
and
b
end
ing
st
rain
s ca
use
d
by
ther
mal
con
trac
tio
n
and
L
ore
ntz
lo
ad
are
add
itio
nal
sou
rces
of
deg
rad
atio
n.
Full Size Cable (3x4x4x4x6, no Cu strand)
05
10
15
20
25
30
020
40
60
80
100
Nominal Current (kA)
Computed %
difference from
nominal current
0x
y
39/41
Parametric Studies
Th
e ca
bli
ng
pat
tern
aff
ects
th
e p
erfo
rman
ce
of
a ca
ble
.
A ca
bli
ng
p
atte
rn 3x3x3x3x6
sho
ws
a 1
0%
larg
er
deg
rad
atio
n
than
a
cab
lin
g
pat
tern
3x5x5x6
(fir
st
pat
tern
le
ss
nu
mb
er
of
con
tact
s).
If t
he 6 petals
of
the
last
sta
ge
are
independen
tly supported
the
tota
l L
ore
ntz
is
red
uce
d.
Th
e d
egra
dat
ion
in
th
is c
on
fig
ura
tio
n w
ou
ld
be
6%
at
11
.3 k
A i
nst
ead
of
the
20
% a
t 6
8 k
A
for
the
stan
dar
d d
esig
n.
0
10
20
30
40
50
60
020
40
60
80
100
120
140
Nominal Current (kA)
Computed % difference from
nominal currentN
s 4
86 3
x3x3
x3x6
Ns 4
50 3
x5x5
x6
0.0
5.0
10.0
15.0
20.0
25.0
30.0
020
40
60
80
10
0Nominal Current (kA)
% difference from
nominal current
Ns
1152
Ns
216
40/41
Research needs
Des
pit
e th
e am
ou
nt
of
wo
rk d
on
e in
th
e p
ast
few
yea
rs t
he
mec
han
ical
beh
avio
r o
f
CIC
C i
s not
wel
l u
nd
erst
oo
d.
Mo
re d
etai
led
mea
sure
men
ts o
f th
e mechanical properties
of
sup
erco
nd
uct
ing
str
and
s an
d
cab
les
are
nec
essa
ry t
o i
mp
lem
ent
fin
ite
elem
ent
sim
ula
tio
ns
and
to u
nd
erst
and
th
e d
etai
led
str
ain
mec
han
ism
s u
nd
er l
oad
ing
co
nd
itio
ns.
A b
ette
r u
nd
erst
and
ing
of superconducting m
agnets limitations
to p
red
ict
thei
r b
ehav
iors
, an
d
mo
re e
ffo
rts
in i
mp
rov
ing
th
eir
des
ign
s ar
e o
f v
ital
im
po
rtan
ce t
o t
he
end
go
al o
f o
per
atin
g f
usi
on
mac
hin
e re
liab
ly.
HE
P i
s al
so t
hin
kin
g a
bo
ut
the
LH
C u
pg
rad
e an
d N
b3S
n c
on
du
cto
r w
ill
be
use
d t
o o
bta
in h
igh
er
fiel
ds.
Un
der
stan
din
g t
he
mec
han
ical
pro
per
ties
of
this
mat
eria
lh
as b
eco
me
of
vit
al i
mp
ort
ance
for
this
co
mm
un
ity t
oo
.
41/41
TH
AN
K Y
OU
42/41
Fusion is an Attractive Energy Source
A
bundan
t fu
el, av
aila
ble
to a
ll n
atio
ns
—D
eute
riu
m a
nd
lit
hiu
m e
asil
y a
vai
lab
le f
or
tho
usa
nds
of
yea
rs
E
nvir
onm
enta
l ad
van
tages
—N
o c
arb
on
em
issi
on
s, s
ho
rt-l
ived
rad
ioac
tiv
ity
C
an’t
explo
de,
res
ista
nt
to t
erro
rist
att
ack
—S
mal
l q
uan
tity
of
fuel
in
th
e ch
amb
er, ch
amb
er b
reac
h s
top
s re
acti
on
L
ow
ris
k o
f nucl
ear
mat
eria
ls p
roli
fera
tion
—N
o f
issi
le o
r fe
rtil
e n
ucl
ear
mat
eria
ls r
equ
ired
C
om
pac
t pow
er s
ourc
e re
lati
ve
to s
ola
r, w
ind a
nd b
iom
ass
—M
od
est
lan
d u
sag
e
N
ot
subje
ct t
o d
aily
, se
asonal
or
regio
nal
wea
ther
var
iati
on
—N
o l
arg
e-sc
ale
ener
gy s
tora
ge
or
lon
g d
ista
nce
tra
nsm
issi
on
C
an p
roduce
electricity or hydrogen
—O
ther
po
ten
tial
use
s:
d
esal
inat
ion
of
wat
er
d
eact
ivat
ion
of
reac
tor
was
te
43/41
Comparison of Fission and Fusion
Radioactivity After Shutdown
1 10
-2
10
-4
10
-6
10
-8
10
-10
Fis
sion
:L
ight
Wat
erR
eact
or
10
,00
0
Yea
r A
fter
Sh
utd
ow
n
Fu
sio
n:
Sil
icon
Car
bid
eC
om
po
site
Fu
sio
n:
Van
adiu
mA
llo
ys
Fu
sio
n:
Red
uce
d A
ctiv
atio
nF
erri
tic
Ste
el
1,0
00
100
10
1
Coal
Ash
Bel
ow
Reg
ula
tory
Co
nce
rn
Curies/Watt (Thermal Power)
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