MASSACHUSETTS INSTITUTE OF TECHNOLOGY
DEPARTMENT OF MECHANICAL ENGINEERING
DEPARTMENT OF NUCLEAR ENGINEERING
2.64J/22.68J Spring Term 2003
April 24, 2003
Lecture 8: Stability
Key magnet issues vs. Top
� Magnetic and thermal diffusion
� Winding pack; stability; power density equation
� Disturbances; energy density spectra; energy or stability margin
� E(J ) & V(I ) characteristics of “high-current” superconductor
� Important stability issues: cryostable & adiabatic magnets
� Cryostability; Stekly criterion; Equal area criterion; CICC
� Heat transfer data
� High-performance (adiabatic) magnets; MPZ concept
� Mechanical disturbances—premature quenches & training
� AE technique
� Stability of HTS
Y. Iwasa (04/24/03)
1
Key Magnet Issues vs Top
Cost or Difficulty
Protection
Conductor
Mechanical
Stability
Cryogenics
0
~100
LTS
Y. Iwasa (04/24/03)
Top [K]
HTS
2
Magnetic Diffusion
r
H
r
Jf
r
B
t
r
E
2
e
Hy
x
2
e
0
Dmg
( 1 -D)
Hy
x
Hy
2
x
e
By
0
t
e
0
2
Dmg
Hy
t
Dmg
t
Ez
Jz
Ez
x
0
2
Hy
Hy
x
Hy
2
t
mg
1 2a
Dmg
2
0
2a
2
e
e
0
mg
1 2a
Dmg
Y. Iwasa (04/24/03)
2
0
2a
2
e
3
Thermal Diffusion
2
k
T
2
x
C
T
t
2
k T
C x2
2
Dth
T
2
x
Dth
k
C
Y. Iwasa (04/24/03)
T
t
4
Data for Cu & Nb-Ti
K
[W/m K]
C
[J/m3K]
Copper
~400
~1000
Nb-Ti
~10-3
~500
Dth
Cu
Dth
SC
Dmg
Cu
Dm g
SC
~ 2 105
~ 6 10
3
Dth
[m2/s]
Dmg
[m2/s]
~3 10-10
~0.4
~3 10-3
~5 10-7
~2 10-6
~0.5
[
m]
Temperature wave travels much faster in Cu—no
temperature concentration in Cu.
Magnetic wave travels much slowly in Cu—no flux
motion induced local heating concentration in Cu.
Best to use Nb-Ti with Cu
Y. Iwasa (04/24/03)
5
Winding Pack
Structure
Awpk
Astr
Acs
Am
Ains
Aq
Coolant
Conductor
Ins.
Matrix
SC
Coolant
Insulation
Superstructure
Matrix (e.g. Cu)
Superconductor
Structure (e.g. epoxy, conduit)
Winding Pack Cross Section
Y. Iwasa (04/24/03)
6
Jc
Ic
Asc
Ic
JnonCu
Ac d Am
Jc
Jeng
Je
Jm
Iop
Am
Joverall
Y. Iwasa (04/24/03)
(Nb 3Sn; HTS)
(Nb - Ti)
Ic
Acd
(Qunech propagation &protection)
I op
Awpk
7
Stability
Stability of a superconducting magnet refers to the
phenomenon of the magnet to operate reliably despite the
presence of disturbance events.
Tcd
limit set by design
Disturbance may be mechanical, electromagnetic, thermal,
or even nuclear in origin.
Distributed: energy density [J/m 3]
Point: energy [J]
Y. Iwasa (04/24/03)
8
Power Density [W/m3] Equation
e h gk g j gd gq
(6.1)
Cooling:
f p Pcd
Acd
q (T )
Disturbance: gd
Joule heating:
Conduction:
cd
(T )J cd2
kcd (T ) T
T
Storage: Ccd (T )
t
Ccd (T )
T
t
Y. Iwasa (04/24/03)
x
kc d(T )
T
x
2
cd (T )Jcd
x
gd
kcd (T )
T
x
f p Pcd
q (T )
Acd
9
Stability Concepts Derived from Eq. 6.1
ėh
gk
gj
0
0
**
0
Application
Flux jump
Cryostability *
0
Dynamic stability
0
0
“Equal area” *
0
0
0
MPZ *
0
0
Protection
0
0
Adiabatic NZP * *
0
0
†
gq
0
0
*
gd
†
Covered in today’s lecture
Minimum Propagation Zone
Normal Zone Propagation
Y. Iwasa (04/24/03)
10
Sources of Disturbance
Mechanical—Lorentz force; thermal contraction
Wire motion/”micro-slip”
Structure deformation
Cracking epoxy; debonding
Electrical/Magnetic —Time-varying current/field
Current transients, includes AC current
Field transients, includes AC field
Flux motion, e.g., flux jump
Thermal
Conduction, through leads
Cooling blockage (poor ventilation)
Nuclear radiation
Neutron flux in fusion machines
Particle showers in accelerators
Y. Iwasa (04/24/03)
11
Disturbance Energy Density Spectra
Courtesy of Luca Bottura (CERN, Geneva)
Y. Iwasa (04/24/03)
12
Energy Margin or Stability Margin:
eh; emin
Minimum energy density (or energy) that leads to a quench
Disturbance energy <
Disturbance
eh
T < Tcs
Disturbance energy >
T
t
T
t
<0
Stable
>0
Quench
T > Tcs
T
Not-stabilized
Y. Iwasa (04/24/03)
Stable
eh
Stabilized
Disturbance
<0
t
13
E(J) & V(I) Characteristics of “High-Current” Superconductor
E(J )
J
Ec
Jc
n
I
V ( I ) Vc
Ic
n
n: “Index” of a superconductor: “ideal” superconductor, n=
E( J )
n
n1
n2
Ec
Jc
Y. Iwasa (04/24/03)
J
14
Typical Values of n for “Magnet-Grade” Conductors
Nb-Ti: 20--100
(50--100 for NMR/MRI persistent-mode magnets)
Nb3Sn: 20--80
(40--80 for NMR/MRI persistent-mode magnets)
BSCCO2223: 10--25
Y. Iwasa (04/24/03)
15
Important Stability Issues—Cryostable & Adiabatic Magnets
Cryostable Magnets
Circuit model for a well-cooled composite conductor.
“Current-sharing.”
Cryostability (Stekly)—“linear”cooling.
Cryostability—nonlinear cooling.
“Equal Area” stability.
CICC
Cooling data—bath & forced-flow.
Adiabatic Magnets
Premature quenches; training.
Minimum propagation zone (MPZ).
Disturbance spectra.
Acoustic emission (AE) technique.
Y. Iwasa (04/24/03)
16
Cryostable Magnets
Coolant—bath; CCIC;pipe
Matrix normal metal
Normal zone size >> “MPZ;” in bath-cooled magnets, can
extend over the entire magnet volume.
Best design: sufficient cooling with the minimum coolant space.
Y. Iwasa (04/24/03)
17
Adiabatic Magnets
Structural material, e.g., epoxy
Matrix normal metal
“Localized” normal zone permitted, but its size < “MPZ”
(~mm in most windings).
Best design: elimination of all disturbances.
Y. Iwasa (04/24/03)
18
Cryostability
Circuit Model for Ideal Superconductor (n =
Vcd
0
Gj
Vcd It
Ic
0
o
Rs
+
Vcd
–
o
Real
Ideal ( n=
Rn
)— It
)
I
Ic
n
Im=0
It Ic
Matrix Rm
It
Ic= It
0
Y. Iwasa (04/24/03)
Ic
Is
Superconductor Rs
19
Cryostability
Circuit Model for Ideal Superconductor (n =
Vcd
Rm Im
Rs
Rm
Gj
Vcd It
Gj
Rm It (I t
It
Ic
Rm ( It
Ic )
Rs Ic
At Ic , superconductor will have Rs between 0
and Rn >> Rm to satisfy the circuit requirements
1
Ic )
o
Rs
+
Vcd
–
o
Real
Ideal ( n=
Rn
)— It ≥ Ic
)
I
Ic
n
Im
It > Ic
Matrix Rm
Ic
0
Y. Iwasa (04/24/03)
Ic
Is
Superconductor Rs
20
Temperature Dependent G j(T )—Stekly Model
It
I c (Top )
Ic 0
Ideal superconductor (n =
)
Ic (T )
Gj (T )
It=Ic0
RmIt2
It – Ic
Current-sharing
Ic
0
Top=Tcs
Y. Iwasa (04/24/03)
Tc
T
0
Top=Tcs
Tc
21
Cryostability—Stekly Criterion
T Tcs
Tc Tcs
2
G j (T )
Rm It
Gq (T )
f p Pcd hq (T
gq (T )
f p Pcd hq (T Top )
Acd
f p Pcd hq (T
m
Note: Tb
Top
Ic20 T Top
I
sk
f p Pcd Am hq ( Tc Top )
1
2
m c0
sk
m
I
I c0
Acd
Y. Iwasa (04/24/03)
J c0
Ic 0
As
Am
I c20
(6.8)
Note that the conventional definition
of sk is upside down of Eq. 6.8
2
m c0
f p Pcd hq (Tc Top )
cd
Tc )
Acd Am Tc Top
f p Pcd Am hq (Tc Top )
J c0
T
Tb )
Top )
Acd
Am
(Tcs
1
s
c/s
22
Stekly (continued)
2
Dissipation:
Power density
m
I
m
I c0 T
Top
Acd Am Tc Top
Cooling:
f p Pcd hq (T
Top )
Acd
Not stable
2
c0
Acd Am
Stable
0
Top Tb
Y. Iwasa (04/24/03)
T
T < Tc
23
General Case ( It < Ic0 or Tcs > Top )
G j (T ) 0
G j (T )
Ic 0
Rm It It
It
Ic 0
Tc T
Tc Top
Tc Top
G j (T )
Tc Tcs
Rm I t
Ic(T )
2
T Tcs
Tc Tcs
(Top
T
Tcs )
(Tcs
T
Tc )
(Tc s T
Tc )
Gj(T )
Superconductor
Ic0
Current-sharing
RmIt2
It
Matrix
T
Top
Tcs
Y. Iwasa (04/24/03)
Tc
Top
Tcs
Tc
T
24
Nonlinear Cooling Curves
[J c 0 ]cd
[Jt ]cd
[J op ]cd
f p Pc dAm q fm
Am )2
m (As
f p Pcd q f m
m Am
[A/m3 ]
q(T ), gj(T )
qpk
qfm
q(T )
Stekly
gj
General
Top Tb Tcs
Y. Iwasa (04/24/03)
I2
f p Pcd Am
m t
[w/m2 ]
T
Tc
25
Example
fp
0.5; Pc d = 2.6 c m ; Am
As
Acd
2
Am
Acd = 0.273 cm ;
1
f p Pcd Am q fm
Am ) 2
m ( As
[J op ]cd
m
2
0.3 cm ;
3 10
-8
Am
As
cm; q fm
= 10;
2
0.3 W/cm ;
(0.5)(2.6cm)(0.273 cm2 )(0.3 W/cm 2 )
( 3 10 -8 cm)(0.3cm2 )2
2
6280 A/cm
[J op ]s
(1
)[J op ]cd
2
69,080 A/cm
LHe
Iop
Acd [J op ]cd
1884 A ( = 10)
Iop
Acd [J op ]cd
1803 A
Y. Iwasa (04/24/03)
10 mm
( = 5)
3 mm
26
V vs. I Traces of a Composite Conductor
Matrix alone at T = Tb
SC alone at T = Tb
V
V
Rs >> Rm
Rm
0
Ic0
0
I
0
0
I
Rs / Rm ~1000-10000
Y. Iwasa (04/24/03)
27
V vs. I Traces of a Composite Conductor
G j (Top
T ) VI
f p Pcdlhq (T Top )
T
V
Rm I ( I
Rm I
Tc (Top
T)
Tc Top
I
Rm I ( I
Ic 0 )
Ic0 T
Tc Top
f p Pcdlhq T
I c0 )(Tc Top )
f d Pcd lhq (Tc Top )
Rm ( I
I c0
Ic 0 )
Rm Ic 0 I
I c0
Tc Top
Rm I ( I
I c 0 )(Tc Top )
f p Pcd lhq (Tc Top )
Rm Ic0 I
2
Rm ( I
Ic0 )
Y. Iwasa (04/24/03)
Rm I ( I Ic0 )(Tc Top )
f p Pcdlhq (Tc Top ) Rm I c0 I
28
V vs. I Traces: Dimensionless Expressions
v
V
Rm Ic 0
i
I
Ic0
sk
f p Pcd lhq (Tc Top )
Rm I c20
v( i)
( i 1)
i( v)
sk
(v
sk
Y. Iwasa (04/24/03)
i( i 1)
i
sk
f p Pcd Am hq (Tc Top )
2
m Ic 0
sk
( i 1)
i
sk
1)
v
29
Numerical Illustrations
Ic 0
5
2
1 0 0 0 A ;Tc 5.2 K ; Top 4.2 K; Am 2 10 m ;
m
= 4 10
-10
m;
hq = 104 W/m2 ; Pcd= 2 10-2 m2
fm=1: Entire conductor surface exposed to coolant
sk
(1)(2 10 2 m)(2 10 -5 m2 )(10 4 W/m 2 K)(5.2 K - 4.2 K)
(4 10 -10 m)(1000 A) 2
10
v
1
v vs. i for
sk
= 10
i
1
1.1
v
0
0.11 0.59
1.5
2
T
1.25
0
0
Y. Iwasa (04/24/03)
1
Tb
i
30
Numerical Illustrations
fm=0.1: 10% of conductor surface exposed to coolant
sk
(0.1)(2 10 2 m)(2 10 -5 m2 )(10 4 W/m 2 K)(5.2 K - 4.2 K)
(4 10-10 m)(1000 A) 2
1
v
1
0
0
Y. Iwasa (04/24/03)
1
i
31
Numerical Illustrations
fm=0.05: Only 5% of conductor surface exposed to coolant
v vs. i for
sk
= 0.5
v
0
0.125
0.25
0.5
0.625
0.707
i
1
0.9
0.833
0.75
0.722
0.707
v
i
0.5( i 1)
0.5 i
or v
i
v
0.707
0.5
0.5(v 1)
0.5 v
1
0
0
Y. Iwasa (04/24/03)
0.707
1
i
32
Y. Iwasa (04/24/03)
33
“Equal-Area” Criterion
0
gk (T ) g j (T ) 0 g q (T )
gk (T )
d
dT
kcd (T )
dx
dx
gq (T )
g j (T )
S (T )
kcd (T )
dT
dx
dS(T )
dS(T ) dT dS(T ) S (T )
gq (T ) g j (T )
dx
dT dx
dT kcd (T )
dS(T )
S(T )
kcd (T ) gq (T ) g j (T )
dT
T2
1 2
S (T2 ) S 2 (T1 ) k0 T gq (T ) g j (T ) dT
1
2
S(T1 ) S (T2 ) 0because dT/ dx x
T2
T1
Y. Iwasa (04/24/03)
gq (T )
1
dT/ dx x
g j (T ) dT
0
2
0
34
Equal Area (continued)
2-D Case
kcd (T ) T
d
dT
kcd (T )
dr
dr
dT
d
kcd (T )
dr
dr
gq (T ) g j (T )
dT
1
kcd (T )
dr
r
dT
1
kcd (T )
dr
r
Because the last term dT/dr is negative, it has the same effect
as that of increasing cooling or decreasing Joule heating.
Y. Iwasa (04/24/03)
35
q(T ), gj(T )
qpk
q(T )
Equal Area
qfm
Stekly
gj
2
m c0
I
f p Pcd Am
Stekly
(Tcs>Top)
Top Tb Tcs
Tc
T
[Ic0]equal area > [Ic0]Stekly
Y. Iwasa (04/24/03)
36
Recovery Processes
“Stekly”
T
x
T
“Equal Area”
x
Y. Iwasa (04/24/03)
37
CICC
Transposed 37-Strand Cable (c. 1970)
Courtesy of Luca Bottura (CERN, Geneva)
Y. Iwasa (04/24/03)
38
Power Density Equation—CICC
Conduit
Fluid
Composite
Vfl(T )
Ccd (T )
T
t
x
C fl (T )
T fl
t
f p Pcd
q (T )
A fl
hfl
kc d(T )
T
x
cd
f p Pc d
h fl
Af l
k
T
0.0259 f l Re 0.8 Pr 0.4 fl
Dhy
T
Y. Iwasa (04/24/03)
(T )J cd2
(T
gd
f p Pcd
q(T )
Acd
T fl )
0.716
39
Stability Margin vs. Current in CICC
eh [mJ/cm3]
Well-Cooled
~1000
Dual
Stability*
Ill-Cooled
~100
~10
0
Ilim
Iop
* J.W. Lue, J.R. Miller, L. Dresner (J. Appl. Phys. Vol. 51, 1980)
Y. Iwasa (04/24/03)
40
Stability Approach for CICC
Because CICC is mostly applied for “large” (“expensive”) magnets,
cryostability (Stekly) is the accepted approach.
Choose Iop
Ilim given by:
I lim
f p Pcd Am hq (Tc Top )
m
Y. Iwasa (04/24/03)
41
Helium Heat Transfer Data—Nucleate & Film Boiling
10
Approximate N2 data
multiply:
qpk
q(T ) [W/cm2]
1
y-scale by 10-30
x-scale by 10
0.1
qfm
0.01
0.001
0.01
0.1
1
10
100
T [K]
Based on data from Luca Bottura (CERN, Geneva)
Y. Iwasa (04/24/03)
42
Helium Heat Transfer Coefficient Data
hq(T ) [W/cm2]
10
qpk
1
0.1
0.01
0.01
0.1
1
10
100
T [K]
Based on data from Luca Bottura (CERN, Geneva)
Y. Iwasa (04/24/03)
43
Computation of Ilim for ITER CS (Central Solenoid) CICC
Strand dia. (dst ) 0.81 mm
Cu/non-Cu (γ)
1.45
Cable
3×4 ×4 ×4 ×4
# Strands (Nst )
1152
Am = Acu
3.51 ×10−4 m2
fp
5/6
Pcd = Pst
2.93 m
hq
600 W/m2 K
Tc (13 T); Tb
11.2 K; 4.5 K
m
Acu
(13 T)
dst2
N st
4
Y. Iwasa (04/24/03)
6.8×10−10 Ω m
1
Pst
dst N st
44
Ilim
(5/6)(2.93 m)(3.51 10-4 m2 )(600 W/m2 K)(11.2 K - 4.5 K)
6.8 10 -10 m)
71kA
Iop (40 - 46 kA) < I lim
Ic (96 kA)
This CICC design as with CICC designs for the rest of
ITER coils are highly stable, i.e. very conservative.
Y. Iwasa (04/24/03)
45
High-Performance (“Adiabatic”) Magnet
Jover enhanced by:
Combining superconductor and high-strength normal
metal (stability; protection; mechanical).
Eliminating local coolant* and impregnating the entire
winding space unoccupied by conductor with epoxy,
making the entire winding as one monolithic structural entity.
(Presence of cooling in the winding makes the winding
mechanically weak and takes up the conductor space.)
High-performance approach universally used for NMR, MRI,
HEP dipoles & quadrupoles in which R J B manageable with a
combination of “composite conductor” & “monolithic entity.”
* The conductor always requires cooling but not necessarily exposed
directly to the coolant.
Y. Iwasa (04/24/03)
46
MPZ Concept*
Even in an adiabatic magnet, a small normal-state region may remain
stable: gj is balance by thermal conduction to the outside region.
Corollary: Even an adiabatic magnet can tolerate a disturbance
without being driven to a quench
How large is this normal state region, Rmz , and a permissible
disturbance energy?
y
Region 1
Region 2 ( r> Rmz)
Rmz
x
* A.P. Martinelli, S.L. Wipf (IEEE, 1971)
Y. Iwasa (04/24/03)
47
0
gk
gj
0 0
kwd d 2 d T1
r
dr
r 2 dr
gj
kwd d 2 d T2
r
r 2 dr
dr
gj
(Region 1)
0
(Region 2)
C
A
B;
T2 ( r )
r
r
6kwd
Boundary conditions:
At r
, T2 Top
D Top ; r 0, T1
T1 (r )
dT1
dr r
At r
Rmz
r2
g j Rm g
3kwd
Rm z, T1
T2
dT2
dr
C
2
Rmz
r R mz
T1 (r )
A 0; r
C
gj r 2
B
; T2 (r )
6kwd
2
T1 (r ) Top
Y. Iwasa (04/24/03)
D
g j Rm z
1
2kwd
Rm z, dT1 / d r
dT2 / dr :
3
g j Rmz
3kwd
Top
3
g j Rmz
3kwd r
1 r
3 Rm z
B Top
2
g j Rmz
2kwd
2
48
Total Joule Heating G j
Gj
3
4 pRmz
gj
3
Because g j
Tc
Top
4 pRm3 z
dT
kwd 1
3
dr
m
J m2 and T1
2
m z wd
4 pR k
r Rmz
Tc at r
2
g j Rmz
2kwd
2
3Rmz
4 Rm3 z
gj
3
Rmz :
2
J m2 Rmz
3kwd
m
3kwd (Tc Top )
Rm z
m
With kwd
400W/mK;Tc
6K; Top
Jm2
4K;
Rmz 1
3(400W/mK)(6K - 4 K )
( 2 10 10 m)(300 106 A/m2 )
Rmz 2
kwd 2
R
kwd 1 mz 1
Y. Iwasa (04/24/03)
0.1W/mK
R
400W/mK mz 1
m
2 10
10
m; J m
6
2
300 10 A/m :
12mm
0.2mm
49
With kwd
400 W/mK; Tc
6 K ;Top
4K;
Rmz 1
3(400W/m K)(6K- 4K)
( 2 10 10 m)(300 106 A/m2 )
Rmz 2
kwd 2
R
kwd 1 mz 1
0.1W/m K
R
400W/m K mz 1
m
2 10 10 m; J m
300 10 6 A/m2 :
12mm
0.2mm
2Rm z2
2Rm z1
Y. Iwasa (04/24/03)
50
Energy margin or stability margin, Eh :
Tc
Eh
mz
With Rmz 2
and h(Top )
mz
T op
Cwd (T )dT
4
2 10 m, Rmz 1
2
4 Rmz
2 Rm z1
h(Tc )
3
cu
3
2
1.2 10 m, h(Tc )
cu
3.9kJ/m ,
3
cu
1.3kJ/m :
4 ( 2 10 4 m)2( 1 . 2 10 2 m)
3
Y. Iwasa (04/24/03)
h(Top )
9
3
2 10 m
Eh
5.2 10 6 J ~ 10 J
eh
2.6kJ/m3
2.6mJ/cm3
51
Cryostable vs. Adiabatic (High-Performance ) Magnets
Basic power density equation:
e• h
gk
gj
gd
gq
Cryostable Magnets
•
eh
0; gk
Jc0
Y. Iwasa (04/24/03)
gj ; gd
gj
gj
f p Pcd Am q fm
cd
m ( As
Am )
gq
Jc 0
s
52
Cryostable Magnets (continued)
Observations
[Jc0]cd determined by external parameters.
Applied for “large magnets” (e.g. fusion) in which non-conducting
structural materials occupy a significant fraction of the winding
pack, making the condition [Jc0]cd << [Jc0]s not as important as in
adiabatic magnets.
Note that coolant, though a key component in a cryostable magnet,
is a structural detriment.
Y. Iwasa (04/24/03)
53
Adiabatic (High-Performance) Magnets
•
eh
gk
gj
gd
gq
0
Observations
Elimination of coolant within the winding: 1) enhances the overall
current density; 2) makes the winding pack structurally robust.
[Jc0]cd no longer limited by external parameters but primarily by [Jc0]s .
Disturbances (gd) must be eradicated or their energies minimized—
impregnation of the winding with epoxy resin a widely used technique.
High-performance magnets: NMR, MRI, HEP.
Y. Iwasa (04/24/03)
54
Mechanical Disturbances—Premature Quenches & Training
Important for adiabatic magnets; not so for cryostable magnets.
Through the use of AE (acoustic emission) technique, it has been
demonstrated that virtually every premature quench in adiabatic
magnets is induced by a mechanical event, primarily either conductor
motion or epoxy fracture.
Mechanical events usually obey the “Kaiser effect,” mechanical
behavior in cyclic loading in which mechanical disturbances, e.g.,
conductor motion, epoxy fracture, appear only when the loading
responsible for events exceeds the maximum level achieved in the
previous loading sequence.
An adiabatic magnet thus generally “trains” and improves its
performance progressively to the point where it finally reaches
its design operating current.
Y. Iwasa (04/24/03)
55
Training Sequence for an SSC Dipole
S. Ige (MIT ME Dept. Ph.D. Thesis, 1989)
Y. Iwasa (04/24/03)
56
AE Technique
Acoustic signals emitted by sudden mechanical events in a body
being loaded or unloaded, e.g., a magnet being charged or discharged;
useful for detection and location of a premature quench caused by
conductor motion or epoxy fracture event in adiabatic magnets.
Piezoelectric Effect
The coupling of mechanical and electric effects in which a strain in a
certain class of crystals, e.g. quartz, induces an electric potential and
vice versa. Discovered by P. Curie in 1880.
Y. Iwasa (04/24/03)
57
AE Sensor
Commercially available sensor: expensive ($500-$1000) and even
those claimed to be for use in “low temperatures” generally fail.
Home-made (FBML) differential sensor: reasonable ($50/disk +
labor); withstands 4.2 K RT cycles.
Differential Sensor
from Copper pipe cap
Sensor: two half-disks
+–
– +
Y. Iwasa (04/24/03)
Cu foil (~25 m)
Brass foil (~75 m)
58
AE Instrumentation
LabVIEW
Oscilloscope
AE Sensor
Filter
10k–1MHz
Pre-amp
e.g. 40 dB
Filter
200k–230kHz
Amplifier
e.g. 43 dB
Discriminator
<0.1 V
Counter
Recorder
Y. Iwasa (04/24/03)
59
Identification of Quench Causes
A combination of voltage and AE monitoring permits identification
of three distinguished causes of a quench in adiabatic magnets.
Conductor motion: a voltage spike and the start of AE signals.
Epoxy fracture: no voltage spike but AE signals.
Critical current: no voltage spike nor AE signals.
Y. Iwasa (04/24/03)
60
Epoxy cracking
Three Causes of Quench
NO voltage pulse
AE
Conductor-motion
Critical current
Voltage pulse
AE
O. Tsukamoto, J.F. Maguire, E.S. Bobrov, Y. Iwasa (Appl. Phys. Lett. Vol. 39, 1981)
Y. Iwasa (04/24/03)
61
A Conductor-Motion Induced Quench
— “Isabella” Dipole
AE
AE
5 ms
50 ms
V
O. Tsukamoto, M.F. Steinhoff, Y. Iwasa (IEEE, 1981)
Y. Iwasa (04/24/03)
62
Conductor-Motion Induced & Critical-Current Quenches
— An SSC Dipole
Located farthest from the source
Due to heating
AE
AE
AE
NO AE signals!
Voltage
Voltage
Voltage scale too large for a spike
Iq = 6510 A
Ic = 6828 A
S. Ige (MIT ME Dept. Ph.D. Thesis, 1989)
Y. Iwasa (04/24/03)
63
Conductor Motion
Frictional heating energy release, ef , due to a Lorentz-force
induced conductor motion (“slip”) of rf :
ef
With
f
f
fL r rf
0.3, J
f
J Bz rf
6
2
200 10 A/m , Bz
5T, ande f
hcu (5.2K) - hcu (4.2K)
= 1300J/m 3 :
rf
ef
f J Bz
3
(1300J/m )
20 m
(0.3)(200 106 A/m2 ) ( 5 T )
Actually a conductor slip as small as ~1 m (“microslip”) can drive a
short length of the conductor to the normal state, leading to a
premature quench.
Y. Iwasa (04/24/03)
64
Friction/Quench Experiment
Ft
AE Sensor
Fn
B (5 T)
G705
Fn
Fn
Ft
I
AE Sensor
Search Coil
Conductor Braid
I
Ft
I B
Fn
Helmholtz Coil
Based on O. Tsukamoto, H.Maeda, Y. Iwasa (Appl. Phys. Lett. Vol. 40, 1982)
Y. Iwasa (04/24/03)
65
Slip Distance from Extensionmeter
V (t )
z
d
dNAB
dt
dt
V ( t ) dt
NA
dB dz
dz dt
B(z )
mea
dB
NA
dz
V(t )
known
V(t )
Slip Distance from Voltage Pulse
V (t )
z
d lzB
d
dt
dt
V ( t ) dt
mea
lB
Y. Iwasa (04/24/03)
known
z (t )
Search coil (N, A)
lB
dz
dt
Ft ; z
I
l
B
66
Friction Experiment
Quench Experiment
Slip-Induced voltage spike
Search Coil
2 mV
AE
1 ms
Slip distance: ~1 m
Peak slip velocity: ~ 1 cm/s
Fn=2000 N; Ft~400 N
Slip distance: ~1 m
Peak slip velocity: ~ 3 cm/s
Fn=2000 N; Ft=500 N
[=(0.025 m)(4000 A)(5 T)]
Y. Iwasa (04/24/03)
67
Observation of Kaiser Effect
Friction Experiment
Quench Experiment
H. Maeda, O. Tsukamoto, Y. Iwasa (Cryogenics Vol. 22, 1982)
Y. Iwasa (04/24/03)
68
Y. Iwasa (04/24/03)
69
Epoxy Cracking Inducted Heating
Stored elastic energy density, eel, typical epoxy resin:
e el
2
el
2 Ee l
(15 10 6 Pa) 2
2(10x109 ) 2
3
1100J/m
ef
Nb-Ti/Cu composite
Epoxy coating
Y. Iwasa (04/24/03)
70
Epoxy Cracking Inducted Heating
— Experimental Results
T1
Ft
T2
T1
Nb-Ti/Cu composite
max
T2
T3
Epoxy coating
1K
T4
max
T3
AE Sensor
AE
T4
0
from Y. Yasaka, Y. Iwasa (Cryogenics Vol. 24, 1984)
Y. Iwasa (04/24/03)
50 100 150 200
Time [ms]
71
Stability of HTS
Operating Temperature Ranges
0 ~10
LTS
~100
Top [K]
HTS
[Tcs – Top]HTS > ~10 [Tcs – Top]LTS
Y. Iwasa (04/24/03)
72
Heat Capacity Data
[C p (Top Range)]H T S
[C p (TopRange)] L T S
A.
B.
C.
D.
E.
F.
G.
H.
I.
1
Helium (10 atm)
Helium (1 atm)
GE varnish
Stainless steel
Nb-Ti
Epoxy
Silver
Copper
Aluminum
Y. Iwasa (04/24/03)
73
Enthalpy Data
[e min ]H T S
[e min ]LTS
1
1. Silver
2. Copper
3. Aluminum
Y. Iwasa (04/24/03)
74
Minimum Thermal Energy Density
— Cp(T): copper; Tc: Superconductor—
Top+∆T
e min
e = ∫T
Top
min
Y. Iwasa (04/24/03)
op
T op
C pT(TC)dT( T ) d T
op
cd
75
HTS Stability >> LTS Stability
Y. Iwasa (04/24/03)
76