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CERN-ACC-2014-0008
HiLumi LHC
FP7 High Luminosity Large Hadron Collider Design Study
Deliverable Report
THERMAL-ELECTRICAL MODEL OF
HILUMI SC LINKS
Y. Yang SOTON
et al
23 January 2014
The HiLumi LHC Design Study is included in the High Luminosity LHC project and is
partly funded by the European Commission within the Framework Programme 7
Capacities Specific Programme, Grant Agreement 284404.
This work is part of HiLumi LHC Work Package 6: Cold powering.
The electronic version of this HiLumi LHC Publication is available via the HiLumi LHC web site
<http://hilumilhc.web.cern.ch> or on the CERN Document Server at the following URL:
<http://cds.cern.ch/search?p=CERN-ACC-2014-0008>
CERN-ACC-2014-0008
THERMAL-ELECTRICAL MODEL OF
HILUMI SC LINKS
Doc. Identifier:
HILUMILHC-WP6 Del-D6_2_final
Date: 23/01/2014
Grant Agreement No: 284404
HILUMI LHC
FP7 High Luminosity Large Hadron Collider Design Study
S e ve n t h F r a m e w o r k P r o g r a m m e , C a p a c i t i e s S p e c i f i c P r o g r a m m e , R e s e a r c h I n f r a s t r u c t u r e s ,
C o l l a b o r a t i ve P r o j e c t , D e s i g n S t u d y
DELIVERABLE REPORT
T HERMAL -E LECTRICAL M ODEL OF
H I L UMI SC L INKS
D ELIVERABLE : D6.2
Document identifier:
HILUMILHC-WP6 Del-D6_2_final
Due date of deliverable:
End of Month 24 (Oct 2013)
Report release date:
23/01/2014
Work package:
WP6: Cold Powering
Lead beneficiary:
University of Southampton
Document status:
Final
Abstract:
This document reports the results of the preliminary thermal-electrical model of the
superconducting links (SC links) proposed for the cold-powering of superconducting
magnetics at P1 and P5 for Hi-Luminosity Upgrades. The thermal-electrical model is
concerned with the global characteristics of the superconducting link under both static and
transient conditions. The model provides an outline assessment of the electromagnetic
environment produced by the SC link and the heating dynamics upon different quench
scenarios.
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Copyright notice:
Copyright © HiLumi LHC Consortium, 2014
For more information on HiLumi LHC, its partners and contributors please see www.cern.ch/HiLumiLHC
The HiLumi LHC Design Study is included in the High Luminosity LHC project and is partly funded by the
European Commission within the Framework Programme 7 Capacities Specific Programme, Grant Agreement
284404. HiLumi LHC began in November 2011 and will run for 4 years.
The information herein only reflects the views of its authors and not those of the European Commission and no
warranty expressed or implied is made with regard to such information or its use.
Delivery Slip
Name
Partner
Date
Authored by Y. Yang (SOTON), A. Ballarino (CERN)
SOTON
24/11/2013
Edited by
Ballarino
CERN
26/11/2013
L. Rossi [Project coordinator]
CERN
29/11/2013
A.
Reviewed by A.
Approved by Steering Committee
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TABLE OF CONTENTS
1.
INTRODUCTION ........................................................................................................................................ 4
2.
BASELINE CONFIGURATION OF HI-LUMI SC LINK ....................................................................... 4
3.
STATIC THERMAL ELECTRICAL CHARACTERISTICS ................................................................. 5
3.1.
3.2.
4.
THERMAL CONSIDERATIONS AT STATIC CONDITIONS .............................................................................5
ELECTROMAGNETIC PROPERTIES AT STATIC CONDITIONS ......................................................................6
TRASIENT THERMAL ELECTRICAL CHARACTERISTICS ........................................................... 7
4.1.
HEATING DYNAMICS OF A THERMALLY QUENCHED CABLE ....................................................................8
4.2.
HEATING BY INDUCED CURRENT IN THE SC LINK UPON A FAST DISCHARGE OF AN INNER TRIPLETS
CIRCUIT ..............................................................................................................................................................10
4.2.1.
Field transients due to magnet discharging .................................................................................10
4.2.2.
Induced current in the SC link cables by the discharging field transients ...................................11
5.
REFERENCES ........................................................................................................................................... 15
ANNEX: GLOSSARY ..........................................................................ERROR! BOOKMARK NOT DEFINED.
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Executive summary
This document reports the results of the preliminary thermal-electrical model of the
superconducting links (SC links) proposed for the cold-powering of the superconducting
magnets at P1 and P5 for Hi-Luminosity Upgrades. The model provides an outline
assessment of the electromagnetic environment produced by the SC link and the heating
dynamics upon different transient scenarios.
1.
INTRODUCTION
Thermal-electrical models for the superconducting links at P1/P5 for LHC High Luminosity
Upgrade have been developed to evaluate the global of electromagnetic and thermal
behaviours under static and transient conditions. At this stage of the project, the models do not
focus on local analysis but on the overall characteristics. The main objectives of the models
are to scrutinize the SC link baseline configuration against the required working envelope.
The models also aim at identifying the critical aspects in the SC link design for further
optimization, detailed local modelling and experimental studies/tests.
2.
BASELINE CONFIGURATION OF HI-LUMI SC LINK
The baseline configuration of the Hi-Lumi SC links powering the magnets in the insertion
regions at P1 and P5 has been proposed [1] to fulfil the requirements of the updated baseline
powering layout (Fig. 1) [2].
Fig. 1 Baseline powering layout for the Triplets and D1 at P1 and P5 [2].
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The proposed SC link (Fig. 2) has a total current capacity of 150 kA, consisting of six 20 kA
cables, seven 3 kA coaxial cables, four 0.4 kA cables and eighteen 0.12 kA cables [2]. The 20
kA cables uses hexagonal configuration of six sub-cables, which are constructed using 18
MgB2 round wires of 0.85 mm diameter twisted around copper stabilizer. The matrix of the
MgB2 wire is predominantly Monel. The twist pitch is 100 mm - 300 mm. The same sub-cable
is also used to form the inner leg of the 3kA co-axial cable. The outer return leg consists of 18
MgB2 wires and 6 copper wires of the same diameter.
Cu
MgB2 ,  = 0.85 mm
18 MgB2 wires
 = 6.5 mm
20 kA
Six cables,  = 19.5 mm
Concentric  3 kA
Seven cables,  = 8.4 mm
0.4 kA
Four cables
0.12 kA
Eighteen cables
ext  65 mm
Fig. 2 Configuration of the P1/P5 SC link and its cable component [1].
The SC link contains two nominally 17.3 kA circuits for the quadrupoles (Q1+Q3 and
Q2a+Q2b respectively) and one 11kA circuit for the dipole D1.In the SC link, these six cables
will be identical and designed for transporting a maximum DC current of 20 kA at 25 K.
3.
STATIC THERMAL ELECTRICAL CHARACTERISTICS
3.1.
THERMAL CONSIDERATIONS AT STATIC CONDITIONS
The thermal landscape at static conditions is a simple one. The helium gas cooled SC link
operates between 5 K at the cold to the LTS bus-bar and maximum at about 20 K at the warm
end near to the current leads. The present cable baseline gives a relative current loading of
hence there is zero or negligible heat generation from within the SC link
(
)
along the whole length. The forced flow helium gas should maintain a stable temperature
gradient of ~0.15-0.2 K/m while removing the heat load from inner cryogenic envelope.
Without a sudden interruption of the helium supply or failure of the vacuum envelope, such a
static thermal condition is stable and does not interplay with the static electrical operation of
the SC link. In theory, there is also a longitudinal conduction heat load along the link.
However, the thermal conduction due to the ~ 10 cm2 copper stabilizer with the link only
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amounts to about 0.2 W at the 4.2 K end, negligible when compared to the helium gas flow
for the link.
3.2.
ELECTROMAGNETIC PROPERTIES AT STATIC CONDITIONS
The main electromagnetic considerations are the magnetic fields produced by the current flow
within the link and the inductances of the cables. The distribution of the magnetic field
impacts on the critical current of the wires in the sub-cables. Since the low current cables
(0.12-0.4 kA) are located inside the six 20kA-class cables, their exposure to the field produced
by the high current system is minimal. Furthermore, the coaxial cables do not generate
magnetic field to their exterior. Hence the focus is on the 20 kA system.
0T
0.8T
Fig. 3 (a) Lines of force and (b) modulus of magnetic field of 6×20 kA cables
arranged symmetrically for 3 circuits. The x-y scales are in mm.
The six 20 kA cables in the SC link are configured with the cable-pair of one circuit placed
next to each other to minimize their self-inductance. The magnetic field produced by the six
20 kA cables with the same ± current is similar to that of a sextupole magnet, as shown by the
lines of force and field modulus in Fig. 3 (a) and Fig. 3 (b) respectively. In such a symmetric
configuration, the maximum field occurs at the closest proximity between the opposing
polarities, both intra-circuit and inter-circuit. For the mechanical stability of the cables, it is
not desirable to break the symmetry polarity configuration. If all six cables are fully loaded to
20 kA, the maximum field is at
, which is more than 50% above the
(
)
maximum field of
produced by a single 20 kA cable. With only one circuit
powered, the magnetic field of the corresponding cable-pair at ±20 kA reaches a maximum
of
. Such a high field should be considered if the quadrupoles are not ramped
up simultaneously. The calculations assumed that all the wires within a sub-cable carry the
same current and no redistribution of current due to the change of magnet field along
individual wires within the twist pitch takes place. It is further assumed that the sub-cables of
a 20 kA cable also transport the same current.
The field distribution within the SC link produced by the six 20kA cables becomes
asymmetric (Fig. 4) when the magnets are powered to their nominal strength. In this case, the
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cables are configured into two pairs of ± 17.3 kA and one pair of ±11 kA. The maximum
field, which now appears at the closest proximity between the ± wires of the same circuit, is
0.66T, almost (3.6% excess) proportionally to the reduction of current from 20 kA to 17.3 kA.
The field between circuits are further reduced.
0T
0.7T
Fig. 4 (a) Lines of force and (b) modulus of magnetic field of SC cables when powered at nominal currents:
2×(±17.3 kA) and 1×(±11kA). The x-y scales are in mm.
The inductances of the cables are also obtained as
for a single pair of
20 kA cables (i.e. two neighbouring 20 kA cables (+/-) in series) and
for
the six 20 kA cables arranged symmetrically for the three circuits. For these calculations, the
twist pitch of the wires in the sub-cables is not considered as it has minimal impact on the
field distribution of cables pairs. The inductance is higher with the current MgB2 wires due to
the weakly ferromagnetic monel sheath. The focus on the cable-pair inductances is because
the self-inductance of a single straight cable has a logarithmic singularity and is only become
defined with a return current leg.
The cable/link inductances are clearly very small and should not impose any restriction on the
charging characteristics of the circuits. The mutual inductances between two neighbouring
cable-pairs are of similar magnitude, again not important for field charging consideration. It
should be noted that the wires within sub-cables are twisted, and the current mutually induced
by the charging cross-talk between neighbouring circuits near the maximum field regions does
not form loops longer than the twist pitch.
4.
TRASIENT THERMAL ELECTRICAL CHARACTERISTICS
The global dynamic models focus on SC link response to two likely transient events: (a) the
quench of a cable and (b) the fast discharge upon quench of a magnet or a superconducting
cable in the link. For the former, the main concern is the maximum temperature rise within the
quenched cable and its capability to allow the safe discharge of the relevant magnets within
the circuit. The latter is concerned with the transient magnetic field generated by the fast
discharging circuit and the corresponding induced current heating in the neighbouring circuits.
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Date: 23/01/2014
HEATING DYNAMICS OF A THERMALLY QUENCHED CABLE
The model only considers the adiabatic temperature rise within a cable after a local normal
zone has exceeded the minimum propagation zone (MPZ) and an irreversible longitudinal
propagation has started. The heat diffusion to the un-quenched section at the propagation front
can be safely neglected when the quenched length becomes much longer than MPZ. The
model makes no assumption of the causes for triggering a (localised) quench, although they
are likely to originate from some local mechanical and/or thermal disturbances. The model
further assumes sufficiently small thermal/electrical contact resistances between the MgB2
wires and the copper core to allow full current sharing with the stabilizer. It is noted that the
sub-cable is thermally equivalent to the 20 kA cable, although the quench of a single subcable is unlikely not spread to the others.
With the assumptions given above, the temperature rise upon a cable quench is given by:
̅ ̅ ( )
( )
( ( )) (
)∫
∫
∫ ( )
( )
( )
∫
(
100
Monel
10-1
Cu
10-2
10-8
cm-1
The specific heat of the cable consists of a portion of
the superconductor wire and
of the copper
stabilizer. The superconductor wire is primarily monel
and Ni, which has a similar heat capacity characterised by
a high electronic heat capacity at low temperatures and a
high Debye temperature of ΘD=460K for the phonon heat
capacity. For the present model it is sufficient to use
simple analytical expressions in J∙mol-1K-1:
( )
( )
Cv, Jkg-1K-1
Where ( ( )) is known quench load and is determined as function of temperature by the
thermal electrical property (density ̅ , heat capacity ̅ and stabilizer resistivity ρ) and the
superconducting wire portion λ in the cable. The equation
determines the cable temperature ( ) due to resistive
(a)
102
heating at a current density of ( )
( ) for a period
t. Here the current density is referred to the total cross101
section area A of the cable.
(b)
10-9
RRR
50
100
)
For
and
monel/Ni:
for
Cu:
. For quench load calculation, cv is converted to
J∙kg-1K-1 (Fig.5(a)). With a resistivity between
at 10K-300K, monel’s contribution to current
sharing is not considered. The copper resistivity [4] as
function of temperature depends on the RRR (Fig. 5(b))
with a room temperature value of ~
.
10-10
300
1
10
100
Temperature, K
Fig. 5, (a) The relevant specific heat for
the SC link cable and (b) resistivity of
copper at different RRR as functions of
temperature.
In case of resistive transition of a cable in the link, a fast discharge of the corresponding
magnet chain shall be triggered. While final values for the time constants of the circuits are
not yet available, indicative values in the range from 1 s to 3 s were given by the magnet
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designers. It is noted that the sub-cable and 20 kA main cable have the same quench load due
to their identical superconductor fill factors and the nominal current density. The present subcable design has a
with a superconducting wires area of 0.102 cm2 with 18 wires of
0.85 mm diameter and a copper cross-section of 12.5 cm2 (about 50% of the available centre
core area). The sub-cable has a current density of
for the nominal 17.3 kA of the
20 kA cable. The results (Fig. 6) show that at a constant nominal current (2833/sub-cable or
(
) ( )) and room
17.3 kA/cable), the cables will reach 75 K in 1 second (
temperature in 3.5 s. A higher RRR=300 (blue lines) reduces the temperature rise to 50 K and
225 respectively. Although the time for heating is slightly longer for starting at T0=5 K, the
assumption of a fully established quench region means the onset temperature is more likely at
20 K or above.
109
(12.5kAcm-2)2(3.5s)
(12.5kAcm-2)2(1s)
300K
50K
U(T), A2cm-4s
108
75K
RRR=100
RRR=300
10
225K
7
T0=20K
10
6
T0=5K
10
100
Temperature, K
Fig. 6 Quench load of the baseline SC link cable.
Let’s assume that the quench is detected at its onset and the magnet is subsequently
discharged at a time constant τ with ( )
. In this case the quench load becomes:
( ( ))
∫
( )
(
)
The effective constant current heating time
for an exponentially discharging current is
(
) which is shorter than the actual time t and terminal temperature at
is
arrived at
. For example,
s is equivalent to the full course of
discharging at
. In this case the cable temperature will not exceed room temperature
for time constants of the circuit in the range from 1 to 3 s. The practical indicator for
temperature rise is at
or
, e.g. at
for
the temperature
rises to 220 K with RRR=100 and 150K with RRR=300.
For of a reduced time constant of τ = 1s, then cable temperature rise is significantly lower. At
the corresponding effective heating time of
is only 0. 43s after 1s discharge at τ=1s and
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the maximum temperature rise will be at 46 K and 30 K for RRR=100 and RRR=300
respectively.
Fig. 7 The distribution of field change in the SC link due to the discharging of a quadrupole circuit.
10
105
-1
(a)
(b)
r/RCable
75
120
60
135
45
150
10-2
dB/dt, Ts-1
90
30
165
10-3
15
180
0
195
10-2
1.5
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
345
210
330
225
315
240
10-1
300
255
270
285
Fig. 8 The detailed field change imposed on the wires from the neighbouring cables immediate adjacent to the
fast discharging cables.
4.2. HEATING BY INDUCED CURRENT IN THE SC LINK UPON A FAST
DISCHARGE OF AN INNER TRIPLETS CIRCUIT
4.2.1. Field transients due to magnet discharging
The largest field transient within the SC link occurs upon the fast discharge of quadrupole
circuit at 17.3 kA. The present model examines the field change rate ̇ ( ) in the link by using
( )
( ( )) with ̇ ( )
the field produced by the discharging circuit
(
) is the field produced by the 20 kA cable-pair for the circuit. As shown in
where
Fig. 7, the largest field change is within the circuit cable-pair itself with a peak value of
(
) 0.77 T. However, a significant field of 0.3 T is imposed on the
immediate adjacent ~3 wires in the neighbouring circuits (at 30o and 150o in Fig. 7), as shown
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) is
the Fig. 8(a). For a discharging time constant of τ=7 s, the initial ̇ (
)= (
o
o
shown in Fig. 8(b), where 40 mT/s is found near the 30 and 150 regions of the neighbouring
cables. The shaded area in Fig. 8(b) represents the region occupied by the cables of the
discharging circuit. Note that the field change rate will increase significantly to 0.3 T/s if the
quadrupole discharge time constant is decreased to 1s.
4.2.2. Induced current in the SC link cables by the discharging field transients
4.2.2.1. Magnetisation energy of the critical state upon field discharge
The superconducting wires in the SC link reacts to the field transients by the induction of
“super” current to resist the field change. As the result, work is done by the discharging field
to the neighbouring circuits by increasing their Gibbs’ energy
, for a
discharging field
and a critical state magnetisation
to retain the flux. The
overall energy deposited is proportional volume
enclosed by the induced current loop, i.e.
. Assuming the super-current penetrates only a portion
of the
superconducting strands, then the magnetisation is approximately
, where
is the width of the induced current loop,
is the longitudinal length of the induced
current loop, and Ic is the critical current of the superconducting wire. The overall
magnetization energy of the critical state upon field discharge is
When the stored energy is released due to flux diffusion, e.g. flux creep of the critical state or
the power-law E-J characteristics of most superconductors, the magnetization energy is
converted irreversibly to heat with an effective power of
When the flux diffusion time constant
becomes comparable to or shorter than the field
discharge constant , as often the case for high temperature superconductors (HTS), the heat
generation is almost simultaneous:
̇
(
)
4.2.2.2. Size of the magnetization loops
STRAIGHT UNTWISTED FILAMENTS
For a superconducting wire with fully coupled filaments, the coupling width is approximately
the wire diameter
and the induction loop is extended to the whole length of the
conductor, hence the energy stored per unit volume (of wire) is
If the filaments are completely uncoupled, e.g. by a high matrix resistance, then the coupling
width is reduced to the filament diameter
. The corresponding energy (per unit volume
of wire) by induction for uncoupled filaments is
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Since
most low temperature superconductors (LTS) have very fine filaments,
, the induced energy in a filaments-uncoupled wire is much lower, even though the
critical current penetration in the fine filaments is higher (
). Clearly filaments
uncoupling is essential to reducing the induction energy upon field change.
TWISTED FILAMENTS
In practice, however, high matrix resistance for filaments uncoupling is not practical for the
cryogenic stabilization, which requires a low normal resistivity for current sharing upon
magnet quench. Filaments uncoupling in technical superconductors are achieved by twisting
the filaments in a wire at a short pitch
so that the coupling loop
across the wire
diameter is broken as the twisted filaments are displaced from one side of the wire to the
other. It should be noted that finer filaments for lower induction energy requires a shorter
twist pitch:
√
̇
where
is the critical coupling length between filaments separated by a resistive ( )
matrix. The matrix resistance that breaks coupling loop also limits the effective induced
̇
current across the wire
which is significantly less than the typical critical
current density . However, this coupling current among the twisted filaments leads to a
resistive (eddy-current) type of loss known as the coupling current loss
̇
( )
A successful filament architecture should always have
.
INDUCTION LOOPS AND CORRESPONDING HEATING IN THE SC LINK CABLES
A. Estimated temperature rise due to adiabatic induction heating of different loop sizes
We first estimate the upper limit of temperature rise due to adiabatic induction heating by
different loop sizes. Although the terminal adiabatic temperature rise is independent of the
discharge rate, it is assumed that the flux diffusion is faster than the discharge rate for an
instantaneous heat rate per unit length
, where the electrical field
̇
and
of complete flux penetration in the wire with full critical current ( )
induced.
Consider the reference nominal case of a MgB2 round wire of
resistivity
and a wire critical current (
filaments of diameter
with a filament
( )
. There are three distinct
coupling widths
to consider:
1. Fully uncoupled filaments:
2. Fully coupled filaments:
3. Inter-wire coupling across the Cu stabilizer in
the sub-cable:
. The
thermal mass includes the contributions from the
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, matrix (monel)
. The wire has 30
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Fig. 9 An example of MgB2 round wire
used for reference calculation.
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monel matrix and the copper stabilizer. This large coupling loop requires a negligible
resistances in the wire matrix and at the contact between the wire and stabilizer.
Similar to the quench load calculation, the temperature rise by induction heating for an
exponential magnet discharge of time constant is given by
̅ ( )
( )
( )
where
is the cross-section heated by the induction current with an instantaneous heat
diffusion, and ̅ and ̅ are the weighted average of the specific heat and density respective to
the composition of
. Thermal diffusion to the copper stabilizer is ignored for case 1-2,
i.e.
, consistent with a sufficiently high contact resistance to prevent the large
coupling loop across the sub-cable. For the same reason, a portion of the stabilizer thermal
mass should be included in case 3.
25
20
Temperature, K
T0=20K
15
Uncoupled filaments
Coupled filaments without Cu
Inter-wire coupling with Cu
10
T0=5K
5
10-2
10-1
100
t/
Fig. 10,Adiabatic temperature rise in a MgB2 round wire by inductive current heating due to exposure to the
field change by the adjacent cable of a discharging magnet. Three different loops are considered.
The differential temperature rise equation is integrated to give an explicit expression of
elapsed time to reach temperature :
̅
̅ ( )
(
∫
)
( )
( )
( )
Fig. 10 shows the time for temperature rise at
for the three cases assuming a
wire critical current ( ) linearly reducing with increasing temperature from 590A at 5K to
zero at 37K. As expected, fully uncoupled filaments heat up the least, with a maximum
temperature rise <2K at the cold end of 5K. Although wire coupling across a sub-cable
through the stabilizer has the highest heating power, the temperature rise was tempered by the
thermal mass of the copper. An assumed 30% increase of copper limits the cold end
temperature rise to 4.5K. In fact, for temperature rise for case 1 and 3 reduces rapidly with
increasing temperature, the upper temperature limit of 20K is not exceeded. In contrast, the
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full coupling of filaments leads to substantial inductive heating within the limited thermal
mass of the wire. At cold end (5K), the temperature is increased to above 17.5K, and the
warm end to almost 23K. Actually, fully coupled wires initially at
(covering
about 1/3 of the total Hi-Lumi SC link length at the warm side) will be heated above upper
temperature limit of 20K, hence likely to quench or thermally runaway.
B. Filament uncoupling by twisting
The MgB2 wires in the SC link sub-cables are twisted around the copper stabilizer core at a
pitch
~400mm. Even without filament twisting, the effective induction loop length with a
wire immediate adjacent to the discharging circuit is
, where
is the number of wires in close vicinity of the discharging cables and
the number of
wire in the sub-cable. The coupling length is reduced to the filaments twist pitch if the wire it
is shorter.
For ̇
at a discharging time constant of 1s, the reference wire of the critical
(
)
coupling length at 20K
with (
)
.
The coupling length at lower temperatures will increase further as
increases. Therefore,
even if untwisted, the filaments of the reference wire can only be partially-coupled. The
coupling current heating through the resistive matrix of partially coupled untwisted filaments
is
̇
( )
(
) ̇
Which is much less than
of fully coupled filaments,
hence the conductor will have a negligible temperature rise by the coupling current across the
wire matrix. It should be noted that the critical current density for a coupled length of
is only
(
) for the reference wire and much lower
than the nominal transport current loading of
(
). Hence the contribution by the
filament coupling current to E-J heating can be safely ignored within the working temperature
range
for the SC link cables.
Further reduction of inductive heating can be achieved by twisting the filaments within the
wire at a pitch less than 90mm, which is the target for the MgB2 round wire.
5.
CONCLUSIONS AND FUTURE WORK
Static and transient models for the HiLumi SC link cables were established for their outline
assessment against the baseline operation conditions. The main conclusions from the
modelling analysis are:
1. A maximum field of 0.8-1.0T, corresponds to the powering up of a 20kA single
circuit, should be allowed in the wires specification.
2. The self-inductances of the cables are small compared to the magnets in the circuit.
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THERMAL-ELECTRICAL MODEL OF
HILUMI SC LINKS
Doc. Identifier:
HILUMILHC-WP6 Del-D6_2_final
Date: 23/01/2014
3. With a sufficiently good electrical contact to the copper stabilizer, the wires in the subcables undergo moderate temperature rise upon cable thermal quench. For a reference
RRR=100 for the stabilizer, the temperature rise is less than 80K if the magnets are
discharged at 1s upon quench detection. Slower discharge at 7s leads to a temperature
rise to 220K.
4. Upon fast discharge of a quadrupole circuit following a magnet quench (discharging
time constant of 7 s), a field change of 0.3T is imposed on the immediately adjacent
wires for the neighbouring cables.
5. Fully coupled filaments in these adjacent wires would suffer significant inductive
heating leading to potential quench or thermal runaway in cable section at
temperatures above 14-15K.
6. With a matrix resistance of
and filaments of diameter
, the critical filament coupling length
at ̇
is much longer than
the exposed wire section of 90mm because of the sub-cable twist pitch of 400mm.
Therefore the filaments should only be partially coupled.
7. The coupling current loss for a matrix resistance of
and filaments
-1
of diameter
is about 0.001Wm at ̇
, insufficient to cause
wire to quench or even to heat up significantly.
8. Filament twist pitch <90mm within the wire will help to further reduce inductive
heating and uncouple the filaments.
9. Matrix resistivity between the filaments should not be reduced below at
. In-wire stabilizer should be place on the outside of the filaments.
Further to the above conclusions, following future studies are recommended:
1. Determine the minimum wire to stabilizer electrical and thermal contact resistances
necessary for full current sharing and full transverse thermal diffusion upon thermal
quench.
2. Study the minimum quench energy and quench propagation velocity for the sub-cable
and cables to establish the criterion for quench detection and the identification of
possible quench triggers. Work in this direction has already been done for the SC-Link
proposed for LHC P7 [5].
3. Experimental study and modelling of filaments coupling in MgB2 round wires.
4. Optimize filament architecture and wire configuration to ensure full uncoupling upon
imposed field changes from magnet discharge in neighbouring circuits.
5. Study of the e.m. coupling between the different cables to be sure that there is no
spurious quench signal due to fast dump of a circuit
6.
REFERENCES
[1] A. Ballarino, Development of Superconducting Links for the LHC Machine, EEE/CSC &
ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), October 2013
[2] A. Ballarino, Presentation at 4th LHC Parameters and Layout Committee, 26th March 2013,
https://indico.cern.ch/conferenceDisplay.py?confId=239311
[3] NIST
Cryogenic
Materials
database:
www.cryogenics.nist.gov/MPropsMAY/material%20properties.htm
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THERMAL-ELECTRICAL MODEL OF
HILUMI SC LINKS
Doc. Identifier:
HILUMILHC-WP6 Del-D6_2_final
Date: 23/01/2014
[4] R. L. Powell and F. R. Fickett, Cryogenic Properties of Copper, International Copper
Research Association, Dec. 1979.
[5] J Spurrell, W Bailey, E A Young, A Ballarino, Y Yang, Cryogenic Stability and Quench
Characteristics of Twisted-pair Cables Assemblies of MgB2 tapes, Presented at EUCAS
2013, to be published
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