![](media/image1.png){width="0.9020833333333333in"
height="0.8361111111111111in"} Fermilab

TD-03-024

May 30, 2003

Quench Study on HFDA-03A, (TC1 & TC2), with Consideration on Possible
Relation to Boundary Induced Coupling Currents

Ryuji Yamada

1\. Introduction

At Fermilab we have been working on the Development of Nb~3~Sn High
Field Model Dipole Magnets for the last couple of years. We are doing R
& D to make a model dipole magnet in the field range 10 to 11 Tesla. In
the past year, we tested the cosine theta model magnets HFDA-03 \[1\]
and HFDA-04 \[2\]. They reached roughly the 50 (9700A) and 60 (12000A)
percentage of the short sample data. Both of magnets showed that many of
the quenches started near the power leads.

In order to expedite the investigation and development, we started the
series of mirror magnets. First we made the mirror magnet HFDA-03A,
utilizing one half coil of the existing HFDA-03 magnet \[3\]. Its
magnetic field distribution was calculated and reported \[4\]. Its
magnetic field distributions around the power leads and the magnet ends
are reported separately \[5\].

Most of the quenches of HFDA-03 occurred near leads, so we had some
notion that the cable near the leads might have been damaged
mechanically during handling the cured coil. To investigate this
possibility, an additional pair of leads, which were made of NbTi
Rutherford cable were added 13.5 cm inside from the ends of the existing
old splices in order to bypass that suspected part of the cables. Also
for the purpose of possible current redistribution, a pair of NbTi
Rutherford cables, 14.9 cm long, was soldered on the same median plane
at the return end side of the coil, as shown in Fig 1.

The magnet HFDA-03A was tested on two separate occasions. First the
magnet was excited and tested using the original old splices in December
2002. This series of tests is called Thermal Cycle 1, namely TC-1. The
second series of tests was done in January 2003, and is called Thermal
Cycle 2, namely TC-2. In this case the newly installed NbTi lead cables
were used for the excitation of the coil. The extensive test results on
both TC-1 and TC-2 are reported in another report on many test items,
including Temperature Margin Test, Spot Heater Test, as well as on the
Quench Tests \[6\].

**2. Observation of Precursory Voltage Signals at Soldered Places**

In this note we will report the test results from a little different
viewpoint to investigate the detailed origin of the quenches, mainly to
trying to understand the effects of the supercurrent. The effects
include InterStrand Coupling Current, ISCC, Boundary-Induced coupling
Current, BICC, and InterStrand Coupling Loss, ISCL \[7\]. Also we want
to understand the effect of Splice Joints to the supercurrent and the
quench current value \[8\].

In our quench data files, we observed some precursory voltage signals,
especially at fast ramp rates, ranging from 1 to 20 mV signals across
the new splice at high field or across the soldered NbTi cable piece
also at high field. They are estimated to generate heating power in the
order of 0.1 to 2 Joules. They are preceding a few to 45 ms relative to
the regular normal quench. These voltage signals usually diminish to the
order of 1 mV at the nominal ramp rate of 20 A/sec, but occasionally we
observe the voltage signal at the soldered NbTi cable piece even at 20
A/sec.

Stability of the magnet depends on the supercurrent effects and also on
cryogenic thermal cooling, especially around splice and other soldered
regions. The splice joint is made up by connecting to NbTi cables, which
has a much lower Tc(0) than that of Nb~3~Sn cable. Also we have to be
concerned with the ripple effect in the transport current because the
inductance of the model magnet is much smaller than that of a long
magnet. Although its amplitude is quite small, its frequency is quite
high, in the range of 120 to 720 c/s, and it constantly exists even on
the flattop.

**3. Characteristic Structure of HFDA-03A Magnet from Stand Point of
BICC**

The Nb~3~Sn Rutherford cable is made of 28 strands of 1.000 mm diameter,
made by MJR method by Oxford Superconducting Technology. Its width is
14.24 mm, and the median thickness is 1.8 mm. Its compaction factor is
88 %, and it is keystoned with 1.02 degree angle. The cable has an
annealed 316 stainless steel core, 25 μ thick and 9.5 mm wide, to reduce
the crossing resistance Rc.

The strand has 54 subelements, and each subelement is made by a Nb
sheet, and a copper sheet, rolled up together around a tin core. The Nb
sheet has many vertical short intermittent slots, and is expanded
side-ways to make many filament-like structures before rolling. The
effective size of the filament, deff is about 108 to 115 μ, and the RRR
is rather low and in the range of 4 to15. Therefore the filament
coupling and hysteresis loss are quite high.

The locations of the pair of the **Old (original) set of Splices** and
the **New set of Splices** on the median plane of the HFDA-03A are shown
in Fig.1, together with the added **NbTi Cable Pieces** on the return
end.

In Fig.2, the picture of the new splice joints on the lead end is shown.
The voltage taps across the new inner splice joint for the inner coil
(in the upper portion of the picture) and those across the new outer
splice joint for the outer coil (in the lower portion) are shown. In the
end coil region voltage taps QILE8 and QILE3 can be seen. The voltage
taps on the individual strands, QI1CR, QI7CR, QI14CR, QI21CR, QI28CR,
and QI35CR can be seen soldered and glued down with green patty on the
inside edge of the inner coil median conductor cable (in the lower
portion). In Fig.3, the current shunts, made of NbTi Rutherford cables,
148 mm long, are shown soldered on the top surfaces of the inner and
outer coils at the return end of the magnet. In this picture the voltage
taps across both shunts, and the temperature sensor TS3 at the right end
of the outer shunt can be seen.

In Fig.4, the whole coil of the HFDA-03A mirror magnet is shown before
the instrumentation. At the lower left corner, the original old current
leads are shown under the new NbTi current leads, which are not
insulated yet but soldered to the top surfaces of the Nb3Sn cables. The
original slice joints are solidly epoxied into the end parts of the coil
assembly.

The parameters of the cable along the length of the cable are described
in Table I, together with related parameters of strands, cable and
magnet. The Rc value is described in another report \[9\].

The length of Nb~3~Sn cables between the old and new splices is 13.5 cm,
which is a little over the cable pitch length of 11 cm. The length of
the Old Splice is 14.6 cm. The stainless steel core of the Nb3Sn cable
at the old splice was removed and soldered together with NbTi Rutherford
cable. The length of the new splice is 14.9 cm, which is a little over
the pitch length of the cable. At this splice only the top surface of
the Nb~3~Sn Cable was soldered together with a NbTi Rutherford cable,
because it is not possible to remove the stainless steel core.

At this coil end region, the **boundary conditions of cable for the
supercurrent is quite complicated**. First the old splice is at the low
field region, and is soldered to NbTi lead cable together with top and
bottom layers of the Nb~3~Sn cable. Then there is a cored Nb~3~Sn cable,
**about a cable pitch length, in the high gradient field region**, as
shown in Fig.6. Next is followed the new splice, at high field region,
which are **soldered to the NbTi lead cable at only top layer of the
Nb~3~Sn cable**. This region should be studied for the possible effects
from the Boundary Induced Coupling Currents.

The measured resistances of the splices are as follows, \[6\]

> Inner Coil :
>
> Inner Old Splice : \~1 ± nΩ QISoL2-QLSoL1
>
> Inner New Splice : 2.31 ± 0.03 nΩ QISnL2-QISnL1
>
> Outer Coil:
>
> Outer Old Splice : \~1 ± nΩ QOSoL1-QOSoL2
>
> Outer New Splice : 1.14 ±0.03 nΩ QOSnL2-QOSnL1

**4. Field Distribution**

The field distribution in the straight part of the magnet was calculated
with ROXIE and reported \[4\]. The detailed field distribution in the
cross section of the HFDA-03A is shown in Fig.5 for the currents of 2
and 20 kA.

The field distribution around the lead end was calculated in 3-D, using
TOSCA, and reported in another note \[5\]. The detailed field along the
inner and outer lead is shown in the Fig 3 of the Reference 5, but it is
shown again in Fig. 6, for convenience. It was calculated at 6 kA,
corresponding to the maximum current achieved in the Test Run TC-1. The
field values shown are the peak field \|B\|, regardless of the
orientation and across the width of the cable. The length of the new and
old splices and the distance between them as well, are close to the
pitching length of the cable, which is 11cm.

The field gradient at the new splice region and in the spacing between
the new and old splice regions are very steep, which will tend to
generate unbalancing voltages among the different strand sets. Also, the
new splice cables are soldered only on the top surfaces of Nb3Sn cable,
which will cause more complication from the stand point of BICCs.

**5. Experimental Quench Data**

The experimental setup for quench test is described in another report in
details \[6\]. Its data for the ramp rate study (Fig.2 of Reference 6)
is shown again as Fig. 7. For the data analysis in this report, we are
using the subset of data, but not all of them. With this mirror magnet
two series of tests were done. The first series of test for measuring
quench current using the old splice is called TC-1. The second test
series, TC-2, was done using the new splice, short circuiting the
original old splice joints, suspecting the cables near the original
splice joints might have been mechanically damaged during assembly of
the coils for the previous magnet HFDA-03.

In Fig. 7, the ramp rate dependence of both TC-1 and TC-2 is shown. In
the lower ramp rate region below 140 A/sec, two sets of data are widely
separated. In the TC-1 run, the quench currents are from 6,000 A to
7,000 A, but in the TC-2 run, the quench currents are in the region from
10,000 to12,000 A. We should expect quite different origins for causing
quenches in the TC-1 run and TC-2 run in this ramp rate region. The
experimental quench data are summarized in Table II for the TC-1 run and
in Table III for the TC-2 run.

In the TC-1 run, a short piece of Nb~3~Sn Rutherford cable between the
Inner Original Old Splice and the Inner New Splice are causing quenches.
Its length is about a pitch length of the Rutherford cable, and it is
placed at high gradient field at the magnet end. The length of the New
Splice is also about a cable pitch length, with only the top side of the
cable soldered to a NbTi cable. **This is a perfect condition for
generating BICCs in this region.** In TC-2 run, this cable and the Inner
Old Splice were eliminated. Therefore the quench current went up much
higher, and all of the quenches originated in the Outer Coil.

On the other hand, in the ramp rate region above 150 A/sec, both TC-1
and TC-2 runs show identical behavior, with quench current ranging from
6,000 A down to 4,000 A. In both cases, we see the inner coil regions
start quenches as explained in later chapters.

During ramping up of the current for data taking, the quench data are
being taken continuously in time into a circular disk storage. The power
supply is triggered off when the balanced coil voltage signal exceeds
500 mV. At this time the clock is set to 0.0 seconds. Therefore the real
starting point of a quench is in the negative time region. At this time
of t = 0.0, the power supply is triggered off. But during the fast ramp
rate test runs, the current wave form just before t = 0 already has the
effect of some resistive load due to the quench starting part, and the
nominal ramp rate is reduced. The dump resistor is usually kicked in at
+100 ms for TC-1 runs, and + 25 ms for TC-2 runs.

**5.1. Quench Data of TC-1 using Original Old Splices**

The quench data of the TC-1 run is summarized in Table II. It is
arranged in the descending order of the ramp rate. In the first and
second columns, the regular quench test number and its quench data file
name are given. In the third, fourth, fifth, sixth columns, the nominal
ramp rate, dB/dt, its quench current, and its percentage of the short
sample data are shown.

In major 7^th^, 8^th^, and 9^th^ columns, the voltage signal at the
Inner New Splice, the voltage signal at the Inner Shunt, and the voltage
signal in the cable piece next to the New Splice are given. In the major
10^th^ column, the quench location and quench starting time are given,
when the 0.5 V trigger volt was generated.

The Table II is divided into two groups; one with the ramp rate above
200 A/sec, and the other with the ramp rate below 100 A/sec, because
they show different quench patterns from each other.

1.  **Quench Data of TC-1 with Ramp Rate from 200 to 380 A/sec**

The quench data of this group with the ramp rate of 380 and 200 A/sec
are shown in Fig. 8 and Fig. 9. Quench No.13 (Fig.8) with a ramp rate of
380 A/sec case shows a voltage signal at the Inner Shunt at t = -45 ms,
and also another voltage signal at the Inner New Splice at t = -40 ms.
These voltage signals are estimated to deposit about 0.8 J and 1.5 J at
their locations. These energy deposits can be considered big enough to
start quenches at these points, but due to the fairly large heat
capacitance of these parts and due to the well cooled outside surface,
the next adjacent cable parts under these soldered and heated places may
be starting to quench. (This needs a simulation to be verified.) Another
possibility is that BICCs may cause heating of cable at some other weak
spots, like at the magnet end. Actually **the triggering** **quench is
observed starting in and propagating in, QILE8-QI1CR, the Inner Coil of
2^nd^ and 3^rd^ turns and the one half turn of the 1^st^ coil, at t =
-25 ms**, which is 20 and 15 ms later than the voltage signals. The
cable parts next to these soldered places are not propagating quenches
in this event. The voltage drop at t = 0 in QILE8-QI1CR, the part of the
inner coil, is due to the inductive reaction to the sudden current drop
in the current as shown. The quench in QILE8-QI1CR is propagating
continuously through t = 0 transition time region to the end of t = +100
ms.

In Quench No.14 with a ramp rate of 200A/sec, only the Inner New Splice
shows the voltage signal, which persists all the way to the end. There
is no signal at the Inner Shunt. The cable parts on both side of the
Inner New Splice show quenching signals at later stage.

**5.1.2. Quench Data of TC-1 with Ramp Rate from 5 to 100 A/sec**

In this ramp rate range the data of Quench No.15 (RR of 100), and Quench
No.4 (RR of 5) are shown in Fig. 10 and Fig.11. There are no clear
voltage signals at both New Splices and Shunts. But the **short Cable,
QISnL1-QISol2**, which is **between two Inner Splices, starts a normal
quench and completes a quench propagation cycle**, as shown in these
pictures.

This phenomenon of spontaneous quenching in the cable, not at any
soldered parts seems caused by BICCs due to the complicated boundary
condition in this region. It seems to be not due to any mechanical
damage in the local cable. It is probably due to Electro-Magnetic
Phenomenon.

In both cases, during the current decay, a quench is started at t = +79
ms in QILE8-QI1CR, the Inner Coil part, containing the 2^nd^ and 3^rd^
turns of the Inner Coil. It seems the excessive heating at the short
Cable between two Inner Splices, caused lateral quench propagation to
the underlining 2^nd^ turn cable through the insulation.

2.  **Quench Data of TC-2 using New Splices**

The quench data of the TC-2 run is summarized in Table III. It is
arranged in the descending order of the ramp rate. It is divided into
two major parts; one with the ramp rate above 150 A/sec, and the other
below 140 A/sec.

**5.2.1.** **Quench Data of TC-2 with Ramp Rate from 150 to 300 A/sec**

The data for this ramp rate are shown in Fig. 12, 13, 14, and 15,
corresponding to 300, 200,175, and 150 A/sec. As summarized in the Table
III, we can observe voltage signals either at the Inner New Splice or at
the Inner Shunt, from a clear 10 mV signal and getting smaller down to 1
mV. Then the QILE8-QI1CR, the 2^nd^ and 3^rd^ turns of the Inner Coil
starts quenching.

The higher the ramp rate, the lower the quench current. The higher the
ramp rate, the bigger the voltage signal. These facts can be interpreted
that the amplitude of BICCs is getting smaller with a slower ramp rate.

**5.2.2.** **Quench Data of TC-2 with Ramp Rate from 2 to 140 A/sec**

The quench currents Iq in this ramp rate range drastically increase
above10,000 A, up to 11,700 A. This Iq range is twice as high as the Iq
range for the previous group at ramp rates higher than 150 A/sec. The Iq
values at slow ramp rates are practically it is flat. The very sharp
change in Iq for the ramp rate change from 140 to 150 A/sec should be
noticed with care.

In this ramp rate of TC-2 run, the Iq value increased almost twice
compared with the case of TC-1 run. This means the elimination of the
Original Old Splice, and subsequently the elimination of the Short Cable
Piece of a twist pitch length at the high gradient field, helped to
increase the Iq values.

As summarized in the lower part of Table III, in this ramp rate of TC-2,
all the quenches are in the Outer Coil, QOSR1-QIOLE1. As we do not have
other voltage taps on the Outer Coil, we could not pinpoint the origin
points of the quenches. But as we observe small voltage signal, in the
order of 1 to 2 mV, at the Outer Shunt at the beginning time of regular
quenches in the outer coil, we may be able to assume the regular
quenches start from the edge of the Outer Splice.

**6. Improvement of Splice Design**

The design of the splice should be improved. The spice should be placed
as far away from the body of the magnet for two reasons. The better
cooling of splice region is accomplished by extending it out into the
liquid Helium region, and the splice should be put far away from the
magnetic field of the coil.

The splice should be made by sandwiching the Nb~3~Sn cable with two NbTi
cables and covered with Copper box as a heat sink. The splice region
should be well cooled directly with liquid Helium, and we should avoid
Helium vapor gas being trapped.

The splice is made by soldering together the Nb~3~Sn cable and NbTi
cables. Its critical temperature is determined by the Tc of NbTi cable,
not by the critical temperature of Nb~3~Sn. The critical temperature of
the NbTi is given by,

Tc(B) = Tc(0) \[ 1- (B/14.5)\] ^0.59^,

where Tc(0) is about 9.4 K at B = 0, J = 0 for NbTi. If B is not zero,
Tc(1) = 9.0 K, Tc(3) = 8.2 K, Tc(6) = 6.8 K, Tc(10) = 4.7 K. Therefore
it is better to keep the splice as far away from the body of the magnet.

By separating away the splice region from the magnet coil region, the
temperature margin of the coil itself can be determined by the Tc of the
Nb~3~Sn itself. It is given by,

Tc(B) = Tc(0) \[ 1 -- (B/26)\] ^0.59^,

where Tc(0) is18 K at B = 0, J = 0, Bc2(0) = 26 for Oxford MJR Nb~3~Sn.
If B is not zero, Tc(1) = 17.6 K, Tc(3) = 16.7 K and Tc(5) = 15.9 K.

**7. Other Problems**

We have to consider the effect of the current ripple. Because the
inductance of the short model magnet is very low, in the order of 1 mH,
there are current ripple as can be seen in Fig.16. It has a basic 120 Hz
component with the amplitude of ±3 A. There are eddy current loss and
Hysteresis loss, and the ripple is inducing noises in all signals, as
can be seen in Fig.16.

The present strand has a large deff in the order of 120 μ, and very low
RRR in the order of 5 to 15. They have to be improved.

8\. Summary

As long as we are using Rutherford cables to make superconducting
magnets, we cannot avoid the effects of InterStrand Coupling Currents
and Boundary Induced Coupling Currents. Therefore we should reduce the
causes of creating bad boundary conditions as much as possible to reduce
the effect of them. For instance, we should avoid any soldered splice
joints and shunts as much as possible. They especially should not be
placed in high magnetic field nor in high gradient field region. If
necessary they should be placed away from the magnet body as far away as
possible.

Comparing the data of TC-1 and TC-2, definitely the elimination of the
short cable pieces together with the original old splice joints helped
to increase the Iq value by a factor of 2 at slow ramp rate. The short
cable piece is always quenching at slow ramp rate in TC-1.

Even in the setup of TC-2, the New Splice Joints and Shunts are in the
high field region. Without them in the high field region, we could have
gone to higher Iq values because the quench may be occurring in the coil
region next to the outer Shunt. We do not need Shunts.

It seems realized that, at high ramp rate, the effect of the BICC is
enhanced. With higher supercurrents, it generates more heat at the
soldered splice joints and shunts, and initiating the regular quenches,
which are manifested by the precursory voltage signals. These voltage
signals are reduced with the slower ramp rate, but still the
supercurrent should be there with reduced magnitude. We are not yet in
the current region, where the n-value matters.

At present stage, the problem of these ISCC and BICC boils down to the
problem of thermal balance between the heating due to these coupling
currents and cooling by the coil structure, namely to the problem of
cryostability. We should try to make the splice joint, which contains a
NbTi cable, to be away from the coil body and well cooled with liquid
Helium. The Nb~3~Sn cable is completely epoxied, and does not have space
to be permeated with liquid He, like NbTi cable. This will make a
difference for the cooling and for supercurrent, even though the Hc2
value is higher.

References:

\[1\] D.R. Chichili et.al., "Nb~3~Sn Cos(θ) Dipole Magnet, HFDA-03
Production Report", TD-01-064, September 5, 2001.

\[2\] D.R. Chichili et.al., "Nb~3~Sn Cos(θ) Dipole Magnet, HFDA-04
Production Report", TD-02-025, May15, 2002.

\[3\] D. Chichili, "Mechanical Design and Analysis of Mirror Magnet for
Shell-Type HFM Dipole Coils", TD-03-xxx, 2003.

\[4\] V.V. Kahskin, A.V. Zlobin, "Magnetic Design of Mirror Magnet Based
on Fermilab's Nb~3~Sn Cos-theta Coils. TD-02-045. December 9, 2002.

\[5\] V.V. Kashikin A.V. Zlobin, "Magnetic analysis of the splice fields
in HFDA magnets", TD-03-010, March 27, 2003.

\[6\] S. Feher et.al., "HFDA-03A Test Summary", TD-03-015, April 7,
2003.

\[7\] A.P. Verweij, "Electrodynamics of Superconducting Cables in
Accelerator magnets", Thesis, 1995.

\[8\] M. Breschi, M. Fabbri, F. Negrini, P.L. Ribani, "Coupling of Cable
and Joint/Termination Models for the Electromagnetic Analysis of
Superconducting Cables" to be published in the proceeding of ASC2002.

\[9\] B. Kasper, G. Ambrosio, P. Bauer, L. Imbasciati, "Interstand
Resistance measurements in Nb3Sn Rutherford-type Cable", TD-02-039,
September 26, 2002.

  ---------- -------------- ---------------- -- ---------- ------------ ------------ ------- ---------- ------------ ----- --------- ------------ --------
  **TABLE I                                                Parameters   3/25/2003            R.Yamada                                             
  HFDA-03M                                                                                                                                        
  Cable**                                                                                                                                         

                                                material   dia mm       strands      twist   core       Rc           Ra                           
                                                                                     pitch                                                        

  **Power                                       NbTi       0.8          36           0.11 m  no                                      inner coil   3+5+3
  Lead                                                                                                                                            turns
  Cable**                                                                                                                                         

  **Coil                                        Nb3Sn      1            28           0.11 m  25 µ SS    100 µ ?      1.8 µ           outer coil   6+5+2
  Cable**                                                                                                                                         turns

  **R of a                                                 10 nΩ on                                                                               
  strand in                                                both ends of                                                                           
  soldered                                                 a strand,                                                                              
  joint**                                                  total 20 nΩ                                                                            
                                                           per strand                                                                             
                                                           (Guess for a                                                                           
                                                           strand)                                                                                

                                                                                                                                                  

             **distance**   **Connection**      **old      **coil       **solder**           **new      **solder**         **lead    **solder**   
                                                lead**     cable**                           lead**                        strip**                

             in meter                                                                                                                             

  -2         -0.9                               lead                    **solder**           lead       **solder**                                

  -1         -0.75                              lead                    **solder**           lead       **solder**                                

  -1         -0.75                              lead                                         lead                                                 

  0          0              **Old Splice**      lead       cable no     **solder**           lead                                                 old
                                                           core                                                                                   splice
                                                                                                                                                  starts

  1          0.146          **Old Splice**      lead       cable no     **solder**           lead                                                 inner
                                                           core                                                                                   coil
                                                                                                                                                  starts

  1          0.146                                         cable                             lead                                                 

  2          0.281          **New Splice**                 cable        **solder             lead       **solder**                                
                                                                        top**                                                                     

  3          0.429          **New Splice**                 cable        **solder             lead       **solder**                                
                                                                        top**                                                                     

  4          0.674                                         cable                                                                                  

  5          0.73                                          cable                                                                                  

  6          0.874          **NbTi Strip**                 cable        **solder                                           lead      **solder**   
                                                                        top**                                              strip                  

  7          1.023          **NbTi Strip**                 cable        **solder                                           lead      **solder**   
                                                                        top**                                              strip                  

  8          1.698                                         cable                                                                                  

  9          1.754                                         cable                                                                                  

  10         5.887                                         cable                                                                                  

  11         14.358                                        cable                                                                                  

  12         17.381                                        cable                                                                                  inner
                                                                                                                                                  coil
                                                                                                                                                  ends

  12         17.381                                        cable                                                                                  outer
                                                                                                                                                  coil
                                                                                                                                                  starts

  13         41.14          **NbTi Strip**                 cable        **solder                                           lead      **solder**   
                                                                        top**                                              strip                  

  14         41.29          **NbTi Strip**                 cable        **solder                                           lead      **solder**   
                                                                        top**                                              strip                  

  14         41.29                                         cable                                                                                  

  15         41.72          **New Splice**                 cable        **solder             lead       **solder**                                
                                                                        top**                                                                     

  16         41.87          **New Splice**                 cable        **solder             lead       **solder**                                
                                                                        top**                                                                     

  16         41.87                                         cable                             lead                                                 

  17         42             **Old Splice**      lead       cable no     **solder**           lead                                                 outer
                                                           core                                                                                   coil
                                                                                                                                                  ends

  18         42.15          **Old Splice**      lead       cable no     **solder**           lead                                                 old
                                                           core                                                                                   splice
                                                                                                                                                  ends

  18         42.15                              lead                                         lead                                                 

  19         42.9                               lead                    **solder**           lead       **solder**                                

  20         43.05                              lead                    **solder**           lead       **solder**                                
  ---------- -------------- ---------------- -- ---------- ------------ ------------ ------- ---------- ------------ ----- --------- ------------ --------

  ----------------------------------------- ----------------------------- ---- ---- ---- ---- -- ---------- ---- ---- ---- ---- ---- ---- ---- ---- -----------
                                            **TABLE II TC-1 Quench Data**                        Thermal                                            5/23/2003
                                                                                                 Cycle 1                                            
                                                                                                 data of                                            
                                                                                                 HFDA-03A                                           
                                                                                                 Mirror                                             
                                                                                                 Magnet.                                            
                                                                                                 Data taken                                         
                                                                                                 in Dec.                                            
                                                                                                 2002                                               

                                            **of HFDA-03A**                                                                                         

                                                                                                                                                    

  mdtf35:/vmtf/data/Quench/vmtf_1.fhda03a                                                                                                           
  NN\>                                                                                                                                              

                                            quenchXmgr                                                                                              
                                            hfda03a.Quench.\"0212File\"                                                                             

                                                                                                                                                    
  ----------------------------------------- ----------------------------- ---- ---- ---- ---- -- ---------- ---- ---- ---- ---- ---- ---- ---- ---- -----------

  ----------- --------------------------------------- ----------------------- ----------------- --------------------- ------------------- ---- ----------------------------- --------------------- --------------- --------------------------- ----------------------- ------------- --------------------------------- ----------------------- ----------------------------------------- -----------------
                                                      **Ramp**                                                                                                                                                                                                                                                                                                                           

  Q \#        02-12-File                              **Rate**                dB/dt             **Iq**                \% of                    **In Spl Vol**                                                      **In Sld Vol**                                                    **Cbl next**                                              **Quench Loc.**                           Start at

                                                      **A/sec**               T/sec             **A**                 SS                       **start at**                  **mV**                                **start at**                **mV**                                **to In Spl**                                             to 0.5V                                   

                                                                                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                                                                                                                                         

  13          18180930.62                             **380**                 0.19              **3689**              18.82                    **-40 ms**                    **14mVp**                             **-45ms**                   **7mVp**                              **none**                                                  **ILE8-I1CR**                             -25 ms

                                                                                                                                               3.8µΩp                        51Wp                  1.5 J           1.9µΩp                      26Wp                    0.8J                                                                                                              

                                                                                                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                                                                                                                                     **to In Spl**                                                                                       

  14          18182827.43                             **200**                 0.1               **4786**              24.42                    **-22 ms**                    **20mVp**                                                         **0**                                 **Del Q at +71ms**                                        **ILE8-I1CR**                             -13 ms

                                                                                                                                                                             Vp at -11ms                                                                                                                                                                                                 

  \-\-\-\--   \-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--   **\-\-\-\-\-\-\-\--**   \-\-\-\-\-\-\--   **\-\-\-\-\-\-\--**   \-\-\-\-\-\-\-\--   \-   \-\-\-\-\-\-\-\-\-\-\-\-\--   \-\-\-\-\-\-\-\-\--   \-\-\-\-\-\--   \-\-\-\-\-\-\-\-\-\-\-\--   **\-\-\-\-\-\-\-\--**   \-\-\-\-\--   **\-\-\-\-\-\-\-\-\-\-\-\-\--**   \-\-\-\-\-\-\-\-\-\--   **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--**   \-\-\-\-\-\-\--

                                                                                                                                                                                                                                                                                     **Cbl btwn 2 Inn Splices**                                                                          

  15          18184511.84                             **100**                 0.05              **6501**              33.17                                                  **0**                                                             **0**                                 **-13 ms**                                                **ISnL1-ISoL2**                           -13 ms

                                                                                                                                                                                                                                                                                                                                               Perfect Q propaga.                        

                                                                                                                                                                                                                                                                                     **Cbl btwn 2 In**                 **n Splices**                                                     

  1           17185124.48                             **20**                  0.01              **6189**              31.58                                                  **0**                                                             **0**                                 **-15 ms**                                                **IsnL1-IsoL2**                           -15 ms

                                                                                                                                                                                                                                                                                                                                               Perfect Q propaga.                        

                                                                                                                                                                                                                                                                                     **Cbl btwn 2 Inn Splices**                                                                          

  4           17200528.38                             **5**                   0.003             **6063**              30.93                                                  **0**                                                             **0**                                 **-14.4 ms**                                              **ISnL1-ISoL2**                           -14.4ms

                                                                                                                                                                                                                                                                                                                                               Perfect Q propaga.                        
  ----------- --------------------------------------- ----------------------- ----------------- --------------------- ------------------- ---- ----------------------------- --------------------- --------------- --------------------------- ----------------------- ------------- --------------------------------- ----------------------- ----------------------------------------- -----------------

<table style="width:100%;">
<colgroup>
<col style="width: 3%" />
<col style="width: 10%" />
<col style="width: 5%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 3%" />
<col style="width: 2%" />
<col style="width: 9%" />
<col style="width: 4%" />
<col style="width: 4%" />
<col style="width: 6%" />
<col style="width: 9%" />
<col style="width: 1%" />
<col style="width: 10%" />
<col style="width: 5%" />
<col style="width: 8%" />
<col style="width: 5%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td colspan="5"><strong>TABLE III TC-2 Quench Data</strong></td>
<td></td>
<td></td>
<td colspan="8">HFDA-03A Mirror Magnet, Thermal Cycle 2 Data taken in
January 2003</td>
<td>5/29/03</td>
</tr>
<tr class="even">
<td></td>
<td colspan="5"><strong>of HFDA-03A</strong></td>
<td></td>
<td></td>
<td colspan="8"></td>
<td></td>
</tr>
<tr class="odd">
<td colspan="11">mdtf35:/vmtf/data/Quench/vmtf_1.fhda03a NN&gt;
quenchXmgr hfda03a.Quench."0301+File"</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td><strong>Ramp</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>Q #</td>
<td>0301+File</td>
<td><strong>Rate</strong></td>
<td>dB/dt</td>
<td><strong>Iq</strong></td>
<td>% of</td>
<td></td>
<td colspan="2"><strong>In Spl Vol</strong></td>
<td></td>
<td colspan="2"><strong>In Shunt Vol</strong></td>
<td></td>
<td><strong>Cbl next</strong></td>
<td></td>
<td colspan="2"><strong>Quench start</strong></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td><strong>A/sec</strong></td>
<td>T/sec</td>
<td><strong>A</strong></td>
<td>SS</td>
<td></td>
<td><strong>start at</strong></td>
<td><strong>mV</strong></td>
<td></td>
<td><strong>start at</strong></td>
<td><strong>mV</strong></td>
<td></td>
<td><strong>to In Spl</strong></td>
<td></td>
<td>to 0.5V</td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>9</td>
<td>21213603.63</td>
<td><strong>300</strong></td>
<td>0.15</td>
<td><strong>3720</strong></td>
<td>19</td>
<td></td>
<td><strong>-45 ms</strong></td>
<td><strong>3 mV</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-45ms</strong></td>
<td><strong>-5 mV</strong></td>
<td><strong>ILE8-I1CR</strong></td>
<td>-30 ms</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>0.8 µΩ</td>
<td>11W</td>
<td>0.4 J</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>10</td>
<td>21220131.91</td>
<td><strong>200</strong></td>
<td>0.1</td>
<td><strong>4695</strong></td>
<td>24</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-34 ms</strong></td>
<td><strong>10 mV</strong></td>
<td></td>
<td></td>
<td></td>
<td><strong>ILE8-I1CR</strong></td>
<td>-22 ms</td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>2.1 µΩ</td>
<td>47 W 1.7J</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td colspan="2"><strong>Cbl next In Spl</strong></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>20</td>
<td>24151439.35</td>
<td><strong>175</strong></td>
<td>0.088</td>
<td><strong>5142</strong></td>
<td>26.2</td>
<td></td>
<td><strong>-25 ms</strong></td>
<td colspan="2"><strong>2 mVp</strong></td>
<td><strong>-14 ms</strong></td>
<td><strong>1mVp</strong></td>
<td></td>
<td><strong>-25 ms</strong></td>
<td></td>
<td><strong>ILE8-ISR2</strong></td>
<td>-14 ms</td>
</tr>
<tr class="even">
<td></td>
<td colspan="6">(with a Recovered Jump at -440ms, 5050A)</td>
<td>0.4 µΩ</td>
<td>10Wp</td>
<td>0.13J</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td colspan="2"><strong>Cbl next In Spl</strong></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>14</td>
<td>22160607.25</td>
<td><strong>150</strong></td>
<td>0.075</td>
<td><strong>5799</strong></td>
<td>29.6</td>
<td></td>
<td><strong>-20 ms</strong></td>
<td><strong>1 mV</strong></td>
<td></td>
<td><strong>-10 ms</strong></td>
<td><strong>1mVp</strong></td>
<td></td>
<td><strong>-20 ms</strong></td>
<td><strong>7.5 mV</strong></td>
<td><strong>ILE8-ISR2</strong></td>
<td>-10 ms</td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>0.17µΩ</td>
<td>5.8W</td>
<td>0.1J</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>18</td>
<td>24110615.83</td>
<td><strong>150</strong></td>
<td>0.075</td>
<td><strong>6345</strong></td>
<td>32.4</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>----</td>
<td>------------------</td>
<td>--------</td>
<td>--------</td>
<td><strong>-------------</strong></td>
<td><strong>-------------------</strong></td>
<td>--</td>
<td><strong>---------------------</strong></td>
<td><strong>----------</strong></td>
<td><strong>------------------</strong></td>
<td>-----------</td>
</tr>
<tr class="even">
<td>------</td>
<td>--------------------</td>
<td><strong>-----------</strong></td>
<td>---------</td>
<td><strong>---------</strong></td>
<td>------</td>
<td>----</td>
<td>------------------</td>
<td>--------</td>
<td>--------</td>
<td><strong>-------------</strong></td>
<td><strong>-------------------</strong></td>
<td></td>
<td><strong>Cbl OSpl-O</strong></td>
<td><strong>Shunt</strong></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>17</td>
<td>23212333.27</td>
<td><strong>140</strong></td>
<td>0.07</td>
<td><strong>11152</strong></td>
<td>56.9</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-3 ms</strong></td>
<td><strong>-5 mV</strong></td>
<td><strong>OSR1-IOLE1</strong></td>
<td>-2 ms</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td colspan="2"><strong>Cbl next to In Spl</strong></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-3 ms</strong></td>
<td><strong>-5 mV</strong></td>
<td><strong>Ish1a-ISnL2</strong></td>
<td></td>
</tr>
<tr class="even">
<td>16</td>
<td>23114649.75</td>
<td><strong>125</strong></td>
<td>0.063</td>
<td><strong>10032</strong></td>
<td>51.2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>11</td>
<td>22132928.23</td>
<td><strong>100</strong></td>
<td>0.05</td>
<td><strong>10597</strong></td>
<td>54.1</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td>12</td>
<td>22151703.09</td>
<td><strong>100</strong></td>
<td>0.05</td>
<td><strong>11538</strong></td>
<td>58.9</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>13</td>
<td>22154223.89</td>
<td><strong>50</strong></td>
<td>0.025</td>
<td><strong>11015</strong></td>
<td>56.2</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><h3 id="out-spl-vol">Out Spl Vol</h3></td>
<td></td>
<td></td>
<td colspan="2"><strong>Out Shunt Vol</strong></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>1</td>
<td>21162246.34</td>
<td><strong>20</strong></td>
<td>0.01</td>
<td><strong>11625</strong></td>
<td>59.3</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-1.2 ms</strong></td>
<td colspan="3"><strong>1.5mV at 0ms</strong></td>
<td></td>
<td><strong>OSR1-IOLE1</strong></td>
<td>-1.2 ms</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td>20mV at17ms</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>3</td>
<td>21172729.54</td>
<td><strong>20</strong></td>
<td>0.01</td>
<td><strong>11657</strong></td>
<td>59.5</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-1.0 ms</strong></td>
<td><strong>1mV at 0ms</strong></td>
<td></td>
<td></td>
<td></td>
<td><strong>OSR1-IOLE1</strong></td>
<td>-1.8 ms</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>6</td>
<td>21190443.92</td>
<td><strong>20</strong></td>
<td>0.01</td>
<td><strong>11720</strong></td>
<td>59.8</td>
<td></td>
<td></td>
<td></td>
<td></td>
<td><strong>-2 ms</strong></td>
<td><strong>1.7mV at 0ms</strong></td>
<td></td>
<td></td>
<td></td>
<td><strong>OSR!-IOLE1</strong></td>
<td>-1.7 ms</td>
</tr>
<tr class="even">
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td></td>
<td colspan="2"></td>
<td></td>
<td></td>
</tr>
<tr class="odd">
<td>8</td>
<td>21201546.6</td>
<td><strong>2</strong></td>
<td>0.001</td>
<td><strong>11292</strong></td>
<td>57.6</td>
<td></td>
<td><strong>-1.5ms 3mVp</strong></td>
<td></td>
<td></td>
<td><strong>-1.8 ms</strong></td>
<td><strong>1mV at 0 ms</strong></td>
<td></td>
<td></td>
<td></td>
<td><strong>OSR1-IOLE1</strong></td>
<td>-1.8 ms</td>
</tr>
</tbody>
</table>

Fig. 1. Layout of Splices and Instrumentation of Mirror Magnet
HFDA-03A![](media/image2.png){width="9.0in"
height="5.895833333333333in"}

![](media/image3.jpeg){width="4.375in" height="3.3652777777777776in"}

Fig. 4. Coil of Mirror Magnet HFDA-03A

> The coil with original old and new splices and shunts are shown before
> installation of instrumentation. Under the new splice cables, which
> are not yet covered with Kapton tape, the original splice cables are
> seen at the far left ends.

![](media/image5.jpeg){width="7.625in" height="5.722222222222222in"}

![](media/image6.png){width="6.5in" height="3.00625in"}Fig. 5. Field
distribution in the mirror magnet HFDA-03A at two different currents. I
= 2kA on the left, and I = 20 kA on the right.

Fig. 6. Peak field distributions along the lead cables of the mirror
magnet HFDA-03A at 6 kA for the inner and outer cables. The regions of
the original old splices and the new splices are shown.

Fig. 7. Ramp rate dependence of mirror magnet HFDA-03A. In the first
thermal cycle TC-1 (with triangle marks), the magnet was excited with
the original splices. In the second thermal cycle TC-2 (with diamond
marks) it was operated with the newly added splices. Both runs were
tested at 4.45K.

![](media/image8.wmf){width="6.46875in" height="5.625in"}

![](media/image9.png){width="6.501388888888889in"
height="5.309722222222222in"}

Fig. 8. **Quench No. 13 of TC-1**. The highest **Ramp Rate of 380
A/sec** of TC-1. **Iq = 3689 A**.

**The part of inner coil, QILE8-QI1CR** **(black line)**, the 2^nd^ and
3^rd^ turns from the median plane, starts quenching at --25 ms. When its
voltage grows to 0.5 V, it turns off the power supply. Its quench
voltage is still growing due to the quench propagation, but at t = 0,
its voltage is shifted down inductively due to the rapid decaying
current at the rate of --9,500 A/sec. From the voltage drop of 0.45 V,
the effective inductance of that part of the coil is estimated 0.047 mH.

Before the coil starts quenching, **a voltage signal of 7 mV peak** is
generated at the **Inner Shunt, QISR2-QISR1** **(green line)**, at --45
ms. And **another voltage signal of 14 mV peak,** at the **Inner New
Splice, QISnL2-QISnL1** **(red line),** shows up **at --40 ms**. These
voltages are not due to the simple eddy current effect, because they are
not increased beyond t = 0, where the value of \|dB/dt\| is 25 times
higher. These voltage signals may be due to BICCs.

There is no quench voltage signal propagating directly from these parts
to the 2^nd^ and 3^rd^ turns on the inner coil. There is a possibility
that the Nb3Sn cable part just under the inner new splice was heated up
due to heating of the inner new splice. The quench of the inner coil
starts 15 ms later from the start of signal at the inner new splice, and
at its peak voltage.

![](media/image10.png){width="6.486111111111111in"
height="6.876388888888889in"}

Fig.9. **Quench No.14 of TC-1** at the **ramp rate of 200 A/sec**. **Iq
= 4786 A**. **A voltage signal of 20 mV** **peak** shows up at the
**Inner New Splice, QISnL2-QISnL1 (red line),** at --22 ms. This voltage
signal diminishes after t = 0, but it lingers to the end. At --13 ms,
which corresponds to the peak time of the **Inner New Splice, the 2^nd^
and 3^rd^ Turns of the Inner Coil, QILE8-QI1CR** **(black line),**
starts to quench.

In this quench, there is no voltage signal at the Inner Shunt (brown
line). The cable part (green line) next to the Inner New Splice quenches
at +72 ms, and the cable (blue line) between the Inner New Splice and
the Inner Old Splice quenches at +93 ms.

![](media/image11.png){width="6.497916666666667in"
height="6.374305555555556in"}

Fig. 10. **Quench No. 15** **of TC-1** at the Ramp Rate of **100
A/sec**. **Ic = 6501 A**.

The quench starts at the **short** **Cable piece, QISnL1-QISoL2 (black
line)**, **between the Inner Old Splice and Inner New Splice** at --13
ms. Its voltage grows to 0.5 V at t = 0 sec, triggering off the power
supply. Its voltage signal shows a **complete quench cycle** during
whole current decay cycle. There is no kink in this voltage signal at t
= 0 because it is a short Cable piece and not an inductive coil.

There is no significant voltage signal in the Inner New Splice (red
line), Inner Shunt (blue line), nor in the cable (green line) next to
the Inner New Splice.

The **2^nd^ and 3^rd^ turns of the Inner Coil, QILE8-QI1CR** **(brown
line)** starts to quench at t = +69 ms. This may be caused due to the
heat transmission from **QISnL1-QISoL2 (black line) to its underlining
Inner 2^nd^ turn cable part.**

![](media/image12.png){width="6.486111111111111in"
height="6.497916666666667in"}

Fig. 11. **Quench No. 4** **of TC-1** at the slowest Ramp Rate of **5
A/sec**. **Iq = 6063 A**. The ramp rate was 20 A/sec up to 6000 A, then
5 A/sec until the magnet quenched.

The **short cable piece, QISnL1-QISoL2 (red line), between the Inner Old
Splice and Inner New Splice**, where the field gradient dB/dz is highest
due to the magnet end, starts to quench at t = -14.4 ms. Its voltage
signal goes up to 0.5 V at t = 0 sec, triggering off the power supply,
and shows a complete quench cycle.

There is no significant voltage signal in the Inner New Splice, (green
line), Inner Shunt, (brown line), nor in the cable (blue line) next to
the Inner New Splice.

The **2^nd^ and 3^rd^ turns of the Inner Coil, QILE8-QI1CR**, (black
line) starts to quench at t = +69 ms. This may be caused due to the heat
transmission from **QISnL1-QISol1 to its underlining Inner 2^nd^ turn
cable part.**

![](media/image13.png){width="6.486111111111111in"
height="5.753472222222222in"}

Fig.12. **Quench No. 9** **of TC-2** with the fastest ramp rate of **300
A/sec**. **Iq = 3720 A**.

A **voltage signal of 3 mV peak** appears at the **Inner New Splice,
QISnL2-QISnL1** (red line), at **t = -45 ms**. There is no voltage
signal in Inner Shunt, but there is a **1.5 mV voltage pulse at** **t =
-30 ms** in the cable piece, **QISR1-QIsh1b (blue line)**, next to the
Inner Shunt toward the Inner New Splice.

**The part of inner coil, QILE8-QI1CR** (black line), the 2^nd^ and
3^rd^ turns from the median plane, starts quenching **at --30 ms**. The
quench of the Inner Coil starts 15 ms later from the start of voltage
signal at the Inner New Splice, and at its peak voltage. When the coil
voltage grows to 0.5 V, it turns off the power supply. Its quench
voltage is still growing due to the quench propagation, but at t = 0,
its voltage is inductively shifted down due to the rapid decaying
current at the rate of --10,160 A/sec.

The current I is shown as V1_Cu (purple line), and its ripple can be
seen, which is ±2 A peak at 120 cycle. The noise in the coil voltage
shows the pattern of the ripple.

![](media/image14.png){width="6.497916666666667in"
height="6.624305555555556in"}

Fig. 13. **Quench No. 10 of TC-2** with the ramp rate of **200 A/sec**.
**Iq = 4695 A**.

At this ramp rate **the part of Inner Coil, QILE8-QI1CR** (black line),
the 2^nd^ and 3^rd^ turns from the median plane, starts quenching **at
--22 ms**.

In this case, there is no voltage signal in the Inner New Splice (red
line) in contrast of the previous case with a ramp rate of 300 A/sec.
But there is much stronger voltage signal, **10 mV peak, starting at
--34 ms**, in the **Inner Shunt, QISR2-QISR1** (green line). The quench
of the Inner Coil starts 12 ms later than the starting time of the
voltage signal at the Inner Splice, corresponding to its peak voltage.

![](media/image15.png){width="6.498611111111111in"
height="6.127777777777778in"}

Fig. 14. **Quench No. 20** **of TC-2** with a ramp rate of **175
A/sec**. **Iq = 5142 A**.

At this ramp rate, a **voltage signal of 2 mV peak** shows up first at
the **Inner New Splice, QISnL2-QISnL1** (green line), **at --25 ms**.
Also the **Inner Shunt, QISR2-QISR1** (blue line), starts a voltage
signal **at --14 ms**.

**At --14 ms**, **the part of Inner Coil, QILE8-QI1CR (red line),** the
2^nd^ and 3^rd^ turns from the median plane, starts quenching. Also the
voltage signal, **QILE8-QISR2 (black line)**, the 2^nd^ and 3^rd^ turns
plus half of the 1^st^ turn, is shown. It shows a similar voltage shape
to the former one.

The ramp rate is practically at 175 A/sec up to t = -22 ms. From t = -22
ms to 0 ms, the ramp rate is about -50 A/sec. During the current decay,
the ramp rate is --13,300 A/sec from t = 0.005 to 0.025 sec.

![](media/image16.png){width="6.495833333333334in"
height="6.377777777777778in"}

Fig. 15. **Quench No. 14** **of TC-2** with a ramp rate of **150
A/sec**. **Iq = 5799 A**.

This Quench event is quite similar to Quench No. 20 with a ramp rate of
175 A/sec.

At this ramp rate of 150 A/sec, a **voltage signal of 1 mV peak** shows
up first at the **Inner New Splice, QISnL2-QISnL1** **(blue line)** **at
--20 ms**. Also the **Inner Shunt, QISR2-QISR1** **(purple line)**,
starts a voltage signal of 1 mV **at --10 ms**.

**At t = -10 ms**, **the part of Inner Coil, QILE8-QI1CR** **(red
line)**, the 2^nd^ and 3^rd^ turns from the median plane, starts
quenching. At t = 0, it gets about --0.4 V inductive voltage. Also the
more inclusive Inner Coil, QILE8-QISR2 (black line), the 2^nd^ and 3^rd^
turns plus half of the 1^st^ turn shows a similar voltage shape to the
former one.

![](media/image17.png){width="6.498611111111111in"
height="5.997222222222222in"}

Fig. 16. **Quench No. 17** **of TC-2** with a ramp rate of **140
A/sec**. **Iq = 11,152 A**.

Quench voltage pattern changes drastically in the ramp rate region from
140 to 150 A/sec. Above 150 A/sec, the Inner Coil quenches, but below
140A/sec the Outer Coil quenches, and Iq goes above 10,000 and up to
11,720 A.

The **Outer Coil, QOSR1-QIOLE1** (black line), **starts quench at t = -2
ms**, triggering off the power supply at t = 0 ms, and the quench is
propagating beyond t = 0 ms. It gets about --7V inductive voltage. The
**Outer Shunt**, **QOSR2-QOSR1** (blue line), **may have a small voltage
signal, about 1 mV, starting at t = -2 ms**, in coincidence with the
Outer Coil.

The Current, V1-Cu (brown line), shows a ripple current of ± 3 A peak of
120 cycle. Its effect is shown in all of the voltage signals.

![](media/image18.png){width="6.498611111111111in"
height="5.753472222222222in"}

Fig. 17. **Quench No.1** of TC-2 with a ramp rate of **20 A/sec**. **Iq
= 11,625 A**.

**At t = -1.2 ms**, both the **Outer Shunt, QOSR2-QOSR1** **(brown
line)**, and the **Outer Coil, QOSR1-QIOLE1 (black line),** **start
increasing their voltage signals**. They have similar voltage shapes
during the current decay period, although the coil signal is 500 times
bigger. The Outer Coil triggers off the power supply at t = 0 sec, and
gets about --3.5 V inductive voltage.

The Innermost 3 turns of the Inner Coil, QIOLE1-QILE3 (red line), start
showing a quench at t = +15.5 ms, propagating from the Inner Coil. The
Outermost 3 turns of the Inner Coil, QILE8-QISR2 (green line), shows the
beginning of an increasing voltage signal at t = +19.5 ms, while the
inner cable part, QISR1-QIsh1b (blue line), shows a voltage signal
starting at t = +19 ms.

The Current has a ripple of ±2.5 A at 120 Hz. The ramp rate changes near
t = 0, and it is about --880 A/sec from t = -5 ms to 0 ms. The Current,
V1-Cu (light blue line with x), shows a current decay form, which starts
at the rate of -70,000 A/sec to -172,000 A/sec. This indicates the
resistance of the quench propagating cable is rapidly increasing.

![](media/image19.png){width="6.486805555555556in"
height="5.753472222222222in"}

Fig. 18. **Quench No.8** of TC-2 with a ramp rate of **2 A/sec**. **Iq =
11,124 A**.

At **t = -1.8 ms**, the **Outer Coil, QOSR1-QIOLE1 (black line),**
**starts a quench**. And at t = 0, triggers off the power supply,
getting about --2.5 inductive voltage. While **at the same time**, the
**Outer Shunt, QOSR2-QOSR1** (blue line), shows the same voltage
pattern, although about 300 times smaller. (But this may be an induced
voltage in the lead wire?) The Outer New Splice, QOSnL2-QOSnL1 (red
line), shows some erratic pulse peaks of 3 mV around t = 0.

The cable part next to the Internal Splice, QISR1-QIsh1b (green line),
shows a voltage signal of 6 mV peak at t = +5 ms.

The Current, V1_Cu (brown line), is shown decaying roughly at the
constant rate of 40,000 A/sec. This indicates the quench is not
propagating quickly in the coil when compared with the Quench No.1.