[^1]

*Abstract*--- The Superconducting Magnet Group at Lawrence Berkeley
National Laboratory has been developing high-field,
brittle-superconductor, accelerator magnet technology. A brittle
conductor's support system can significantly impact conductor
performance (as well as magnet training). A recent H-dipole coil test
(HD1) achieved a peak bore-field of 16 Tesla, using two, flat-racetrack,
double-layer Nb3Sn coils. However, its 4.5 K training was slow, with an
erratic plateau at \~92% of its un-degraded "short-sample" expectation
(\~16.6 T). Most of the quench-origins correlated well with regions
where low conductor pre-stress had been expected (3-D FEM predictions,
300 K coil size variations). The coils were re-assembled, with minor
coil-support changes and re-tested as "Hd1b", with a 185 MPa average
pre-stress (30 MPa higher than HD1, with a 15-20 MPa pole-turn margin
expected at 17 T). Training started higher (15.1 T), and quickly reached
an only slightly higher but stable plateau at 16 T. A second thermal
cycle started at 15.3 T, but, after peaking above 15.7 T, degraded to a
15.6 T plateau. The temperature dependence of the degraded plateau was
explored down to a bath temperature of 3.0 K. Implications for future
high-field magnet development are discussed.

*Index Terms*--- Superconducting magnets, Dipole, High-Field, Nb~3~Sn,
Test Results.

# INTRODUCTION

[L]{.smallcaps}awrence Berkeley National Laboratory (LBNL) is continuing
a vigorous development program for providing cost-effective, high-field
magnet options for "next generation" particle accelerators and storage
rings. These magnets utilize state-of-the-art Nb~3~Sn superconducting
cable, and require strong, rigid, predictable mechanical support
systems, able to protect the brittle conductor from large Lorentz loads.
While all successful high-field Nb~3~Sn efforts have thus far utilized
wind-and-react technology \[1-5\], react-and-wind technology is being
pursued elsewhere \[6\]. Previous efforts explored the dual-bore,
common-coil geometry, using flat racetrack coil modules \[3-5\], and
achieved 14.5 T bore field. The most recent effort achieved a bore field
of 16 T in a single-bore H-dipole using two double-layer racetrack coils
\[MT-18\]. In all cases, extreme care was taken to avoid conductor
damage from excessive pre-stress, tolerating the slow training, to
determine how well the conductor and structure responded to large
Lorentz loads. While many flux-jumps were recorded, only conductor
movements appeared to initiate quenching, with all models exceeding 90%
of "undegraded short-sample".

HD1's quench initiations below 16 T were clearly initiated by conductor
movements, and its quench origins were strongly correlated with regions
where coil size variations \[7\] and 3D FEM analysis \[8\] had predicted
conductor movement to be likely. This strong correlation, supported by
visual inspection of the disassembled coils, prompted efforts to correct
known pre-load deficiencies and retest the coils, to determine if we
would make progress, without causing any new problems. To emphasize the
re-use of the same coils and magnetic configuration, this test was
called HD1b, and its subsequent thermal cycle test was called HD1b-2.
Their primary results are reported herein.

# Magnet features and test set-up

## Coil inspection and changes

HD1's coils were disassembled, measured and visually inspected. These
2-layer coils had been wound with 36-strand Rutherford cable, 35 turns
(inner layer) and 34 turns (outer layer), using coils 0.8 mm strands of
Oxford's best "restacked-rod processed" Nb~3~Sn conductor
(Jc \> 3000 A/mm^2^ @ 12 T) \[9\]. Additional details can be found
elsewhere \[10-13\]. A crescent shaped region of crazed epoxy was easily
visible at the outer tip of each hard end-spacers (turn #6 away from the
pole). These regions had the approximate shape predicted by our 3D FEM
analysis \[7,8\]. Excepting the high pressure surface impressions left
by the G-10 coil-face shims, the coils appeared as virginal as before
HD1's initial assembly: clear epoxy, no visible cracks. Coil size
measurements indicated that coil-A, where HD1's "plateau" quenching
appeared to have been localized to a region that subsequently exhibited
a 300K pre-stress deficit, resulting from and under-sized coil support
element. These variations were corrected by judicious application of
Araldite-1580 glass-loaded "green-putty", which was subsequently
machined to match the larger coil (coil-B).

## Magnet assembly and Support Structure Changes

The coils were reassembled in the same HD1 geometry (Fig.1) \[ray's and
Al's MT18 papers\], where an aluminum shell pre-stressed the coils
transversely, via the iron yoke, and four axial Z-rods pre-stressed the
coil-ends. As with previous high-field magnets, most of the pre-stress
is only applied while cooling the magnet \[12\].

![](media/image1.png){width="3.282638888888889in"
height="2.859027777777778in"}

#  {#section .Reference-Head}

Fig. 1, HD-1 cross-section: Two horizontal, double-layer pancake coils
were separated by a thin bore-plate, and compressed on all sides by
compression pads, bridges, and iron yokes. Compression was maintained by
a 45 mm thick, 740 mm OD tensioned aluminum shell. G-10 strips
electrically insulated the coil surfaces, while simultaneously
cushioning irregularities in the high-pressure interfaces. Iron
interference keys permitted removal of internal pre-stressing bladders.
Most of the final pre-stress resulted from cool-down.

Four assembly differences are noteworthy:

1\) The shell tension was increased in a manner to produce a \~20%
larger cold pressure along the long edge of each coil. The calculated
average coil-edge pre-stress was increased from 155 MPa to 185 MPa,
increasing the pole-turn margin to 15-20 MPa at 17 T. The intention was
to stop the pole-turn quenching observed in HD1, while providing an
opportunity to observe pole-turn conductor degradation that might
result.

2\) All coil end-shoes were machined in a manner to more effectively
reduce the calculated, Lorentz-induced, coil-end conductor displacements
\[8\].

3\) The end-load, from the tension of the four Z-rods, was increased 15%
above that used in HD1.

4\) The 300K Z-load was applied before the shell tension was raised (in
the hopes of reducing the coils' end-fluff before it was trapped by
friction from the transverse loading.

Interface friction in the model was adjusted to obtain agreement with
HD1 measurements. As with recent LBNL high-field magnets \[4-5, 12-13\]
the pre-stresses were expected to increase significantly during
cool-down (Fig. 2).

## Diagnostic and Test Set-up

The coil protection and diagnostics unchanged from HD1 \[13\]. Each coil
had eleven voltage taps per layer, dividing each layer into 10 segments,
with primary attention to the inter-layer ramp, pole-turn, end-spacer
turn, outer turn, and lead-in Nb~3~Sn/NbTi splices. The average coil
pre-stress was inferred from temperature-compensated strain measurements
of the aluminum shell, and two of the four axial rods. A cold Hall-probe
measured the peak bore field, with the calibration as used for HD1.

# Test results

## Training Preparations

Cool-down (Fig. 2) supplied most of the pre-stressing tension, as
expected, in the shell (30 to 110 MPa) and the Z‑rods (125 to 230 MPa).
HD1's test preparations were repeated \[Al's MT-18 paper\].

![](media/image2.wmf){width="3.4965277777777777in"
height="2.261111111111111in"}

Fig. 2. The expected absolute shell and axial Z-rod tensions for the
following conditions: relaxed onto the keys "293K", b) cold "4.5 K", and
d) various fractions of short-sample Lorentz excitation.

## HD1b training (1^st^ thermal cycle)

In order to differentiate between hypothetical causes for HD1's
strain-gauge ratcheting, the largest fraction of which was observed
after the first quench, the first ramp to quench was changed from our
standard stair-step ramp to an ascending series of triangle ramps. This
allowed measurements of the ratcheting as a function of peak Lorentz
stress (10%, 30%, 50%, 70%, 90% of I~ss~^2^), while affording
observation of stick-slip training retention and flux-jump
repeatability. Most of the fast flux changes have been labeled
"flux-jumps", because they were slow (5-10 ms duration), showed no
deceleration (no negative second time derivative of flux), no ringing,
and recurred repeatedly every ramp, up and down.

HD1b's first training quench (10.2 kA, 15 T) occurred while attempting
the "90%" hysteresis ramp. Training was relatively rapid, reaching a
\~16 T "plateau" after the 8^th^ quench (Fig. 3). This plateau, while
very similar to HD1's peak field, was considerably more stable than
HD1's. As observed with HD1's training quenches, multi-turn,
simultaneous quench starts were observed in the starting coil layer,
with nearly simultaneous quench-starts in the adjacent layer.
Time-of-flight analysis indicated HD1b's training quench-origins were at
the same coil-end locations as HD1: near an end-spacer apex, one on
turn-5 (inside the end-spacer), the others on turn-6 (outside the end
spacer; one in the lead-end, the others in the return end; two in
coil-B's inner layer-1, the others in coil-A's outer layer-2. After the
8^th^ quench, the quench-origin shifted to a dramatically different
location, and a modest ramp-rate dependence was observed (Fig. 4).
Compared to HD1, HD1b's training exhibited a higher initial current,
fewer quenches to reach 16 T, no pole-turn only quench-origins, and a
stable plateau.

![](media/image3.wmf){width="3.45in" height="2.2694444444444444in"}

Fig. 3 HD1b's training started at 15.1 T and reached a stable \~16 T
plateau on the 9^th^ attempt, in dramatic contrast to HD1's training.

![](media/image4.wmf){width="3.45in" height="2.290277777777778in"}

Fig. 4 HD1b's ramp-rate dependence: Quench-origins distinguished
training quenches from "plateau" quenches. Above \~6 A/s, quenches
started in coil-B. While starting slowly, like "short-sample" quenches,
and exhibiting ramp-rate dependence, the simultaneous, multi-turn
initiations of all plateau quenches appeared to be contradict this
conclusion.

Below \~6 A/s, all "plateau" quenches started simultaneously (Fig. 5) in
the five turns adjacent to coil-A's winding pole, in both the high-field
layer (layer-1), and the low-field layer (layer-2). Turn-6 and portions
the mid-coil multi-turn segments started simultaneously 1.6 ms after
quench-initiation. Compensating for the multi-turn segment's inductance,
and applying the respective turn-6 propagation speeds to its neighboring
multi-turn segment, at least 8 outer turns and 9 inner turns
participated in the second, simultaneous, 1.6 ms quench-start. Assuming
one quenching region per turn, 28 turns (41% of coil-A) had quenches
propagating steadily within 1.6 ms of quench initiation.

Plateau quenches also produced propagation signals (Fig. 5) that were
near overlays of each other. The axial time-of-flight to the nearest
voltage tap (9.0-9.6 ms to tap "A1R2") varied slightly with "plateau"
current, and corresponds to 176 mm, assuming the average propagation
speed observed for turns 2-4 (19 m/s) applies to turn-2. The
quench-quench variation translated to +/- 2 mm. The time-of-flight to
the second nearest tap (A1R5) yielded a similar estimate for turn-5.
This places the quench-origin(s) within the high-field straight-section
of the magnet, near the return end.

The propagation signals also revealed that the quenches in turns 1-6
started propagating considerably (2-4x) faster than was sustained
(Fig. 5). This was true for both layers, with the longest lasting
transients speeds in the 3-turn segment A1R5R2, and the largest speed
ratio in turn-6. Assuming the initial speed burst resulted from degraded
margin, the largest degraded region corresponds to distance of 81 mm.

![](media/image5.wmf){width="3.495138888888889in"
height="2.7270833333333333in"}

Fig. 5 Plateau quench-origins: Overlay of propagation signals for two
plateau quenches (Q12 & Q14) illustrate nearly duplicate quench
propagation signals, showing nearly simultaneous multi-turn
quench-origins in both the higher-field (A1) layer (lower four signals)
and the lower-field (A2) layer (upper four signals). The displayed
signals account for 27 of 28 simultaneous quench-front pairs that
exhibited steady propagation 1.6 ms after initiation.

For ramp-rates above \~16 A/s, simultaneous multi-turn quench origins
were also observed, but with several differences: 1) Quenches started in
coil-B. 2) Simultaneous quench-origins were observed only in layer-1,
and only in turns 1-4. 3) Simultaneous quenches in layer-2's turns 5-9
started 3 ms later than those observed for the slower ramp-rate, coil-A
quenching. 4) propagation into the ramp segment from layer-2's lead-end
pole-turn after propagating only 2.5 ms (\~31 mm), 5) A layer-1, turn-6
quench passed tap B1L6 (lead-end) after propagating 5 ms.

## HD1b-2 training (HD1b's 2^nd^ thermal cycle)

Training for the second thermal cycle produced a distinctly different
quench history (Fig. 6). Training started with a massive conductor
movement at 15.4 T, marginally higher than HD1b, and reached a \~15.7 T
"plateau" (\~10.6 kA, \~0.93% of undegraded average short-sample) on the
second attempt (Fig. 6). Subsequent attempts resulted in slightly lower,
stable plateau slightly above 15.6 T. Quench propagation signals were
near replicas of those observed in the earlier HD1b "plateau" quenching,
with two differences: 1) The initial quench-speed surges (immediately
after quench-initiation) lasted longer for turns 2-4, and 2) Turn-5's
quench passed tap R5 \~1 ms sooner, implying its origin was \~125 mm
inward from R5. Higher ramp-rate (20-60 A/s) quench-origins appeared to
be identical to HD1b's 16A/s quench-origin: coil-B's lead-end

![](media/image6.wmf){width="3.53125in" height="2.640972222222222in"}

Fig. 6. Hd1b trainings: HD1b-2 (2nd thermal cycle) started higher and
reached a \~15.8 T plateau" on the second attempt. This plateau was \~2%
lower than HD1b's, and degraded with subsequent attempts to \~15.7 T.

All but the second quench produced propagation signals that wear near
duplicates every quench, indicating tightly clustered quench-origins (as
observed during the previous Hd1b "plateau" quenches). As with HD1b,
HD1b-2's plateau quench signals revealed a near replication, signal for
signal. This implied a common axial origin, which was near HD1b's
"plateau" quench-origins. As with HD1b's "plateau" quenches had multiple
nearly simultaneous (within 1 ms) quench-starts, at a current that was
relatively stable 15.7 Tesla. The turn-6 end quenching and pole-turn
quenching that characterized HD1 training was was completely absent. No
quenches originated in the ramp, in any of HD1's four training runs
(HD1, HD1-2, HD1b, HD1b-2).

## HD1b-2's sub-cooled training (T \< 4.5K)

In an effort to determine if cooling could increase the 4.5 K "plateau",
the magnet was ramped with a low pressure bath (Fig. 7). While cooling
the bath enabled higher fields, it had no impact upon the 4.5 K plateau
current. All quench-initiations, excepting for the highest quench, were
replica's of HD1b's "plateau" quenches. The coldest quench also
exhibited simultaneous initiations in coil-A, but in the first three
turns at the lead-end. The observed temperature dependence departed from
a slightly degraded-Nb~3~Sn, HD1b load-line dependence below \~4 K, when
the leads were no longer immersed.

![](media/image7.wmf){width="3.4930555555555554in"
height="2.654166666666667in"}

Fig. 7. HD1b-2 training, cooled LHe bath dependence: The conductor was
expected to be warmer than the bath when the leads were not immersed
(T\<\~4 K).

# Discussion

## Cool-down & ramping observations

Good agreement with calculations continued to raise confidence in the
3-D stress calculations. The number and size of flux-jumps during magnet
ramping, while disappointing, and requiring desensitization the
quench-detection threshold, failed to limit magnet performance in any
obvious manner.

## Reduction of HD1's coil-end training quenches

Hd1b's coil end-support changes were motivated by the agreement of HD1's
training quench-origins with predicted, Lorentz-induced, conductor
displacements near the coil end-spacer. A delayed onset and large
reduction in these displacements were anticipated. While one can never
be certain that full magnet disassembly, repeated coil handling, flexing
and a similar reassembly will restore the HD1's original "virginal"
condition, the dramatic improvement in training onset and training speed
for HD1b was encouraging. Improvement had been predicted; improvement
was observed; and nothing seriously bad happened.

## Elimination of HD1's "plateau degrading" quenches

More uniform coil-A dimensions, and the larger, 180 MPa average
coil-edge pre-stress were intended to eliminate coil-A's pole-turn
de-training, while affording an opportunity to observe the impact of
conductor strain degradation upon magnet performance. The intended
pole-turn quench-origins that had degraded HD1's plateau, were
completely eliminated, and even allowed a slight increase in the \~16 T
maximum field. Unfortunately, HD1b's field limit appears to have been
conductor-limited, suggesting the possibility that Nb~3~Sn
strain-degradation had been encountered (see further discussion below).

## HD1b's Quench-Origins

The pattern of HD1b's training quench-origins was an abbreviated copy of
HD1: multi-turn simultaneous quenching near a coil end-spacer, primarily
coil-A's return-end, triggered by stick-slip conductor movement. HD1b's
"plateau" quench-origins were new, and near replicas of each other. Five
features of the associated "plateau" are noteworthy: 1) All quenches
started slowly, in the manner observed in previous short-sample
experiences \[4\]. 2) The "plateau" current was only marginally higher
than HD1's maximum, despite the elimination of HD1's limiting pole-turn
quench-origins. 3) Within 1.6 ms of quench-initiation \~41% the coil-A
was quenching, quite similar to that observed when triggered by massive
conductor movement \[5\]. 4) The associated multiple quench-origins were
near replicas, every quench. 6) The plateau current exhibited a slight
ramp-rate sensitivity. This immediately raised several questions: 1)
What is causing the simultaneous, multi-turn quenching, when all other
evidence suggests local loss of conductor margin. 2) Does the plateau
current have the expected Nb~3~Sn temperature dependence? 3) How will
the training, and the newly established "plateau", respond to a full
thermal cycle?

## HD1b's 2^nd^ thermal cycle and sub-cooled training

The massive conductor movement observed prior to the first training
quench is the largest ever observed at this test facility. It is
believed to indicate some loss of mechanical training memory, which in
conjunction with the large improvement upon the second attempt, was
re-established very rapidly. The observed temperature dependence, in
conjunction with the slow-down in quench propagation speed (after
initiation), supported the hypothesis that the quenches were originating
in degraded conductor regions, consistent with the previously observed
(HD1b) slow quench-initiation, quench-origin replication, and plateau
ramp-rate dependence.

## "Plateau" quench-origin mystery and challenge

These results leave the following questions unanswered: 1) How does
degraded conductor, presumably locally, strain-degraded conductor,
generate simultaneous, multi-turn quench-initiation origins? 2) How many
of these "locally degraded" regions exist on the way to 17 T? 3) What is
the best method of raising the plateau current?

# Conclusion

The block dipole magnet "HD1" reached 16 T before falling back. It was
disassembled. The coils were examined in considerable detail, modified
slightly in the end, and reassembled with higher pre-stress in those
regions that had exhhiited HD1 training difficulties. HD1's training
quench-origins were either greatly reduced or completely gone. The
observed 4.5 K 16 T "plateau" was stable, and exhibited ramp-rate and
Nb~3~Sn temperature dependences. However, its quench-initiations
involved simultaneous multi-turn quench-origins, in which nearly half
the coil was quenching within 1.6 ms. All quenches appeared to propagate
away from regions of degraded margin into regions having considerable
margin, leaving a mystery as to what mechanism could locally degrade the
margin of so many turns in a manner to cause such observations.

# Acknowledgements {#acknowledgements .Reference-Head}

This was quite an achievement, albeit only one step along a long
development path toward a reliable energy-doubler option. Particular
mention goes to the conductor manufacturer (OST), and all the
administrators, assistants, and technicians, whose contributions made
these results possible.

# References {#references .Reference-Head}

1.  A.D. McInturff et al., "Test results for a High Field (13 T) Nb~3~Sn
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2.  A. den Ouden et al, "A 10 T Nb3Sn Model Separator Dipole Magnet for
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3.  A.F. Lietzke, "Test results for RT1..." *VLHC Workshop*, FNAL, 2000.

4.  A.F. Lietzke et al., "Fabrication and Test Results of a High Field,
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5.  A.F. Lietzke, et. al., "Test Results for RD3c, a
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6.  G. Ambrosio, et. al., "Fabrication & Test of Racetrack Magnet Using
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7.  S. Mattafirri, et al., "Performance Analysis of HD1: A 16 T Nb3Sn
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8.  P. Ferracin, et al., "Mechanical Analysis of the Nb~3~Sn dipole
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9.  J. Parrell et al., "High Field Nb3Sn Conductor Development at Oxford
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10. R.R. Hafalia et al., "A new support structure for high field
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11. S. Caspi et al., "The use of pressurized bladders for stress control
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12. RH's MT-18 paper

13. AFL's MT-18 paper

[^1]: ^^Manuscript was received 05 October, 2004.

    \*This work was supported under contract DE-AD03-76SF00098 by the
    Director, Office of Energy Research, Office of High Energy Physics,
    U.S. Department of Energy.

    All authors are or were with Lawrence Berkeley National Laboratory,
    Berkeley, CA 94720 (A.F. Lietzke can be reached via e-mail:
    AFLietzke@lbl.gov, phone: 510-486-4572, or fax: 510-486-5310).