*Index Terms*---cryogenics, magnet, superconductivity

# Introduction

[T]{.smallcaps}HE United States contribution to the Large Hadron
Collider (LHC) at CERN includes half of the high gradient quadropole
magnets for the four interaction regions. These quadrupoles will work in
a hard radiation environment produced by secondary particles coming from
collision points, which will generate high heat depositions in the coil
and other parts of the magnet \[1\]. To provide reliable magnet
operation at the expected level of heat deposition, special attention
was paid to the magnet thermal design including coil cooling conditions
and heat extraction from the cryostat \[2\], \[3\]. In particular,
special channels 20.05 mm^2^ were introduced in the outer wrap of the
inner-layer cable insulation to increase the wet perimeter of turns by
penetration of superfluid helium inside the coil \[4\]. However, in the
course of the short model R&D program \[5\] it was found that coils must
be cured at high pressure and relatively high temperature in order to
achieve a high coil compaction with the required elasticity modulus.
That certainly affects the

Fig. 1. High gradient quadrupole cross section.

size of the channels and reduces their efficiency. The practical
importance of this problem along with the expected variations in helium
temperature in the magnet cryostat during operation motivated us to
study experimentally the real coil cooling conditions in these magnets.

A special short model magnet (HGQ08) was wound with stabrite coated
cable. The resulting low interstrand resistance and high AC losses
allowed us to measure magnet quench performance in superfluid helium as
a function of its temperature and heat deposition in the coil. The
results of these studies are reported in this paper.

# HGQ Thermal Design Parameters

The cross section of the high gradient quadrupole cold mass developed at
Fermilab for the LHC IR is shown in Fig.1. The inner coil is cooled by
conduction through the cable insulation to superfluid HeII in the
annular channel. The outer coil is cooled by conduction through the
ground insulation and collar laminations and also through the inner
coil. The heat transferred to the superfluid in the annular space
between the beam tube and inner coils is removed via radial heat
transport through gaps in the collars and yoke to the yoke holes. Heat
from the magnet is removed to the external heat exchanger via superfluid
heat transport through the holes in the iron yoke and special cryostat
pipes.

The details of pressure drop and heat transfer calculations for the
piping and heat exchangers, which connect the inner

![](media/image2.wmf)

Fig. 2. Predicted temperature in pressurized helium II in the iron yoke
holes in the warmest part of Q1 in IP5-left, the warmest inner triplet
magnet string.

triplet quadrupoles to the LHC cryogenic system, are reported in \[3\].
Fig. 2 is a plot of predicted temperature in pressurized helium II in
the iron yoke holes in the warmest cross-section of an inner triplet
assembly. With the expected total heat load to the cold mass of 6 to 12
W/m (corresponding to about 2 to 5 W/m in the coil), the temperature of
superfluid helium in the yoke holes will be in the range of 1.9 K to 2.0
K. The helium temperature at the coil is calculated to be only a few mK
higher than the helium temperature in the yoke holes.

## 

## The azimuthal distribution of the radiation heat power in the magnet reaches maximum in the midplane turns of the coil (see Fig.3 below). Table I shows the temperature rise and operational margin for these turns for two different coil cooling conditions calculated using a simple analytical model \[4\]. Only radial heat transfer in the coil was assumed in this calculation.

TABLE I

Calculated Temperature Rise and Operation Margin

for Midplane Turns and Different Coil Cooling Conditions

  ----------- ----------- ----------- ------------- ----------- -------------
  Cooling     Pmax        Inner layer               Outer layer 

  Channels    (mW/g)      T~cbl~, K   T~c~/T~cbl~   T~cbl~, K   T~c~/T~cbl~

  open        0.6         0.11        21.8          1.3         2.85

  closed      0.6         1.09        2.17          2.8         1.32
  ----------- ----------- ----------- ------------- ----------- -------------

Operational margin is defined here as a ratio T~c~/T~cbl~ at nominal
field gradient G = 205 T/m for the mid-plane turns, where

T~c~ = T~c~-T~HeII~ critical temperature margin,

T~cbl~ = T~cable~- T~HeII~ temperature rise in cable.

"Channels open" assumes that small channels in the insulation, filled
with superfluid, exist within the inner coil. "Channels closed" refers
to the gaps in the insulation within the inner coil being closed (filled
or blocked by cable insulation during coil fabrication). Heat loads in
the analysis are based on early radiation induced heat deposition
estimates \[1\]: a peak power density of 0.6 mW/g corresponding to 0.08
W/m in the inner-layer midplane turn of the superconducting coil and
0.026 W/m in the outer layer midplane turn. The

Fig. 3. Heat deposition versus coil turn number for AC losses in these
tests (dI/dt=100 A/s) and for expected radiation heating in the LHC. AC
loss and radiation heat depositions are normalized to the corresponding
heat depositions at the midplane in the inner coil.

temperature margin at the nominal field gradient of 205 T/m is
calculated to be 2.4 K for the inner layer coil and 3.7 K for the outer
layer coil, with a HeII temperature of 1.9 K.

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

                                                              

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

One can see from Table I that for either cooling condition, warming of
the outer layer of cable should limit magnet performance.

# Experimental Verification

sThe experimental verification of the HGQ coil cooling conditions
(thermal design parameters) is based on measurements of the sensitivity
of the magnet critical current to the AC loss heat depositions in the
coil. Experimental studies were performed on the special HGQ short model
(HGQ08) with high AC losses in the coil.

The calculated distribution of AC losses in this model magnet is shown
in Fig.3. For a comparison the expected distribution of radiation heat
deposition is also plotted in Fig.3. One can see that AC losses, like
the radiation heat deposition, are maximal in the midplane turns of the
inner layer. However, AC losses are more uniformly distributed
azimuthally in each layer than the radiation heat depositions.

Tests were conducted in the large cryostat called the Vertical Magnet
Test Facility (VMTF) \[6\]. The magnet was placed in the superfluid
helium bath with a 3 mm annular space inside the magnet bore. The magnet
quench performance was tested as a function of helium temperature and
ramp rate.

Fig. 4 is a plot of quench currents measured at different temperature of
HeII bath versus current ramp rate. All quenches at current ramp rates
above 50 A/s were detected in the midplane turns of the inner layer as
predicted by the heat distribution plotted in Fig.3.

AC loss measurements provided a correlation between the current ramp
rate and the coil heat deposition due to AC loss heating. The system
used to perform the AC loss measurements \[7\] included two HP3458A
digital multi-meters (DMMs) with matched low pass input filters, a power
supply controller, a GPIB bus, and an embedded VME computer for

Fig. 4. Measured magnet quench current versus current ramp rate.

controlling the measurement. The two DMMs were used to measure the
current and magnet voltage. They both were configured for a 60Hz sample
rate and single line-cycle integration. One DMM measured the magnet
voltage via voltage taps on the coil while the second DMM measured the
current, which was sensed by a Holec Transductor. Since the power
deposited by AC losses is small compared with the change in stored
energy, both DMMs were synchronized to integrate over the same interval
in order to prevent any errors that would be incurred from small timing
differences. The technique employed for measuring AC losses was strictly
digital, and with no bucking. This was accomplished by digitizing the
signals with the DMMs and then digitally integrating the product of the
current and voltage over a closed current loop once the measurement was
complete.

At each current ramp rate, five energy loss measurements were made for
ramps from 500 A to a peak current of 6500 A and back. These were
averaged to yield a net energy deposited in the magnet versus ramp rate.
Similar measurements were made with ramps to 4000 A and 3500 A. By
subtracting the energy losses for different peak currents and dividing
by the time difference for the cycles, we subtracted out the ramp
acceleration and deceleration effects. Dividing by the 1.8 m coil length
gives specific power per magnet unit length. Results for power deposited
in the coil by AC heating versus current ramp rate are plotted in Fig.
5.

Systematic measurement errors for these data are quite small, less than
10%, and their RMS spread is about the size of the deviation of the
points from the curve on the plot. The curve is a quadratic fit, which
is then used to convert current ramp rates to power.

Magnetic field gradient at quench versus average AC heat load in the
coil (Fig. 6) was obtained by converting quench current to magnetic
field gradient and converting current ramp rate to heat load to the data
shown in Figs. 4 and 5.

Figs. 4 and 6 illustrate one important conclusion from this study, which
is that helium temperature of 2.05 K or lower had little effect on
quench current and quench field gradient. One can also see what appears
to be breakdown of the superfluid heat transport in the annular space at
a heat load of 40 W/m.

Fig. 5. Measured AC loss power versus ramp rate for HGQ08.

For the AC loss limit at 1.9 K from Fig. 6 of 20 W/m total, and using
the distribution presented in Fig.3 we estimate 0.19 W/m into the
midplane turn of the inner layer, where quenches initiated. The 0.19 W/m
measured limit divided by 0.08 W/m from the Table I analysis yields a
2.37 heat load margin for the inner layer assuming a linear relationship
between the power dissipation in the cable and its temperature rise. The
margin of 2.37 is in good agreement with the calculated temperature
margin of 2.17 for the inner layer with poor coil cooling conditions at
1.9 K HeII temperature.

This result allows one to conclude that the channels in the inner-layer
cable insulation are practically blocked. Visual inspection of the slice
of collared coil cross-section confirms this conclusion.

# 

# 

#  Operation Margin in the LHC

Experimental studies described above provided the information concerning
the real coil cooling conditions in the coil. To improve and update the
HGQ thermal analysis a 2-D ANSYS® steady thermal model has been
developed. The model includes inner and outer coils, ground insulation,
and stainless steel collars. Real azimuthal and radial distributions of
radiation heat depositions and the heat load value updated for the
nominal LHC luminosity in Fermilab's magnets of 0.4 mW/g have been used
\[8\].

![](media/image11.wmf)

Fig. 6. HGQ08 field gradient at quench versus heat load.

![](media/image12.wmf){width="3.338888888888889in"
height="2.522222222222222in"}

Fig. 7. Temperature distribution in the HGQ coil at nominal LHC
radiation heat deposition.

Fig. 7 shows the calculated temperature distribution in the HGQ coil
with predicted nominal LHC radiation heat deposition. Data analysis
shows that radial and azimuthal temperature gradients are very small in
spite of strong radial and azimuthal dependence of radiation heat
deposition in the coil (see Fig.3). The calculated azimuthal temperature
gradient between the midplane and pole turns in the inner layer is \~60
mK and \~30 mK in the outer layer. The radial temperature gradient in
both layers is less than 5 mK. These results show that the coil's
azimuthal thermal conductivity is an effective mechanism for temperature
averaging the radiation-induced heat which is locally deposited into the
inner and outer midplane turns. This mechanism has the additional
benefit of helping to involve a large amount of the coil surface into
the transfer of radiation heat to the HeII bath.

The results of calculation of turn operation margin for the radiation
heat depositions corresponding to LHC nominal luminosity are reported in
Fig. 8. The operation margin of the inner layer is 11 and determined by
the midplane turns. The operational margin of the outer layer is 7 and
determined by

Fig. 8. Operation margin for inner and outer turns at nominal field
gradient of 205 T/m.

the pole turns. Thus, the outer layer determines the magnet operational
margin that is 7 for the nominal LHC luminosity. This margin is also
sufficient to provide the reliable magnet operation at expected ultimate
LHC luminosity, which is expected to be a factor of 2.5 higher.

# Summary and Conclusion

The experimentally determined inner-layer operation margin (relative to
0.6 mW/g heating) of 2.37 and the fact that quench current does not
change significantly with helium temperature are consistent with the AC
heating thermal model result for closed channel cooling. These results
imply that channels in the inner-layer insulation are blocked. The
blocking of cooling channels with insulation in the assembled magnet was
visually checked and confirmed in a mechanical model. However, the
relatively large azimuthal thermal conductivity of the coil helps to
involve whole coil surface in the transfer of heat deposited in the
midplane turns to the HeII bath.

A thermal analysis of coil cooling based on closed cooling channels,
effective azimuthal thermal conductivity in the coil, and heat deposited
as predicted due to secondary particles in LHC shows that the outer
layer would limit the magnet operation margin to seven times the
predicted nominal heat load. Thus, we conclude that the high gradient
quadrupoles developed at Fermilab for the LHC interaction regions have
sufficient temperature margin for stable operation even in the hard
radiation environment of LHC at nominal and ultimate beam luminosity.

# Acknowledgment {#acknowledgment .Reference-Head}

The authors thank the Fermilab Technical Division, Engineering and
Fabrication Department staff who built magnet HGQ08, and the Development
and Test Department staff who set up and ran the tests.

# References  {#references .Reference-Head}

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8.  

9.  

10. 

11. 

12. N. Mokhov, Fermilab, Batavia, IL, private communication, 1999.

[^1]: ^^Manuscript received September 18, 2000.

    This work was supported by the U.S. Depart­ment of Energy.

    All authors are with Fermilab, P.O.Box 500, Batavia, IL 60510, USA,

    J. Ozelis is with Jefferson Lab, 12000 Jefferson Avenue, Newport
    News, VA 23606, USA