Download The Tracker Solenoid Conductor

Magnet Conductor Parameters
and How They affect Conductor
Selection for MICE Magnets
Michael Green
Lawrence Berkeley Laboratory
Berkeley CA 94720, USA
CM-18 June 2007
1
MICE Conductor Selection Criteria
• Parameters of the Tracker Conductor and the
Coupling Coil Conductor
• Round versus Rectangular Conductor
• Copper to Superconductor Ratio & Copper RRR
• Superconductor Filament Diameter
• Conductor Current Density
• Why jc and n Value are Always Important
• Coil Design Current, Conductor Size and the Coil
Self Inductance
• Comments about the Focusing Magnet Conductor
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The Tracker Solenoid Conductor
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The Tracker Conductor Selection Process
• The INFN tracker magnet design had a much larger
cross-section conductor but the number of turns was
about the same as the LBL tracker magnet design.
• Using a conductor with a lower copper to S/C ratio
resulted in less conductor being used to fabricate the
magnet, but the magnet margin wasn’t changed.
• The smaller conductor resulted in thinner coils and
a lower tracker magnet cold mass. As a result, the
tracker magnet cost was reduced without sacrificing
magnet performance. The conductor selected was
one that LBL knew they could buy at a reasonable
price of $1380 per kilometer.
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The Tracker Solenoid Conductor
• The nominal cross-section dimensions of the tracker
insulated conductor are 1.0 mm by 1.65 mm. It has
rounded corners with a 0.2 mm radius.
• The copper to superconductor ratio is 3.9 ± 0.4. The
copper RRR = ~70.
• The conductor has 222 filaments with a nominal
filament diameter of about 41 microns.
• The nominal conductor twist pitch is 19 ±3 mm.
• The length delivered is 121.5 km, which is ~10 km
short of four billets of conductor.
• The conductor Ic > 760 A @ 5 T and 4.22 K
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Conductor Cross-section
1.65 mm
1.00 mm
41 mm Nb-Ti Filament
RRR = 70 Copper
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Tracker Conductor Mechanical Characteristics
Both tests look for filament breakup
and defects in the filament bundle.
The dimensions are
acceptable.
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Tracker Conductor Electrical Characteristics
The specified conductor critical current is >760 @ 4.2 K and 5 T.
The specified conductor n value is >35.
The specified conductor copper to S/C ratio is 3.9 ± 0.4.
The RRR values for the conductor copper are acceptable.
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Critical Current Vs Magnetic Induction
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The Exposed Conductor Filaments
~2.5 mm
Photo by LBNL
The conductor twist pitch is within the specified range of values.
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A Closer Look at the Filaments
Photo by LBNL
There appears to be no sausaging of the filaments, which suggests the n value
will be high. The surface of the filaments appears to be acceptable. It is likely
that the conductor jc will be uniform across the conductor section.
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The Effect of Various Conductor Parameters
on Magnet Performance
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Round versus Rectangular Conductor
• A number of magnet vendors prefer winding round
conductor because it is easier and faster to wind.
The worst shape to wind is a square conductor.
• The coil packing fraction for a coil wound with
round conductor is lower than for rectangular
conductor of the same thickness. (For the tracker
solenoid the coil packing fraction is 0.64 vs. 0.81.)
• For a given average coil current density and magnet
temperature margin, the copper to superconductor
ratio has to be reduced by twenty-five percent when
the coil is wound with round conductor.
• Wind rectangular conductors the easy way.
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Cu to S/C Ratio and Cu RRR
• A conductor with large copper to superconductor
ratio has increased dynamic stability, which means
larger filaments can be used.
• Modern MRI conductors typically have a Cu to S/C
ratio of 4. MRI conductors are cheaper to buy than
a low Cu to S/C ratio conductor.
• Reducing the Cu to S/C ratio from 4 to 2 increases
the critical current by 67 percent, but this is done at
the expense of conductor stability. As a result, finer
S/C filaments are needed in the conductor.
• It is desirable to have the copper RRR > 70. One
pays more for a larger RRR. There is a trade-off
between RRR and filament diameter.
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Superconductor Filament Diameter df
• Low field MRI magnet conductors have larger Cu to
S/C ratios (as high as 7) and df = ~80 microns. The
higher field MRI magnets have magnet conductors
with df < 50 microns for magnet stability.
• A magnet with conductor with a smaller filament
diameter has lower AC losses. This is important for
magnet charging and discharging while on a cooler.
• A conductor with a smaller filament diameter is
more stable for a given Cu to S/C ratio and RRR.
• Making the filament diameter too small increases
the conductor cost and reduces the superconductor
jc. There is an optimum filament size.
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Conductor Current Density
• The current density in the conductor (matrix plus
S/C) directly affects the quench performance of the
magnet. For given coil dimensions, this is another
reason to use rectangular conductor.
• For a given coil current and inductance, the number
of passive quench protection diode circuits will go
up as the conductor current density to the m power,
where 1 < m < 2. Higher RRR and Cu to S/C ratio
are better in terms of quench protection.
• The desired conductor current density is higher for
solenoids with a smaller ID and where the current is
squeezed due to other constraints. The magnet
stored energy is less for smaller magnets.
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Why jc and n Value are Important
• The key parameter for any superconductor is its
critical current density (jc) at a given magnetic field
and temperature.
• Modern Nb-Ti has a design jc > 2750 A mm-2 at 5 T
and 4.22 K. The tracker conductor jc > 2900 A mm-2
at 5 T and 4.22 K measured at a r = 10-14 W m.
• The higher the conductor jc, the greater the magnet
temperature margin.
• The conductor n value is a measure of current
sharing in the conductor. A conductor with a large n
value is desirable. The n value is a measurement of
superconductor uniformity.
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Coil Design Current, Conductor Size
and the Magnet Self Inductance
• The design current for all of the MICE channel
magnets was set at less than 300 A. MICE will be
powered using six 300-A power supplies (seven if
MICE operates in the mixed flip and non-flip mode).
Four 60 A power supplies are used for the trackers.
• Because the coupling magnet has a larger stored
energy (~12.4 MJ) than any of the other magnets, its
worst-case design current was set at 210 A.
• Increasing the conductor size and current appears to
be desirable for coil quench protection. A study of
this was done at ICST in Harbin.
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A Comparison of Possible Conductors
Tracker Conductor
• Insulated Dimensions
1.00 mm x 1.65 mm
• Length = ~242 km*
• Twist Pitch = 19 mm ± 3
• Copper RRR > 70
• Cu to S/C = 3.9 ± 0.4
• Filament Dia = ~41 mm
• n > 35 @ 5T
• Ic(4.2K, 5T) > 760 A
Larger Conductor
• Insulated Dimensions
1.15 mm x 1.90 mm
• Length = ~182 km*
• Twist Pitch = 19 mm ± 3
• Copper RRR > 70
• Cu to S/C = 3.9 ± 0.4
• Filament Dia = ~ 48 mm
• n > 35 @ 5T
• Ic(4.2K, 5T) > 1010 A
* For two MICE coupling magnets and one MUCOOL coupling magnet
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Basic Parameters for a 285 mm Long Coupling
Magnet with the Tracker Magnet Conductor
Parameter
Non-flip
Flip
Coil Length (mm)
285
285
Coil Inner Radius (mm)
744
744
102.5
102.5
96
96
No. Turns per Layer
166
166
Magnet J (A mm-2)*
90.11
95.53
Magnet Current (A)*
165.2
175.1
Magnet Self Inductance (H)
~564
~564
Peak Induction in Coil (T)*
5.85
6.20
Magnet Stored Energy (MJ)*
~7.7
~8.6
4.2 K Temp. Margin (K)*
~1.8
~1.6
Coil Thickness (mm)
Number of Layers
•Design based on p = 200 MeV/c and beta = 420 mm.
One would like to run the magnet up to 210 A in the flip mode.
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Basic Parameters for the 285 mm Long Coupling
Magnet with a Larger Conductor
Parameter
Non-flip
Flip
Coil Length (mm)
285
285
Coil Inner Radius (mm)
744
744
102.1
102.1
84
84
No. Turns per Layer
144
144
Magnet J (A mm-2)*
90.47
95.89
Magnet Current (A)*
217.6
230.6
Magnet Self Inductance (H)
~325
~325
Peak Induction in Coil (T)*
5.85
6.20
Magnet Stored Energy (MJ)*
~7.7
~8.6
4.2 K Temp. Margin (K)*
~1.8
~1.6
Coil Thickness (mm)
Number of Layers
•Design based on p = 200 MeV/c and beta = 420 mm.
One would like to run the magnet up to 277 A in the flip mode.
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Coupling Magnet Quench Protection
• The coupling magnet has a conducting mandrel,
which promotes quench back. Quench back reduces
the coupling magnet hot spot temperature but has
only a small effect on the voltages in the coil.
• The coupling magnet must be subdivided. Across
each subdivision are diodes and resistors. The diodes
and resistors reduce the magnet voltages. The peak
voltage across the coil (a voltage to ground) must be
less than 2 kV. The layer-to layer voltages must be
less than 350 V. The magnet inductance determines
the number of coil subdivisions. A larger conductor
means fewer coil subdivisions and a lower hot spot
temperature during a quench.
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No Quench Back
Study by X. L Gou of ICST
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No Quench Back
Study by X. L Gou of ICST
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No Quench Back
Study by X. L Gou of ICST
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No Quench Back
Study by X. L Gou of ICST
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Study by X. L Gou of ICST
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Study by X. L Gou of ICST
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Results of the ICST Quench Study
• The use of a larger conductor results in lower
internal voltages, lower layer-to-layer voltages, and
lower magnet hot spot temperatures. Fewer magnet
subdivisions are needed.
• Quench back from the mandrel reduces the hot spot
temperature, but it may increase the internal voltage
and the layer-to layer voltage because the magnet
quench time constant is shorter.
• The resistance in series with the diodes is important.
More resistance yields lower internal voltages, lower
layer-to-layer voltages, and a lower conductor hot
spot temperature.
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Coupling Coil Conductor Selection
• The larger conductor results in lower quench hot
spot temperatures and fewer coil subdivisions.
• A larger conductor is faster to wind into the coil and
there are fewer leads brought out of the coil.
• The larger conductor carries a higher current, which
means the heat leak into the first stage is higher.
The resulting first stage temperature increase
increases the heat flow into the 4 K region.
• Even though the larger conductor is better from a
quench standpoint, the tracker conductor was
selected in order to reduce the total heat load. This
may allow the magnet to be cooled using one cooler.
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What about the AFC magnet conductor?
• The Lab G solenoid is a model for the AFC magnet.
The Lab G magnet has a conductor that is almost
identical to the tracker and coupling coil conductor.
• The AFC magnet quench protection system consists
of quench back plus a single diode and resistor pack
across each of the coils. The diode and resistor pack
can be located at 300 K, because each AFC coil lead
is brought out to 300 K.
• The tracker and coupling coil conductor is relatively
cheap and it fits the design of the AFC magnet very
well. The reduced filament size (41 microns) will
result in lower AC losses. Why not use the same
conductor as the other magnets in MICE?
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How much conductor is needed?
• Each tracker solenoid requires about 54 km of
conductor. Both tracker magnets use 108 km of
conductor. Four billets of conductor was purchased.
• Each coupling magnet will use about 81 km of the
tracker magnet conductor. The two MICE coupling
magnets will use about 162 km of tracker magnet
conductor. Eight billets of conductor will be
purchased for three coupling magnets.
• Each AFC magnet requires about 37 km of the
tracker magnet conductor. The three AFC magnets
will use about 111 km of tracker magnet conductor.
Expect to purchase four billets of conductor.
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MICE Conductor Summary
• The tracker magnet conductor was set to reduce the
magnet cost w/o affecting temperature margin.
• Rectangular conductor is better than round.
• It is always better to have a higher Cu to S/C ratio
and smaller filaments, but one should use a standard
conductor if possible. Jc and n are important.
• While a larger conductor is desirable for a quench
standpoint, a smaller conductor results in a magnet
with lower heat loads on both cooler stages.
• The coupling magnet conductor is the same as the
tracker magnet conductor. The conductor for the
AFC magnet can be the same too.
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