To:
Alice Ying
Neil Morley
Thomas Sketchley
From: Robert Woolley
Possibilities
Date:
9 January 2000
Subject: Liquid Nitrogen Cooling
for LMMHD Toroidal Facility
at UCLA using all 24 TARA coils
Reference 1: R. Woolley, “LMMHD Toroidal Facility”, memo to Neil Morley and Alice
Ying, 1 December 1999.
Reference 2 : N. Simon, E. Drexler and R. Reed, Properties of Copper and Copper
Alloys at Cryogenic Temperatures, NIST Monograph 177, Feb. 1992
Summary
After listing non-cryogenic alternatives in a background overview, this memo provides an
initial conceptual discussion of possible liquid-nitrogen-cooled
options for an
experimental LMMHD Toroidal Facility, calculation results, and a concluding
recommendation.
Background Overview
As discussed in Reference 1, the RapidPowerTechnologiesInc. power converter to be
loaned to UCLA by PPPL has a “nameplate” rating for steady operation supplying up to
3000 amperes of dc current at up to 150 volts, thus developing a total power output of up
to 0.45 MW. It can be powered from a single existing 3-phase 480 vac outlet now in the
proposed experimental area without requiring any ac power upgrade. It may also be
possible to operate it a bit beyond its nameplate ratings.
TARA coils in the MegaLoop facility were operated up to 1500 amperes per winding
using cooling water from existing 120 psi chilled deionized water services. I estimate
5.75 volt steady-state voltage drop per winding at 1500 amperes with those coolant
conditions. There are 24 TARA coils at UCLA available for use in a LMMHD Toroidal
Facility, each with two 14-turn windings. A toroidal configuration of these 24 TARA
coils was depicted in Figure 6 of Reference 1 and is also repeated herein as Figure 6 of
this memo. If the 48 windings are interconnected to form two series strings of 24
windings each, the total estimated voltage drop at 1500 amperes per string would be 138
volts, well within the power converter’s ratings. If the two series strings are connected in
parallel as shown in Figure 5a, their total 3000 ampere current is also within the
converter’s ratings. This low-cost configuration would develop a steady toroidal field
varying from BTF=0.517 Tesla at the R=0.390 meter inner edge of the toroidal field
region, BTF=0.258 Tesla at the R=0.782 meter middle of the experimental region, and
BTF=0.171 Tesla at the R=1.176 meter outer edge of the toroidal field region. The power
converter also may be able to operate beyond its ratings up to 3600 amperes, which would
further increase each of these steady magnetic field values by 20 per cent.
R. Woolley
page 2 of 15
9 January 2000
It is possible to simply mount the 24 coils and their support structures on tables as per
Figure 6, connect them to the RapidPowerTechnologiesInc. power converter and to
water services, install toroidal containments to confine the liquid metal and experimental
equipment to affect and diagnose LM flow, and start experiments with BTF=0.258 Tesla
in the middle of the experimental region. However, there is interest in strengthening the
toroidal field, if possible and cheap, in order to permit liquid metal flow experiments
with the higher field levels more relevant for fusion. That interest motivates this memo.
There are merits to dispensing with the TARA coils entirely and building a toroidal field
system “from scratch” with parameters and characteristics more appropriate for the
experimental needs and for the proposed experimental area’s characteristics. The TARA
coils were not designed for use in a toroidal field system, and inspection of Figure 6
shows that most (over 73%) of the precious “inboard” region near the torus’ central axis
of symmetry is filled with air or structure rather than copper. Additional copper and a
different coil shape including nose wedging could reduce greatly power at the same
operating temperature and magnetic field. Also, the toroidal field system could be made
physically smaller, and the required electrical power would be reduced in direct
proportion to the linear size scale. The “from scratch” toroidal field design could also be
designed explicitly to use liquid nitrogen cooling, if desired, whereas the TARA coils
were designed for a water-cooled solenoid application. It may be possible for such a new
design to permit LMMHD experiments with a toroidal field strength of several Tesla.
However, this memo does not further consider such options.
As detailed in Reference 1, TARA coil data sheets and simple calculations support the
view that they can be safely operated continuously in steady-state with up to 3664
amperes dc current in each winding, using high pressure chilled deionized water as coil
coolant. (A “booster pump” would need to be installed to raise water supply pressure to
about 300 psi.) A toroidal coil arrangement including all 24 TARA coils would then
develop a steady toroidal field varying from BTF=1.263 Tesla at the R=0.390 meter inner
edge of the toroidal field region, BTF=0.630 Tesla at the R=0.782 meter middle of the
experimental region, and BTF=0.418 Tesla at the R=1.176 meter outer edge of the toroidal
field region. The coils could be electrically connected in series as shown in Figure 5b.
The total coil system dc voltage required is estimated to be 714 volts, so the total power
requirement would be (714)(3664)=2.62 MW. At the present time, the proposed
experimental area’s ac power capability cannot support a 2.62 MW load, and
furthermore, no electronic power converter has been purchased or “scrounged” to convert
2.62 MW of ac power to the proper dc voltage and current levels. Funds would need to
be spent to upgrade the ac power in the area. In addition, it would be necessary to
purchase or construct electronic power equipment to convert 2.62 MW of ac power to the
proper dc voltage and current levels. This ac power approach is being considered but is
not the subject of this memo.
Alternatively, dc power (714 volts, 3664 amps) could be provided for pulsed operations
of the LMMHD Toroidal Facility via a bank of electrochemical energy storage batteries,
such as the lead-acid batteries used to power WW2 submarines and modern electrical
R. Woolley
page 3 of 15
9 January 2000
vehicles or those used to start car or truck engines. The batteries could be recharged
slowly between pulses, thus avoiding the expense of upgrading the experimental area’s
ac power. A “booster pump” to increase coolant water pressure could be avoided if the
designed pulse duration were sufficiently brief. This approach would require purchasing
the batteries and their charging systems, devoting space for them and for their chemical
safety features, and constructing electronic controls for their use. This dc battery
approach is being considered but is not the subject of this memo.
Selection of a design approach among these and the liquid nitrogen cooled approaches
should be based on cost/risk/benefit considerations, which have not yet been evaluated.
Liquid Nitrogen Cooling Approaches
Other approaches would cryogenically cool the TARA coils in order to reduce their
electrical resistance and thus reduce their maximum dc voltage drops and power at high
current, which is directly proportional to electrical resistance. The cheapest and least
dangerous possible cryogen is liquid nitrogen. A large liquid nitrogen capability is
available near the proposed experimental area and could likely be pressed into service at
low cost. Typical commercial electrical copper’s electrical resistance is reduced below
its room-temperature value by a factor >7 at liquid nitrogen’s normal boiling point
temperature, or by a factor >12 at liquid ntirogen’s freezing point temperature, depending
on copper purity. However, the dc power supply cost reduction benefit of using
cryogenic cooling is limited not by the cold initial temperature but by the maximum
transient coil temperature occuring during high field operation. Power supply cost is not
reduced if powered coils are allowed to approach room temperature at full current and
field.
Two fundamentally different cryogenic approaches are
1)adiabatic pulsed (inertial) operation,
and
2)thermally steady-state active cooling.
Conceivable pulsed designs would precool the coils prior to each pulse, then remove any
liquid nitrogen which might otherwise create problems by boiling, and only then power
the coils for a time duration limited by the adiabatic heatup of the copper coil windings.
Conceivable actively-cooled designs would pump pressurized liquid nitrogen through
TARA coil cooling passages throughout high field operations, and would restrict
maximum coil currents to avoid internal boiling.
It should be noted that both approaches require more technical sophistication than
typically required for steady-state water cooling, since two-phase cryogenic systems
require sequencing through distinct states with controls based on state feedback (e.g.
pressure & temperature) or on precise timing, and since cryogens have serious safety
issues.
R. Woolley
page 4 of 15
9 January 2000
Pulsed Operation
Figures 1 and 2 describe 24 TARA coils operating adiabatically at 3000 amperes, the
“nameplate” dc output rating of the RapidPowerTechnologiesInc. power converter. In
this circuit, both windings in each TARA coil are connected in series as shown in Figure
5b, so that 3000 amperes flows in every winding. The estimated 24 milliHenry system
inductance and the available 150 volt forcing voltage results in an initial current ramp rate
of 6250 amperes per second, and the full 3000 ampere “flattop” current is reached within
the first second. The toroidal field then varies spatially from BTF=1.034 Tesla at the
R=0.390 meter inner edge of the toroidal field region, BTF=0.516 Tesla at the R=0.782
meter middle of the experimental region, and BTF=0.342 Tesla at the R=1.176 meter
outer edge of the toroidal field region. The initial copper temperature is 63.156°K,
nitrogen’s “triple-point” freezing temperature, the coldest temperature feasible using
liquid nitrogen technology. The initial voltage required from the power converter to
overcome resistive voltage drops in 48 series-connected windings operating at 3000
amperes is only 43.0 volts, well within the converter rating. After 45 seconds of operation
the copper temperature reaches liquid nitrogen’s normal boiling point and the voltage
drop reaches 68.2 volts. After 145 seconds of 3000 ampere current, the copper
temperature reaches 115°K and the resistive voltage drop reaches 150 volts, the power
converter’s nameplate rating. If the converter can be operated beyond its rating up to 166
volts, an additional 14 seconds at 3000 amperes raises copper temperature further to
122°K. After this 159 seconds, the power convertor cannot develop enough voltage to
maintain 3000 amperes, but could either continue to drive a current drooping over time
for several additional minutes, or could be shut down.
The use of nitrogen subcooling would require a suction pump to reduce the liquid
nitrogen pressure below 1 atmosphere. No special cryogenic refrigeration plant would be
required. The pressure reduction automatically reduces liquid nitrogen’s boiling point
temperature below its normal boiling point. Some liquid nitrogen boils as the pressure is
reduced, thus evaporatively cooling the remaining liquid. Nitrogen gas from the boiloff
is compressed in the suction pump and exhausted to the atmosphere. By the time the
pressure of the remaining liquid nitrogen has been reduced to 1/8 atmosphere (the triplepoint pressure), its boiling point has been reduced all the way to reach its 63.156°K
freezing point. The liquid pressure can then be quickly returned to 1 atmosphere or more
without appreciably increasing liquid temperature. The total yielded quantity of
subcooled liquid nitrogen near 63.2°K resulting from this process can exceed 80% of the
initial liquid mass at nitrogen’s 77.395°K normal boiling point.
If liquid nitrogen subcooling were not employed, the initial copper temperature would be
77.395°K. It would then be necessary to modify Figures 1 and 2 by deleting their initial
45 seconds. The resulting experiment pulse at 3000 amperes could be maintained for
145-45=100 seconds before the voltage reached 150 volts, or perhaps for 114 seconds
until the voltage reached 166 volts.
Figures 3 and 4 describe all windings in 24 TARA coils operating adiabatically at 3600
amperes, a current level to which the converter was tested on its highest tap setting even
R. Woolley
page 5 of 15
9 January 2000
though beyond its nameplate rating. This provides a pulsed toroidal field which varies
from BTF=1.241 Tesla at the R=0.390 meter inner edge of the toroidal field region,
BTF=0.619 Tesla at the R=0.782 meter middle of the experimental region, and BTF=0.411
Tesla at the R=1.176 meter outer edge of the toroidal field region. The initial voltage
required from the power converter to overcome resistive voltage drops is only 51.0 volts,
well within its rating. After 34.6 seconds of operation the copper temperature reaches
liquid nitrogen’s normal boiling point and the voltage drop reaches 81.9 volts. By the
time 93 seconds have passed, the copper temperature reaches 104.7°K and the total
resistive voltage drop reaches 166 volts, the maximum output voltage to which the
power converter has been tested (but beyond its ratings).
Explanation of Calculations
Adiabatic and spatially uniform electrical heating of a copper conductor obeys the rule
dT
(1)
(T)C P (T)
 (T) J 2 (t)
dt
where T is copper temperature, t is time, J is the electrical current density in the copper, 
is copper’s density, CP is copper’s specific heat,  is copper’s electrical resistivity, and
where the symbols (T) and (t) signify functional dependence on copper temperature or on
time, respectively. To solve Equation (1), it is customary to define the following
function of temperature:
T
(S)C P (S)
G(T)  
dS
(2)
(S)
T
REF
where S is a dummy temperature variable used to define the integral and where TREF is an
arbitrary reference point temperature. Since the integrand in Equation (2) is positive at
all temperatures, the G(T) function is monotonic and therefore possess an inverse
function, G—1(). With this definition of G(T) and its inverse, the solution to Equation (1)
is written

t

1
(3)
T(t)  G G(T(t 0 ))   J2 (t)dt 


t0
If the current remains constant throughout the pulse time period, this becomes
1
2
(4)
T(t)  G G(T(t 0 )) (t t 0 )* J


If we choose the G(T) function’s arbitrary reference temperature to be the initial
temperature and define the initial time as t0=0, the following simple form results:
1
2
(5)
T(t)  G t *J


The procedure followed herein was to numerically calculate G(T) by evaluating Equation
(2) in order to allow applying Equation (5). The numerical results are graphed in Figure
10. The reference temperature for the Equation (2) integration was chosen to be liquid
nitrogen’s triple-point temperature, 63.156°K, the coldest feasible initial copper
temperature for a system cooled by liquid nitrogen. Kaleidagraph™ 3.0 software for
MacIntosh was used for all calculatons and plots. Reference (2) was the source of
information for the temperature range from 50°K to 300°K, and an engineering handbook
provided further copper information up to 500°K. Compiled data on copper’s linear
R. Woolley
page 6 of 15
9 January 2000
coefficient of expansion, (T), was fit by cubic splines, integrated, and then used along
with copper’s room temperature density to calculate density(T) (graphed in Figure 7).
For the CP(T) information, at 10°K intervals from 50°K to 300°K the medians of
previously published CP measurements compiled in Reference 2 were selected, along
with other measurements of CP up to 500°K. The set was fitted by cubic splines and
interpolated to give CP at 1°K intervals. For the (T) information, Reference (2)
provided an algebraic formula dependent on temperature, with eight specified coefficients
which had been fitted to measurements referenced but not themselves presented. It
should be mentioned that the formula also depended on a ninth parameter called the RRR
and defined as the “residual resistance ratio”,  (273°K)/ (4°K). Reference 2 does not
specify a value for the RRR parameter, but states “Recent measurements of the RRR of
copper that met the C10200 specification ranged from 5 to 520.” I used RRR=51, the
geometric mean of that range. Because that value may not reflect the copper used in the
TARA coils, the actual heatup behavior may differ a little from the predictions of this
memo.
Another useful graph results from plotting (T) vs. G(T) and is shown in Figure 11. The
Figures 2 and 4 graphs were obtained from Figure 11 by appropriately changing scales,
just as the Figures 1 and 3 graphs were obtained from Figure 10 by changing scales and
swapping axes.
Actively-Cooled Operation
Thermally steady-state liquid nitrogen active cooling withdraws liquid nitrogen from a
Dewar storage reservoir and exhausts nitrogen gas to the external environment during full
field magnet operation. It can operate continuously until the supply of liquid nitrogen
has been entirely consumed. A system for maintaining thermally steady-state liquid
nitrogen actively-cooled operation is sketched in Figure 12, which omits features required
for initial cooldown from room temperature. The system evaporatively cools liquid
nitrogen to its 63.156°K triple point, pumps the liquid through the TARA coils with
sufficiently high pressure to inhibit internal boiling, evaporatively cools the exiting liquid
back to its normal boiling point, and heats the exhaust gas before safely releasing it into
the environment.
It is useful to consider the 24 TARA coils operated at 3600 amperes in each winding, a
current level to which the RapidPowerTechnologiesInc. power converter was tested on
its highest tap setting even though beyond its nameplate rating. This provides a toroidal
field which varies from BTF=1.241 Tesla at the R=0.390 meter inner edge of the toroidal
field region, BTF=0.619 Tesla at the R=0.782 meter middle of the experimental region,
and BTF=0.411 Tesla at the R=1.176 meter outer edge of the toroidal field region.
Calculations indicate liquid nitrogen consumption including subcooling would be about
1.2 gallon per second. A 10,000 gallon Dewar could provide steady full-field operation
for over 2 hours.
The large liquid nitrogen Dewar storage reservoir, T1, is located outdoors. Liquid and
gaseous nitrogen in tank T2 is maintained at atmospheric pressure in saturation
R. Woolley
page 7 of 15
9 January 2000
conditions at its normal boiling point, 77.395°K. Two nitrogen streams enter tank T2
and two other streams leave it. The pressurized, super-heated liquid nitrogen stream
emerging from TARA coil cooling passages flows through pressure-reduction valve V3
and then enters tank T2 as a mixed two-phase stream of liquid nitrogen and gaseous
nitrogen at atmospheric pressure and 77.395°K. The liquid and gas separate in tank T2
under the influence of gravity. A “makeup” flow of fresh liquid nitrogen from the Dewar
storage reservoir, T1, flows in through valve V1, which is feedback-controlled to regulate
the liquid/gas level height in T2. Atmospheric pressure nitrogen gas flows out of T2
without hindrance to the nitrogen exhaust heating system. Liquid nitrogen flows out from
T2 though pressure-reduction valve V2.
Tank T3 contains liquid and gaseous nitrogen maintained in saturation conditions slightly
above nitrogen’s triple-point 1/8 atmosphere pressure and 63.145°K temperature. The
pressure conditions are maintained by feedback control of the variable-speed suction
pump, P1, whose outlet is directed to the nitrogen exhaust heating system. The T3
temperature follows automatically from the thermodynamic behavior of nitrogen. Valve
V2 is feedback conrolled to regulate the liquid/gas level height in T3. Tank T3 is
elevated to provide some of the required pressure reduction from 1 atmosphere to 1/8
atmosphere via gravity and to increase the pressure at the suction inlet location for pump
P2.
Pump P2 is a variable-speed liquid nitrogen pump which forces liquid nitrogen through
the TARA coil cooling passages. If 116 gpm of 65°K liquid nitrogen is forced into the
coils carrying 3600 amperes, simple calculations estimate a liquid nitrogen exit
temperature of 90°K, and estimate the pressure drop as 140 psi. An exit pressure of 75
psia is sufficient pressure to avoid internal boiling for temperatures up to 95°K. Thus a
maximum capability of 140+75=215 psi at 120 gpm is adequate for pump P2. Internal
boiling is avoided via the action of pressure reduction valve V3 which produces the
pressure difference between the coils’ outlets and tank T2. The speed of punp P2 and
the modulation of valve V3 need to be controlled jointly as functions of the coil current
level and feedbacks from the measured liquid nitrogen flow rate, the coil outlet
temperature, and the coil outlet pressure.
The nitrogen exhaust heating system depicted in Figure 12 is shown with two subsystems.
The approximately 800 liters/second of 77.395°K cryogenic nitrogen gas is first directed
into an outdoor enclosure with impervious side-walls, where it is confined because it is
>4 times heavier than air. Inside the enclosure a commercial “snowmaker” water spray
and fan like those used at ski resorts produces artificial snow. This cheaply heats the
nitrogen exhaust to 273°K, eliminating cryogenic hazards to personnel. However, the
warmed gas leaving the enclosure (3300 liters/second) is still depleted in oxygen.
Therefore, the gas exit duct on top of the enclosure includes an electrical or combustion
heater, the second subsystem, to heat the exiting gas from 273°K to a temperature several
degrees warmer than the prevailing outdoor air temperature. The exiting warmed
nitrogen is then more bouyant than air and rises away from populated ground level
R. Woolley
page 8 of 15
9 January 2000
regions, providing time for its safe dispersal. The accumulated snow is removed or
allowed to melt between pulses.
Other Issues Introduced by Liquid Nitrogen Cooling
Even though release of the liquid nitrogen boiloff into the environment can be safely
accomplished, there are significant safety and technical issues related to the LMMHD
Toroidal Facility itself. Safety issues arise because of the following phenomena:
(1) Accidental exposure of human flesh to liquid or gaseous cryogens or to
cryogenically cold surfaces can cause serious injury.
(2) Violent explosion caused by pressure build-up when confined liquid nitrogen
boils as it warms up could cause serious injury.
(3) Nitrogen leaks can deplete breathable oxygen in the experimental area,
possibly
causing fainting and/or serious injury.
Other technical issues arise because of the need to provide thermal insulation and
humidity/moisture barriers. If the coils could be cooled to liquid nitrogen temperature
while exposed to room air, their surfaces would quickly become covered by a thick layer
of frost, containing frozen water from the air’s humidity and also “dry-ice” frozen carbondioxide from the air. This situation can be avoided in liquid nitrogen cooled situations by
providing a thick layer of insulation and pure dry nitrogen around the coils and covering
that layer by a”cryostat” gas barrier to keep out moisture and gases that might condense.
Putting thermal insulation and a cryostat barrier around the TARA coils would reduce
space for the LMMHD experimental region from the space available in a roomtemperature approach. It would reduce access to the experimental region through the
spaces between coils which would be narrower due to insulation around each coil. The
insulation also would likely interfere with making the LMMHD facility easily
disassembled, which has been identified in various telephone discussions as a desired
feature to support experiments uning different coil configurations.
Another technical issue concerns cooldown from room temperature. If liquid nitrogen is
forced into the end of an initially warm coolant channel, it instantly boils while cooling
the adjacent copper. If that cooling process is continued, enormous thermal temperature
gradients will develop inside the TARA coils during the cooldown. It is not clear
whether the TARA coils would be damaged by the resulting mechanical stresses. But
there is no way to avoid such extreme temperature gradients if liquid nitrogen is
introduced directly into the coils. An alternative approach would be to cool the TARA
coils from room temperature using initially a flow of cryogenic nitrogen gas resulting
from controlled boiloff. This approach could gradually and uniformly reduce coil
temperature to, say, 150°K, after which liquid nitrogen would be introduced to lower
temperature further.
There is also a concern as to whether the TARA coils are compatible with liquid nitrogen
temperature operations, since they were not designed for liquid nitrogen. It seems likely
that they are OK, but their insulation system may have a significantly different thermal
expansion coefficient that the coils’ copper. I do not have any information about the
R. Woolley
page 9 of 15
9 January 2000
TARA coil’s insulation system material and its behavior at liquid nitrogen temperature.
It seems prudent to obtain and review that information before proceeding further toward a
liquid nitrogen cooled design using TARA coils.
Concluding Comments
A steady-state water-cooled LMMHD Toroidal Facility can be built using available
equipment at near-zero cost, and could develop about 0.3 Tesla steady toroidal magnetic
field at the R=78 centimeter middle of the large toroidal region available for liquid metal
experiments. The field would exhibit its usual 1/R variation in strength, and so would
range between 0.2 Tesla to 0.6 Tesla within the toroidal region.
This memo has discussed alternative possibilities of using liquid nitrogen cooling to
strengthen the magnetic field obtainable using the same TARA coils and the same power
converter electronics. Using liquid nitrogen cooling, the achievable magnetic field
strength during a pulse can be doubled over the steady-state field obtainable with water
cooling. For adiabatic cooling schemes, the pulse duration could be in the range from 1
minute to 2.5 minutes, depending on details. For active cooling schemes, the pulse
duration could be measured in hours. Costs have not been quantified, but significant
costs, complexity, and risks would surely be involved in liquid nitrogen cooling of the
TARA coils.
This memo has not explored the possibilities for a liquid-nitrogen-cooled LMMHD
Torodial Facility using smaller, more optimized coils, designed and made “from scratch”
. Significantly higher toroidal field strengths may become possible and economic. It
seems prudent to explore the possibilities for significantly higher toroidal field strengths
while constructing and initially operating a steady-state water-cooled facility using TARA
coils.
R. Woolley
page 10 of 15
9 January 2000
Figure 1: Adiabatic Heatup of TARA Coils @ 3 kA
(Copper Temperature vs. Time)
400
350
°K Temperature
300
250
200
150
100
77.395°K=Nitrogen's Normal Boiling Point at 1 atmosphere
63.156°K=Nitrogen's Triple Point Freezing Temperature
50
0
0
50
100
150
200
250
300
Seconds at 3000 Amperes (ESW)
350
400
Figure 2: Adiabatic Heatup of TARA Coils @ 3 kA
(Total Voltage of 24 Series Coils)
700
600
Volts
500
400
300
200
166 V PS extension
150 V PS Rating
100
0
0
50
100
150
200
250
300
Seconds at 3000 Amperes (ESW)
350
400
R. Woolley
page 11 of 15
9 January 2000
Figure 3: Adiabatic Heatup of TARA Coils @ 3.6 kA
(Copper Temperature vs. Time)
400
350
°K Temperature
300
250
200
150
100
77.395°K=Nitrogen's Normal Boiling Point at 1 atmosphere
63.156°K=Nitrogen's Triple Point Freezing Temperature
50
0
0
50
100
150
200
250
300
Seconds at 3600 Amperes (ESW)
350
400
Figure 4: Adiabatic Heatup of TARA Coils @ 3.6 kA
(Total Voltage of 24 Series Coils)
700
600
Volts
500
400
300
200
166 V PS extension
150 V PS Rating
100
0
0
50
100
150
200
250
300
Seconds at 3600 Amperes (ESW)
350
400
R. Woolley
page 12 of 15
9 January 2000
• •
•
•
•
•
• •
• •
• •
Figure 5a: Series/Parallel Electrical Circuit using 24 TARA Coils
•
•
•
• •
•
•
•
• •
• •
DC +
Power Supply
• •
• •
• •
•
•
•
•
•
• •
•
•
•
• •
• •
• •
• •
• •
• •
•
•
••
• •
• •
Figure 5b: Series Electrical Circuit using 24 TARA Coils
•
•
••
• •
• •
• •
• •
• •
• •
••
•
•
• •
•
DC +
Power
Supply
•
•
•
•
•
••
• •
• •
••
R. Woolley
page 13 of 15
9 January 2000
Figure 6: 24 TARA Coil Configuration
.
1 meter
R. Woolley
page 14 of 15
9 January 2000
Figure 7: Copper Density vs. Temperature
9050
Kg/m
3
9000
8950
8900
8850
0
100
200
300
°K Temperature
400
500
Figure 8: Specific Heat of Copper vs. Temperature
(Curvefit of compiled measurements)
500
Cp
300
J/(kg•°K)
400
200
100
0
0
100
200
°K Temperature
300
400
500
R. Woolley
page 15 of 15
9 January 2000
Figure 9: Resistivity vs Temperature of OFHC Copper
35
Resistivity
30
25
Nano-Ohm meter
20
15
10
5
0
0
100
200
°K Temperature
300
400
500
Figure 10: Calculated Copper Heatup Function G(T) vs. T
10
G(T) Amp
2
sec meter
-4
/ 10
16
12
8
6
4
2
0
0
100
200
300
°K Temperature
400
500
R. Woolley
page 16 of 15
9 January 2000
Figure 11: OFHC Copper Resistivity vs "J2t"
starting from LN2 Triple-Point Temperature
Nano-Ohm-Meter
Cu resistivity
30
25
20
15
10
5
0
0
2
4
6
2
G(T) Amp
sec meter
-4
8
/ 10
16
10
12
R. Woolley
page 17 of 15
9 January 2000
Fill
warmed
gas
release
Liquid
Nitrogen
Storage
Dewar
additional
heating
water
spray
T1
pressure
control
1 atm
P1
V2
T3
0.125 atm
V1
T2
1 atm
P2
48 PARALLEL
COOLING PASSAGES
in 24 TARA COILS
Figure 12: Thermally Steady-State Active Cooling Using
Subcooled Liquid Nitrogen
V3
5 atm 1 atm