Thermal aspects of a superconducting coil for fusion reactor Page: 3 of 7
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insulated boundary conditions are assumed. The pro-
gram has been debugged and tested by its author. We
have run a few test cases and checked out the
convergence for different time steps and lattice
sizes. Because of the very small specific heat
of copper at cryogenic temperature, very small
time step has to be used initially. Variable time
steps was used to cut down the computer time.
To illustrate the different behavior between copper
and stainless steel during a quench, let us consider a
one-dimensional case with uniform current in copper.
(Fig. 4) The solutions with coarse grid lattice
agrees well wit, those obtained by fine grid lattice.
The temperature in the copper is nearly uniform and
drops very rapidly as one gets into stainless steel.
We note that estimates based on 77K4 (vs. 4K) as the
starting temperature gives more conservative (higher
temperature excursion) results. The results of
Figure 4 is misleading in that actually it is the
insulation which sees most of the temperature gradient,
as is evident from the temperature contour of a uniform
quench of'our coil (Fig. 5). Without insulation, the
temperature gradient will fail in the first few centi-
meters of stainless steel. As Teflon has an even
smaller thermal diffusivity as compared with stainless
steel, the temperature drop across it is even more
spectacular. Figure 5 says that a temperature
difference of more than 200K will develop across the
0.25 cm of Teflon in only 70 seconds. Clearly, Teflon
will see large thermal strain and thermal stress in
such a quench and it may soon crack.
One may simulate a non-uniform quench by assuming
that only one layer of conductor is normal and has
Joule heating. The current will again be approximated
as constant. For such a quench, we see both a large
local temperature gradient near the edge of the layer
which is normal and a temperature gradient in the
direction transverse to the layers. (Fig. 6) Our
result suggests that, however, very little time (a few
seconds) is needed before all the layers went above
the transition temperature, hence the quench really
should behave quite similar to a uniform quench. Of
course, thicker insulation, stainless steel inter-
leaving, and the presence of warm helium gas will tend
to slow down the heat conduction between layers.
Design Considerations for Thermal Protection
From the last section, we see that the combination
of rather extreme conditions (loss of coolant, protec-
tion circuit failure, failure in disconnecting power
supplies or other coils after quenching) could lead to
large temperature gradients in the magnet and the
insulation is likely to crack first. Various means
could be used to prevent such damages during a quench.
One possibility is to use heat drains.5 For our design,
if a thin layer (0.1 cm) of copper-like material (say,
anodized Al) is placed between the conductor and
insulation, then the heat input to the insulation
during a non-uniform quench is effectively diverted,
and the temperature gradient in the insulation is very
much reduced. (Fig. 7) Copper coating has been
suggested as a heat drain for the heat generated
in stainless steel due to neutron capture.6 Figure 8
shows that such copper coating (0.05 cm outside and
in the center of the bottom part of the stainless
steel coil case) is not effective in relieving the
temperature gradient generated in the stainless steel
by a uniform quench.
If power supplies (or other coils) continue to
pump energy into a quenched coil, eventually, the
temperature of the coil will exceed the melting point
of its components. A two components model (copper and
stainless steel) showed that for uniform quenching the
temperature in copper will exceed 300K in 75 seconds
(Fig. 9) and exceed melting point in 200 seconds
Hence the single most important factor in thermal
protection of fusion magnet is to avoid feeding energy
into coil after it has quenched. To achieve this, it
is necessary to adopt reliability concepts and
principles in the magnet protection circuitry design.
For example, manual discharge mechanism should be
provided, so the magnet operator would have a chance
to intervene in case the automatic protection system
failed. Power supplies may be disconnected after the
magnet has been charged up, and used only intermit-
tently afterwards. Redundant switches may be used
in the protection circuit. (Fig. 11) Provided that
no external source can feed energy into a quenched
coil, the energy stored in a cryostatically stable
fusion magnet could be safely handled by the enthalpy
of its copper content alone. (Temperature excursion
less than 100K).7
In conclusion, our results seem to indicate that
the type of thermal excursion which could lead to the
failure/rupture of a fusion magnet is not likely to
occur and can be prevented.
I am very grateful to W. D. Turner for showing me
how to use the HEATING-5 computer program and to L.
Dresner for helpful comments.
1. V. V. Altov, M. G. Kremdev, V. V. Sytchev and V. B.
Zenkevitch, "Calculation of Propagation Velocity
of Normal and Superconducting Regions in Composite
Conductor," Cryogenics, p. 420, 1973.
2. H. S. Carslaw, J. C. Jaeger, "Conduction of Heat
in Solids," Second Edition, Oxford Univeraity Press,
1959. See sections 2.5, 2.16 and 3.5.
3. W. D. Turner, "HEATING-4, An IBM 360 Heat Conduc-
tion Program," (Contract No. W-7405-eng-26)
Computer Science Division, Oak Ridge National
Laboratory, 1975. HEATING-5 is an updated version
of HEATING-4. Temperature-dependent heating rate
is allowed in HEATING-S.
4. J. Powell, et al., "Fusion Magnet Safety Studies
Program," Progress Report, Department of Applied
Sciences, Brookhaven National Laboratory,
5. H. Brechna, "Superconducting Magnets," p. 198. In:
Superconducting Machine and Device, 1973 NATO
6. P. N. Haubenreich, M. Roberts, (Editors), "ORMAX
FlBX, A Tokamak Fusion Test Reactor," Oak Ridge
National Laboratory, ORNL-TM-4634, p. D-71, 1974.
7, H. T. Yeh, "Can an EPR Size Coil be Self-
Protected?" unpublished memo, section 9,
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Yeh, H.T. Thermal aspects of a superconducting coil for fusion reactor, article, January 1, 1975; Tennessee. (digital.library.unt.edu/ark:/67531/metadc863082/m1/3/: accessed February 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.