Cable-in-conduit conductor optimization for fusion magnet applications Page: 3 of 7
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location of current connections and Joints, shape
factors, and required gaps or minimum thicknesses of
certain parts. In other words, reality 1s Introduced.
When this stage is completed, the design process
proceeds by separate and nearly Independent paths.
Mechanical Analysis and Design
In steps 4, 5, 6, and evaluation E2, mechanical
loads In the winding pack are considered in greater
detail, and the distribution of steel around the cable
fs varied to accommodate these loads. Steel
configuration 1s chosen Independently of the cable
Inside, since we do not consider Its load-bearing
capability. To achieve adequate support under
nonuni form load distribution, we often depart from the
simple, square conduit with a uniform wall thickness,
which 1s a typical CICC design. A logical modification
1s to add a heavy structural channel over a thinner,
helium containment sheath (Fig. 2). The stress
analyses of step 6 account for the mechanical response
of the entire magnet system as far as possible. If the
evaluation indicates changes 1n distribution of
structural steel around the conductor, we reiterate
steps 5 and 6; if more steel 1s needed, new Input Is
formulated to reiterate the conductor optimization
process, most likely as a new constraint on minimum
steel fraction In the winding pack.
Thermal Analysis and Design
In steps 4', 5', 6', and E2‘, we consider the
distribution of heat and modifications of the winding-
pack design to accoimnodate the distribution. Heating
may result from nuclear absorption or ac losses 1n the
superconductor; however, calculations to evaluate such
losses are beyond the scope of this paper. Geometry of
the flow path may be modified to better accommodate the
flow needed to remove the heat, while keeping the
helium and conductor temperature within acceptable
bounds 1n the critical regions of the coll. These
modifications may Include varying the hydraulic
diameter or the length of a flow path. Inlet
conditions (pjn, T^n) of the helium are also adjusted
to achieve the most desirable temperature and pressure
profile along the flow path for a given mass flow rate.
The flow analysis of step 6' Includes all the effects
of friction, fluid expansion, and kinetic energy
variation 1n the fluid [2]. Hand's helium properties
code HEPROP [3] as modified by Arp [4] 1s used to
provide calculated values of p and T at any point along
a flow path. If the evaluation of this part of the
design process Identifies problems that can be
accommodated by varying the flow or the state of the
Inlet helium, we reiterate steps 5' and 6'. If changes
to the cable geometry are required, we formulate new
Input for the conductor optimization process. The new
input may redefine the most critical region of the coll
(at least from the thermal prospective). Of course,
the combination of requirements Identified 1n each
analysis 1s examined (step E3) before the full
reiteration 1s begun.
We have described a process for designing large,
high-performance, superconducting magnet systems for
fusion applications. The process incorporates unique
features of the cable-1n-condu1t conductor design to
achieve Improved performance and to simplify the design
process. Examples of application of the design process
to the TF and PF magnet systems of TIBER II are given
1n companion papers at this conference [12,13].
Acknowledgments
This work was performed under the auspices of the
U.S. Department of Energy by Lawrence Livermore
National Laboratory under Contract W-7405-Eng-48.
APPENDIX
Stability Margin
The stability margin provided by a CICC Is the
amount of energy per unit volume of conductor from a
sudden perturbation that can be absorbed without the
conductor being quenched. This margin 1s determined by
the effective heat capacity of the coolant at any point
along the conductor and the temperature margin between
the conductor temperature under normal operating
conditions and the current-sharing temperature of the
conductor. For force-cooled conductors 1n general,
estimation of the stability margin may require detailed
calculations. For CICCs where heat transfer to the
bulk of the Interstitial helium coolant 1s sufficiently
good and rapid (see the constraint on current density
for good heat transfer), a relatively simple expression
can be used:
. V SHe Tc
5 ' . . JVcuc dw •
where if 1s the stability parameter (described below).
The second term In the denominator accounts for joule
heating 1n the conductor during the recovery process.
Since It Is usually quite small, a very simple
approximation 1s used, but one generally consistent
with experimental data If C * 50 x icf6 oi2/W. The
effective heat capacity of the helium ever the
teir^erature range Tfc to Tcs can be approximated by
s -fr ?He CD dT
He ' Tcs - Tb
fig. 2. Model conductor In which the external sheath
of the cable-1n-condu1t conductor has been
augmented by a structural steel channel
(dimensions 1n millimeters).
Stability Parameter
In the conductor optimization procedure, we do not
calculate the stability margin 1n detail for each
2
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Miller, J. R. & Kerns, J. A. Cable-in-conduit conductor optimization for fusion magnet applications, article, October 7, 1987; [Livermore,] California. (https://digital.library.unt.edu/ark:/67531/metadc1092389/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.