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Thermal stability of
superconducting magnet
system in a tokamak
Dr hab. inż. Leszek Malinowski, prof. PS
Dr inż. Monika Lewandowska
Elevation of the ITER magnet system
TF coil conductor
PF coil
conductor design
CS coil conductor
Conductor quantities for ITER magnets
Heat loads
Thermal stability
• Conductors made of pure superconducting material
are thermally unstable
• Cables constituted of the superconducting material
embeded in the normal metal can operate stable.
Full stabilization
 I max 
c R
 
  1
hPTc  To 
 Ic 
Imax - maximum stable operating current, R - normal state resistance, h - heat transfer
coefficient, P - cooled perimeter, Tc - critical temperature, To - coolant temperature.
Main disadvantage of fully stable wires is large
amount of stabilizer. This implies:
• low overall current density of the conductor
• large size and big cost of a superconducting device
Modern superconducting wires are partly stable.
It implies limited amount of energy which can be
dissipated in a cable without disturbing its safe operation.
Critical energy
E  Ecr
E - energy of dissipation
Ecr - critical energy of the conductor.
Critical energy - the minimum energy of the thermal
disturbance destroying the superconductivity
Mathematical model of normal zone
u   u 
 a   g   su  q
x x  x 
 Tn 
V 
 h
u   ph 
T 
 h
 I e 
Tn - temperature of the n thermal component
Vh - volumetric flow in the h cooling channel
ph - pressure in the h cooling channel
Th - temperature in the h cooling channel
Ie - current in the e conducting component
Main goals of studies and anticipated results
• Identification and quantification of energy
disturbances and heat sources in superconducting
magnet system in a fusion reactor.
• Analysis and modelling of heat transfer
phenomena in cable-in-conduit-conductors
(CICC) used in fusion reactor magnets.
• Development of an analytical model of a normal
zone in CICC.
• Formulation of stability criteria for CICC.
• Performance of sample calculations and validation
of the results by comparison with experimental

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