Page 145 - Fundamentals of Magnetic Thermonuclear Reactor Design

Superconducting Magnet Systems Chapter | 5 127

with the MS operation data allow formulating the requirements of winding
SCs, including the optimal current density. Then, technical and economic
optimisation criteria can be used to define the requirements for the critical
characteristics of strands, superconducting cable design, cooling modes and
so on.
ITER coils produce a magnetic field of 5–13 Т. The critical current den-
2
sity for a NbTi SC of the PF and CCs and the CCs is close to 2900 A/mm at
a temperature of 4.2 K and a magnetic field of 5 T. The current density for a
2
Nb Sn SC of the CS and the TFCs should be more than 850 A/mm at 4.2 K,
3
12 T, and a limiting relative strain within 0.25%. The latter parameter sets
because of the brittleness of the Nb Sn intermetallic. The issues on the me-
3
chanical strength and stability of the ITER MS are discussed in greater detail
in Chapter 12.

5.3 PHYSICAL AND MECHANICAL PROPERTIES
OF SUPERCONDUCTORS
5.3.1 Flux Pinning BC 1

Superconductivity, as an ability of a material to carry electromagnetic energy
during quasi-state processes with zero dissipation, only shows up in weak
magnetic fields; with strengths lower than the critical field of type I SCs or
, of type II SCs. If a magnetic strength is higher than BC
the first critical field, B C 1 1
, it is thermodynamically favourable for the magnetic field to penetrate
B C 1
a SC in the form of flux filaments (fluxquantums) with normal-conducting
cores (cernels). Outside the flux filaments the SC is able to carry the transport
current without resistance. The current interacts with the flux filaments by
means of the Lorentz force F =× FL=j×B
j B. In ‘hard’ (non-ideal) type II SCs, the
L
fluxquantums are kept in place, as the Lorentz force is balanced by the pin-
ning force due to microstructural lattice defects (pinning centres). So long as
the F is lower than the pinning force F , there are no electrical resistance,
P
L
fluxquantums movement (flux) and electromagnetic energy losses are absent.
The F = F state is referred to as critical. At F > F , fluxquantums come into
L
P
L
P
movement producing electric field Е and transferring the SC into the resistive
state. In that state, the specific power of energy losses is j × E. These losses
are due to the generation of eddy currents in normally conducting cores of
fluxquantums, when they are moving.
The pinning force depends on the SC structure and temperature. In some
materials, such as Nb Sn, it also depends on the relative deformation. At the
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macroscopic level the information about the SC’s behaviour is acquired from
measurements of the SC’s voltage–amperage and voltage–temperature transient
characteristics (VAC and VTC, respectively). As one can see from Fig. 5.7, the
characteristics cover regions where the E field intensity smoothly increases at
the beginning of the SC transition to the resistive state.