Page 146 - Fundamentals of Magnetic Thermonuclear Reactor Design

128 Fundamentals of Magnetic Thermonuclear Reactor Design

FIGURE 5.7 Normalised actual (A) and idealised (B) VACs and VTCs of ‘hard’ type II SCs. SS,
the superconductive state; RS, the resistive state; NS, the normal state.

5.3.2 Critical Characteristics
A creep (flow ‘creeping’) precedes a settled flow of fluxquantums. The
creep occurs when a flux flow overcomes ‘weak’ pinning centres, but be-
comes captured by stronger ones. The resulting electric field is difficult to
discern due to fluctuations and noises. The transition of a ‘hard’ SC to the
resistive state is actually associated with the appearance on the sample of
consistently detectable electric field strength, E . This point corresponds
С
to the SC critical current, I , current density, j , and current sharing tem-
C
C
perature, T , at which current redistribution between the SC and the ma-
CS
trix begins. The E value is generally taken to be equal to 0.1 µV/cm and
С
1 µV/cm for low-temperature and high-temperature SCs, respectively. The
critical characteristics are the relationships between critical current density,
j , and three variables: magnetic field intensity, temperature and relative
C
deformation.
In the past few decades, extensive investigations have been carried out to pa-
rameterise the NbTi and Nb Sn SCs using the concept of normalised magnetic
3
ε
/
T
b=B/BC (T,ε) field, b = B B ( ,), and normalised temperature, t = T/T (0,ε). Obtained
C
2
C 2
ratios describe the critical characteristics of commercial SCs quite accurately
(Table 5.5) [2,3].
Examples of calculated critical characteristics for a Nb Sn SC are shown in
3
Figs 5.8 and 5.9.
The ratio of the critical current density (Fig. 5.8) to the corresponding value
at the SC zero deformation was used for this value normalisation. These equa-
tions allow to take into account deviations of the j temperature dependence of
C
T
T
jCT=jCT TC−T/TC−T 0 the applied SCs from the linear form, j () = j ( )( T − T) ( T − T ), which
C
0
0
C
C
C
0
is commonly found in the technical superconductivity literature.
To summarise, the Maxwell equations with the coupling equation replaced
with a SC VAC can be used in engineering applications to describe quasi-sta-
tionary electromagnetic fields inside ‘hard’ type II SCs.