92
5 Flux Pinning Phenomena
Fig. 5.21 The penetration
field (H p ) and the apparent
penetration field ( ˆ
H p )
observed for two series of
multi-filamentary Nb-Ti
superconductors [8]. The
solid lines show (5.57), and
the dashed lines are the
relationship H p = J c d f /2
to ˆ
H p = 3
2λ
0 /d f
2 H p , and ˆ
H p increases in proportion to 1/d f , when the filament
diameter decreases. The characteristic field ˆ
H p corresponds to the magnetic field
amplitude H m at which the H m dependence of the AC loss energy density changes
in Fig. 5.20. Thus, the filament diameter dependence of the AC loss energy density
can be seen in the behavior of ˆ
H p in Fig. 5.21. The magnetization curve for H m in the
intermediate region between H p and ˆ
H p is schematically shown in Fig. 5.22. It can
be seen that the magnetization width is very thin in comparison with the prediction
by the critical state mode, which explains the appreciable reduction in the AC loss
energy density. When H m further decreases, the magnetization at the peak field does
not reach the major magnetization curve, resulting in a much smaller AC loss energy
density.
The reversible flux motion surely occurs near the surface, independently of the
size of the superconductor, as shown in Fig. 5.15, when the field sweep direction
is changed. Nevertheless, the AC loss energy density in thick superconductors does
not take a small value but obeys (5.39), derived using the critical state model, when
an AC field of sufficiently small amplitude is applied. This may seem strange. In
Fig. 5.22 Closed
magnetization loop for
H p < H m < ˆ
H p . The dashed
line shows the prediction of
the critical state model
5 Flux Pinning Phenomena
Fig. 5.21 The penetration
field (H p ) and the apparent
penetration field ( ˆ
H p )
observed for two series of
multi-filamentary Nb-Ti
superconductors [8]. The
solid lines show (5.57), and
the dashed lines are the
relationship H p = J c d f /2
to ˆ
H p = 3
2λ
0 /d f
2 H p , and ˆ
H p increases in proportion to 1/d f , when the filament
diameter decreases. The characteristic field ˆ
H p corresponds to the magnetic field
amplitude H m at which the H m dependence of the AC loss energy density changes
in Fig. 5.20. Thus, the filament diameter dependence of the AC loss energy density
can be seen in the behavior of ˆ
H p in Fig. 5.21. The magnetization curve for H m in the
intermediate region between H p and ˆ
H p is schematically shown in Fig. 5.22. It can
be seen that the magnetization width is very thin in comparison with the prediction
by the critical state mode, which explains the appreciable reduction in the AC loss
energy density. When H m further decreases, the magnetization at the peak field does
not reach the major magnetization curve, resulting in a much smaller AC loss energy
density.
The reversible flux motion surely occurs near the surface, independently of the
size of the superconductor, as shown in Fig. 5.15, when the field sweep direction
is changed. Nevertheless, the AC loss energy density in thick superconductors does
not take a small value but obeys (5.39), derived using the critical state model, when
an AC field of sufficiently small amplitude is applied. This may seem strange. In
Fig. 5.22 Closed
magnetization loop for
H p < H m < ˆ
H p . The dashed
line shows the prediction of
the critical state model