5.2 Critical State Model
79
(2) Magnetization
Here, we will estimate the magnetization for the processes of increasing and
decreasing magnetic field that were treated in the last subsection. Since there is no
effect of demagnetization, the magnetization can be simply calculated using (3.49).
In the initial process (0 ≤ H 0 ≤ H p ), a simple calculation leads to
M =
H
2
0
2J c d
− H 0 =
H
2
0
2H p
− H 0 .
(5.20)
For H 0 > H p , we have
M = −
1
2
J c d = −
1
2
H p .
(5.21)
Equation (5.21) represents the magnetization on the major magnetization curve.
When the external magnetic field is decreased from H m , the situation depends on the
value of H m . There are three cases; H m < H p , H p < H m < 2H p and H m > 2H p . We
treat the case of H m > 2H p . In the range of H m > H 0 > H m −2H p , the magnetization
is given by
M = −
2H p − H m + H 0
2
4H p
+
1
2
H p .
(5.22)
For H 0 < H m − 2H p , the magnetization is on the opposite major magnetization curve
and is given by
M =
1
2
H p .
(5.23)
The calculated results are shown in Fig. 5.11. The minor magnetization reaches
the major curve before H 0 is reduced to 0 under the present condition for H m . For
H m < 2H p , the minor magnetization reaches the major curve after H 0 is reduced to
0.
The critical current density is often estimated from the magnetization measurement. In the present analysis, the hysteresis width of the major magnetization curve
is calculated as
M = H p = J c d
(5.24)
using (5.21) and (5.23) (see Fig. 5.11). Hence, we have
J c =
M
d
.
(5.25)