High Temperature Superconducting Magnetic Levitation

7.6 Three-dimensional modeling and simulations Ë 241

Fig. 7.16:Geometrical modeling of the 3D simulation of

the HTS Maglev system.

described in Fig. 7.16. The virtual conductivity of the HTSC is calculated by

1

휎sc

=|Esc|

|Jsc|

, (7.51)

whereEscandJscare the electric field and current density of the HTSC, respectively.
According to theE-Jexponent power law (see Eq. 7.14), the expression to calculate the
conductivity is

1

휎sc

=|Esc|

|Jsc|

=Ec0

Jc

œ|Jsc|

Jc



n− 1

. (7.52)

Based on Ampère’s law [see Eq. (7.1)], we have

Jsc,xx̂+Jsc,yŷ+Jsc,zẑ=¤휕Hz

휕y

−

휕Hy

휕Hz

−

휕Hy

휕Hz

¥x̂+œ휕Hx

휕z

−휕Hz

휕x

ŷ

+¤

휕Hy

휕x

−휕Hx

휕y

¥ẑ. (7.53)

Therefore, the three components of the supercurrent can be expressed in terms of the
magnetic field as follows:

. (^66)
(^666)
(^66)

(^66)
(^666)
(^66)
F
Jsc,x=
휕Hz
휕y −
휕Hy
휕z,
Jsc,y=휕Hx
휕z
−휕Hz
휕x

,

Jsc,z=

휕Hy

휕x

−휕Hx

휕y

.

(7.54)

The anisotropic feature of the critical current density in the HTSC is considered in
the 3D modeling by assuming that the critical current density along thec-axisJcc
is one third of the critical current density within thea-bplaneJabc [47]. In order