222 Ë 7 Numerical simulations of HTS Maglev
whereJc0is the zero-field critical current density depending on the prescribed electric
field criterionEc, andB 0 represents a critical magnetic flux density for which the
critical current density is halved.
7.3.2Anisotropy
The special microstructure of cuprate-based oxide HTSCs, which consists of the
alternating stack of superconductive CuO 2 layers and almost insulating block layers,
results in a remarkably anisotropic behavior in the present HTSC family [38]. Due to
this anisotropic behavior arising from intrinsic pinning and other defects in the HT-
SCs, flux-line curvature will always occur in HTSCs in the presence of a magnetic field.
Consequently,Jcin HTSCs is anisotropic and strongly dependent on the orientation
of the applied magnetic field [39]. Namely, the value of the critical current density
flowing in thea-bplane,Jabc , is larger than that along thec-axis,Jcc[40].
7.4 Calculation of the magnetic field of PMG
7.4.1Two-dimensional case [14]
In the two-dimensional case, it is assumed that the PMG extends infinitely along
the forward direction of the HTS Maglev vehicle, the non-uniform magnetic field
generated by the PMG can be calculated through the combined contribution of each
PM therein, via an analytic model established by resorting to the surface current
model [41]. Using a vertically magnetized PM as a representative, the cross-sectional
view of the surface current model for the designated PM of width 2wand thickness
dis schematically drawn in Fig. 7.1, with two sheet currents counterflowing near the
marginal parts. If the PM is supposed to be magnetized uniformly with magnetization
M=M 0 z, the volume current density is null due to the zero gradient ofMacross
they-zplane and only the surface current density, estimated byjs=M×nremains.
The surface current density is equal toM 0 xand−M 0 x, respectively, for the left and
right parts, as marked in Fig. 7.1. In this way, the problem is reduced to solving for the
magnetic field of two infinitely long current sheets of heightdwith opposite direction
and separated by a dimension of 2w. In this case, the magnetic vector potentialA,
defined asB=∇×A, at point (y,z) due to the combined contribution of the sheet
current element dI 1 =jsdz耠of the left one and dI 2 = −jsdz耠of the right one is given by
dA=¤휇^0 M^0
4 휋ln(y−w)(^2) +(z−z耠) 2
(y+w)^2 +(z−z耠)^2
dz耠¥x. (7.18)