7.6 Three-dimensional modeling and simulations Ë 243situations. Considering the situation of a cubic-shaped HTSC in a non-uniform applied
magnetic field generated by the PMG. The boundary condition between the HTSC
and the dielectric subdomainΩ 1 region is continuity:
휇 1 H 1 n=휇 2 H 2 n. (7.61)The outer boundary of subdomainΩ 2 is a dynamic boundary described by a time-
dependent function:
HΩ 2 (r,t)=fΩ 2 (r,t), (7.62)where the function offΩ 2 (r,t) describes how the non-uniform external magnetic fields
changes with time at the outer boundary of subdomainΩ 2.
7.6.1.2Example of applications: levitation force simulation of HTSC over a
monopole PMG with different cross-sectional configuration
In this section, the proposed numerical method will be applied to study the in-
fluence of the cross-sectional configuration of a monopole PMG on the levitation
forces of a HTSC above the PMG. For the 3D modeling, we consider a cylindrical-
shaped HTSC, which is levitated above a monopole PMG, as shown in Fig. 7.17. The
computational region involves two subregions: R1 of the air domain and R2 of the
HTSC domain.
Based on the proposed 3D method in this section, the levitation forces of a HTSC
over a monopole PMG are simulated. The influence of the cross-sectional configurati-
on of the PMG on the levitation forces is numerically estimated by a set of simulations.
During the simulation, a cylindrical HTSC is used with a dimension of 30 mm in
diameter and 15 mm in height. The calculation parameters areM 0 =9.6× 105 A/m^2 ,
Jc0= 8 × 107 A/m^2 ,E 0 =1.0× 10 −^4 V/m, andn=21. For theE-Jpower law used in these
simulations, the effect of the flux creep is related to the numbern. The shape of
the magnetization loop of the HTSC is determined by its flux creep effect. For HTS
materials,nusually varies between 5 and 25. According to Brandt’s Assumption [34],
whenn→∞, theE-Jpower evolves to the Bean model. For a HTS slab, the value ofn
is dependent on the magnitude of magnetic field and its angle to the top face. For bulk
YBCO, usuallyn=21 is a typical case for theE-Jpower law.
In order to study the influence of the cross-sectional configuration of the PMG on
the levitation performance of the HTSC, two schemes are chosen for the monopole
PMG. Table 7.2 shows the first scheme: keeping the height of the PM constant
(TD=40 mm), and changing the width of PM from 40 mm to 60 mm. Table 7.3 shows
the second scheme: keeping the width of the PM constant (TB=40 mm) and changing
the height of PM from 40 to 60 mm. The magnetic forces with vertical movement of the