230 Ë 7 Numerical simulations of HTS Maglev
Fig. 7.6:Comparison between the calculated and experimental levitation forces as functions of
levitation gap in the asymmetrical field. Levitation forces curve using actual (a) and normalized
(b) data.
the calculated results in these two cases, which indicate that the angle of the applied
field does have the influence on the critical current distribution. Moreover, both the
calculated results are about twice more than the experimental results. Qualitatively,
the calculated results agree well with the experimental results in the symmetrical
applied field as the force normalization curves show in Fig. 7.5b. However, there is both
qualitative and quantitative difference between them in the asymmetrical applied
field, as shown in Fig. 7.6.
The guidance forces were carried out in the FC condition 20 mm above the PMG.
Keeping MH at a gap of 20 mm, the sample was horizontally moved from the center to
the displacement of−20 mm and across the center back to the displacement of 20 mm,
and back to the starting position. The same happens to the guidance forces in Figs 7.7a
and b, i.e. the difference between results without and with angle dependence still
exists and the calculated hysteresis curve does not agree with the experimental curve,
because the HTSC sample during the lateral movement experienced a changing field,
from symmetrical to asymmetrical or vice versa.
7.5.2Generalized magnetic vector potential
7.5.2.1Mathematical fundamentals
With the introduction of a generalized magnetic vector potential and using the Ampè-
re’s law within the quasi-static approximation as the state equation, we have esta-
blished the PDE that governs the electromagnetic field of the levitation system with
single or multiple HTSCs. The prominent advantage of this course is that, for a two-
dimensional problem, only the vector potential along the direction of translational
invariance (x-axis in a Cartesian coordinate shown in Fig. 7.8) needs to be defined