Guang-Tong Ma and Yi-Yun Lu
7 Numerical simulations of HTS Maglev
7.1 Introduction
Numerical simulation is a counterpart of the direct measurement in scientific research.
It has the advantage of low cost and being flexible to tune the geometrical and
material characteristics of the studied object, as well as being able to understand
and verify the macroscopic observations by direct measurements. Before running
the simulation, one should establish a theoretical model to mathematically charac-
terize the physical properties of the studied object and then convert the model into
computer language. Therefore, modeling is the theoretical basis for performing the
simulations.
The theoretical basis for conducting simulations toward HTS Maglev is to properly
establish the partial differential equations (PDEs) for governing the electromagnetic
behavior of HTSC, which has properties being different from the conventional con-
ductors, in the presence of non-uniform magnetic fields. In the early phase after the
discovery of the HTSC withTcover 77 K in 1987, the theoretical models were basically
explored in the framework of the mirror-image principle by considering the HTSC as a
perfect diamagnet [1–3]. This is easy to implement, but the applicable scope is limited
due to the dipole approximation, although its extended form to reflect the hysteresis
of levitation forces has been suggested [4]. This sort of models cannot be used to study
the Maglev performance of the HTSCs above the PMG, which has a large scale so that
the dipole approximation does not hold.
Understanding the HTSC working in the mixture state, a number of electroma-
gnetic models, directly derived from the Maxwell’s equations, have been established
and verified in both two- and three-dimensional levels [5–14] to investigate the Maglev
performance of the HTSCs in a more realistic sense. Using these models, the geometri-
cal and material effects on the levitation performance [15], and the distributions of
the magnetic field and the induced supercurrent [7, 11, 14, 16]. have been studied.
The effect of the mutual interaction among the superconducting constituents of a
multi-blocked HTS unit on the Maglev performance has also been identified [14], apart
from the influence of the lateral movement on the levitation forces [17, 18]. Also,
the propitious configuration of PMG for improving the levitation capability has been
estimated [8, 19, 20], and miscellaneous strategies for the practical design of such
levitation systems have been suggested [8, 21–25].
In this chapter, our emphasis is to present the efforts and achievements of nume-
rical modelings and simulations towards the HTS Maglev system with a configuration
of translational symmetry in J. S. Wang group. The mathematical foundations for
governing the electromagnetic behavior of HTSC subjected to magnetic excitation,