66 Ë 3 Magnetic levitation
3.5 Magnetic levitation
Magnetic levitation refers to the suspension phenomenon associated with the magne-
tic field. The Maglev train has no direct mechanical contact between the vehicle and
its guideway, which achieves vertical support, lateral guidance, and propulsion in the
levitation state simultaneously.
The conditions necessary for magnetic levitation of a magnetizable electrically
conducting sphere depend on its conductivity, permeability, radius, and the spatial
dependence of magnetic field [30].
Earnshaw [15] has shown that no system of permanent magnets can be utilized to
achieve a stable magnetic suspension.
Braunbeck [16] has shown that the instability was due to the values of permea-
bility휇for the materials used being greater than their free-space values, i.e. in static
magnetic fields paramagnets (휇>휇 0 ) and ferromagnets (휇≫휇 0 ) cannot levitate stea-
dily. Therefore, there are exceptions to Earnshaw’s theorem in respect to diamagnetic
materials and superconductors. Stable suspensions have been achieved since using
diamagnetic materials (휇<휇 0 ) and superconductors (휇=휇 0 ). Truly stable levitation
without consumption of energy is possible only in magnetic fields. Energy is stored
in the magnetic field. The energy densityUper unit volume contained in a magnetic
fieldBin MKS is given by
U=^1
2 휇 0B^2 , (3.1)
where휇 0 = 4 휋× 10 −^7 H/m is the permeability of free space.
Although levitation of diamagnetic materials [16, 25] seems to be of no more than
academic interest, levitation of HTS materials [26, 27] is the most spectacular and
promising.
According to attractive and repulsive levitation forces between the vehicle and
guideway, Maglev systems include permanent magnet suspension (PMS) [31], EMS
[32–38], EDS [35–42], and HTS Maglev [42–48]. The PMS includes Maglev between on-
board PMs and DC electromagnet guideways or PMG, as well as Maglev between an
onboard combination of PMs and DC electromagnets and steel rails, etc. The EMS is
a Maglev between on-board DC electromagnets and steel rails. The EDS is a Maglev
using eddy currents induced by an electromagnet moving over a conducting plate.
The HTS Maglev is between on-board HTSCs and PMs and has several modes of stable
levitation: repulsive levitation at Meissner state in a type I superconductor (small
levitation forces), repulsive levitation based on both partial flux exclusion (levitation
forces) and flux pinning (guidance forces) in type II superconductors, and suspension
levitation based on flux pinning forces in a type II superconductor.
EMS and EDS are two basic types of magnetic suspensions developed prior to
HTS Maglev. The technology is basically mature and has already begun trial operation
development.