*2.1. Levitated LTS*

Levitated LTSs mainly use electromagnetic suspension. These systems, Maglevs, can be divided into Permanent Magnet (PM)- and superconductor-based levitating systems. According to the postulate on the stability of bodies in various static force fields given in 1842 by Earnshaw [5], no object placed in an inverse square law force field (e.g., magnetic field) could be in a stable equilibrium; thus to achieve stability, PM flux should be modulated by the respective control coil currents that depend on the size of the air gap. Such controlled electromagnets are utilized in many different levitation systems, for both side and vertical stabilization [6]. Efficient operation of these systems depends on the advanced optimization of the magnetic field distribution within the air gap by means of proper geometry design and proper selection of material and power supply characteristics [7,8].

The first Maglev line to open to public traffic was the Birmingham Maglev in 1984 (propelled by a LIM), the second was the M-Bahn in Berlin (also 1984), and the third was the Shanghai Transrapid Maglev (the latter two using a long-stator synchronous linear-motor-based propulsion).

Braunbeck [9] extended stability investigations to the systems containing diamagnetic materials. The characteristic feature of a diamagnetic material is that it opposes the external field variations, the feature exhibited by the superconductors. Since their inception, superconducting levitation systems have been used in many different industrial applications. The principle of these systems is based on the interaction between the magnetic field and high-temperature superconductors [10,11]. Two examples of superconducting levitation systems are the Miyazaki and Yamanashi Maglevs. In the early stages of Maglev development, at the Miyazaki test track (1977), a purely repulsive electrodynamic suspension system was used [12]. A major advantage of the repulsive electrodynamic suspension system is its inherent stability—a decreasing distance between the track and the vehicle results in strong reactive forces bringing the system to its original position. The magnetic field can be produced by either superconducting magnets (as in JR-Maglev) or an array of permanent magnets (as in Inductrack). The disadvantage of the electrodynamic suspension is that the repulsive forces are speed dependent and are low at low vehicle speeds. For this reason, the vehicle must use support wheels until it reaches take-off speed.

In [13], the hyperloop all-in-one advanced LIM system (propulsion, levitation, and guidance) was proposed. The Superconducting Transverse Flux Linear Motor with integrated levitation, guidance, and propulsion system was described in [14]. Another superconducting levitation system for linear drives was proposed in [15].

In 2015, an SC-Maglev train operated by the Central Japan Railway Company (JR Central) broke the train speed world record by clocking in at 603 km/h (374 mph); a new Chinese Maglev system intended for speeds up to 620 km/h was unveiled in January 2021 by CRRC in Chengdu.
