This thesis project involved the design and analysis of a prototype Maglev systems which incorporate diverse technologies, including high-temperature superconductors, precision electronics, electrodynamics, and highly stressed mechanical structures. Therefore, an extensive review of the literature was performed focusing on many different design case studies. The references are organized in sections indexed in the Chapter 9 of this thesis. Following is a summary of some of the more interesting and/or germane results found.
2.1. HTSC Coil Design and Analysis
Low-temperature superconducting magnet design is a field that has matured, partially through the process of having some spectacular failures . Although the science of HTSC coil design is still in its infancy, there have been several attempts to build prototype HTSC coils to determine how close to design limits these coils may be operated. A literature review was performed prior to the design of our HTSC coils in order to determine the state-of-the-art, and, more importantly, to gain understanding of some design errors that have been made previously.
The papers reviewed focus on many unique features of HTSC coils as compared to their low temperature superconducting (LTSC) counterparts, including:
· The current state-of-the art for HTSC is a silver-sheathed tape form. Therefore, standard coil winding techniques which rely on wires of round or square cross section may not be used. Nb-Ti low temperature superconductor is available in a round wire geometry, and standard coil geometries may be used.
· While all superconductors’ critical current densities (Jc) are degraded by applied magnetic field, HTSC is anisotropic in that regard. The Jc is degraded more by an applied field perpendicular to the wide tape surface than a field parallel to the tape. The degradation may be anisotropic by a factor of 10 to 1 or more. The effect is more pronounced at higher temperature than lower temperature .
· At cryogenic temperatures, the heat capacity of a metal varies approximately as Cv µ T3  while the thermal conductivity k varies more slowly . The thermal diffusion time constants depend on the ratio of Cv/k. Therefore, the growth of a normal zone (which in LTSC coils results in a magnet quench) is much slower in HTSC than LTSC, due primarily to the higher heat capacity of the magnet. The thermal time constant, which is proportional to this heat capacity, is ~105-106 times larger at 77K than at 4.2K. Also related to this is the energy density required to initiate a magnet quench, which may be ~106 times higher for HTSC [291, pp. 319]. Therefore, HTSC coils are expected to be much more robust with regard to mechanical disturbances.
· HTSC tape is much less prone to degradation in critical current density Jc due to flux jumping because of the higher heat capacity of the material [291, pp. 192].
· While low temperature superconducting magnets may be made self protecting (that is, if the magnet quenches, the normal zone propagates quickly and the magnet energy is dissipated through the whole magnet volume) the slow thermal time constant in HTSC coils precludes self-protection. Therefore, active normal-zone detection and protection is warranted for large coils. Sensing voltage taps may be placed inside the magnet winding to sense normal regions.
· The critical current density Jc is more affected by tensile and compressive strain in HTSC than in LTSC. While Nb-Ti wire may be strained up to 1% with no significant affect on Jc , strains in HTSC must be kept e < 0.2-0.4% or so  or significant degradation occurs. Furthermore, HTSC wire may be irreversibly damaged by strains in excess of a few tenths of a percent. This means that practical HTSC coils must be designed with a minimum bend radius of a few centimeters. If higher strains are necessary, the wind-and-react method may be used where the coil is wound with unreacted superconductor, and heat treated after winding [295, pp. 317].
2.1.1. Prototype Coils and HTSC Design Issues
Since the discovery of high temperature superconducting ceramics in 1987, a number of engineering prototype HTSC magnets have been built. There are new proposed applications for HTSC in Maglev, nuclear magnetic resonance (NMR), superconducting power leads and transmission cable, and superconducting magnetic energy storage (SMES).
In 1988, shortly after the discovery of high-temperature superconductivity, Kirschner et. al.  built several high-temperature superconducting magnets using individual yttrium-barium-copper-oxide (YBCO) superconducting ceramic rings. The resulting spiral of YBCO ceramic was a primitive version of today’s HTSC solenoid coils. Central fields of ~20 milliTesla were produced when operated in liquid nitrogen.
Later workers have built coils using silver-sheathed HTSC tapes. Aized  presents data for coils made from silver-sheathed lead-BSCCO tape, tested in magnetic fields of up to 20 T in the temperature range 1.8K to 77K. Comparisons were made for background fields parallel and perpendicular to the coil axis. Overall current densities of 20,000~30,000 A/cm2 were achieved at 20T fields and 4.2K. Ariante et. al.  present data for silver-clad Bi-2212 coils from 4.2 to 80K, and show that the critical current is on average 50% of the short sample value, reaching 80% in the best case. Degradation is explained by noting that the critical current degrades with bending strain. Since the wind-and-react method was used for these coils, the details of the heat treatment also affect the ultimate performance of the coils. Hazelton et. al.  describe the design and test of a prototype Bi-2223 magnet designed as a high-field insert for an NMR application. The coil was operated at 4.2K with a 17 T applied field and produced an additional central field of 0.24 T. The results show that HTSC has very good properties when operated at LTSC temperatures. Jenkins et. al. [9, 10] describe the design of several different HTSC coils from BSCCO-2212 with test data from 4.2 to 77K. It is shown that the anisotropy of the tape response to perpendicular fields is significantly worse at 77K than at the lower temperature. In a later experiment, Jenkins et. al.  describe the design of a small-scale attractive Maglev test fixture, with an HTSC coil operating on an iron core. They describe design criteria that are unique to using HTSC on an iron core, specifically the problem of leakage fields which degrade the performance of the HTSC tape. Vo et. al.  built several high temperature superconducting coils made from multifilamentary Bi-2222 tapes. They were able to generate a field of ~0.04T at 77K. They found that by using the wind-and-react technique it was possible to retain ~97% of the short-sample critical current.
Edick  presents the case that HTSC windings may be cost effective for
large motors from an economic standpoint. He cites data from small prototype
motors (< 100 Watts) and predicts a ~ 50% reduction in motor losses and
motor size for a 10,000 HP synchronous motor using HTSC, based on a design
study. Schoenung et. al. [15, 16] presents a
conceptual design for superconducting magnetic energy storage using HTSC. Their
results show that for HTSC to be competitive with low temperature
superconductors in energy storage that the cost of HTSC material must be
reduced and the performance at high fields and moderate strains must be
improved. A study of a superconducting magnetic energy storage system using
HTSC with 0.5 megaWatt-hour storage capacity with 30 megaWatt discharge power
was conducted by Niemann et. al.
Foner  discusses the effects of new material technology on magnet design. He reports results for BSCCO tape with Jc = 1.5´104 A/cm2 at 26T and 4.2K and states that HTSC may be better for large scale applications at 4.2K than low temperature superconductors if the problems of strain tolerance can be solved.
Gamble  summarizes the benefits and limitations of HTSC wires. The case is made that while a dissipative energy density inside the magnet winding of ~1-10 kJ/m3 is sufficient to quench a Nb3Sn magnet operating at 4.2K, expected quench energies for an HTSC magnet operating at 30-40K is orders of magnitude higher.
Iwasa  compares cooling requirements, quench protection, and thermal stability for low temperature superconductor magnets at 4.2K and HTSC magnets at 77K. The results show that HTSC magnets will be much more stable with regard to mechanical disturbances and flux jumping. However, a magnet at 77K will require some sort of active normal-zone detection and protection, since the normal conductor zone will propagate very slowly. Hence, a small normal zone inside an HTSC magnet is likely to heat up significantly if the quench does not propagate through the entire winding. Work has been done to analyze and increase the quench propagation velocity in multifilamentary superconductors .
Okada et. al.  present a methodology for evaluating the stress in superconducting solenoids. A case study is done for a solenoidal 8T Nb-Ti coil operating at 4.2K. This methodology is useful, especially for HTSC coils where magnetic and thermal strains may significantly degrade coil performance.
Ries  concludes that passive quench protection for HTSC coils will not be sufficient, as the energy will be dissipated in a small fraction of the total magnet volume due to the slow velocity of the normal propagating zone. He concludes that in large HTSC magnets an active quench detection and active dissipation methods must be used, although he offers no methods of detection or protection.
2.1.2. HTSC Material Properties and Test Data
Since the discovery in 1987 that the ceramic material YBa2Cu3O7 has a critical temperature of 95K , significant progress has been made in producing usable wires, tapes, and coils made from HTSC material. Test data has been compiled on HTSC tapes with regard to critical current density and thermal stability, and the affects of applied field, temperature, and strain.
Murakami  tested samples of YBCO crystals. Results showed that Jc exceeded 30,000 A/cm2 at 77K and 1T. The paper focuses on the chemistry and performance of the raw YBCO crystals and makes no comment on the application of YBCO to practical wire conductors.
Haldar et. al.  present data for small coils fabricated in 1993 from silver-clad Bi-2223 which were run at 4.2K and 77K. They found that once the coil was wound there was a difference of 60-80% in Jc between long lengths and short samples due perhaps to the effects of bending strain and self field. They concluded that the HTSC composite tapes show promise for operation in low applied fields at the pumped liquid nitrogen temperature of 64K. Measurements were also made of the temperature dependence of the Jc-Ba measurements for short samples of Bi-2223 over the temperature range 4.2K-90K. Data shows the anisotropy of the Jc degradation, and shows that the anisotropy is especially pronounced for temperatures below ~60K. At 77K the short sample Jc was degraded by 70% for an applied perpendicular field of 0.1T, 75% for a field of 0.2T, and 98% for an applied field of 1T. At 1 T perpendicular to the wide face of the tape and 77K, the short sample Jc was found to be ~500 A/cm2 compared to ~25,000 at zero field. The performance was significantly better at pumped liquid nitrogen temperature (64K). This anisotropy was verified experimentally by Maley et. al.  in 1994
Hazelton  says that for the strain for multifilamentary tapes should be limited to 0.2-0.3%. Haken et. al.  investigated the effects of tensile and compressive strain on the critical current density of Bi-2212 HTSC tape. It is shown that a compressive strain of ~0.4% and a tensile strain of ~0.5% cause a 10% degradation in Jc at 4.2K and high field. It is unclear from their results what the effects would be at higher temperatures. Montanari et. al.  studied the effects of mechanical, thermal, and environmental stresses on multifilamentary HTSC tapes with specific application to superconducting cable design. In an interesting result, it is shown that exposure to high temperature (~100 C) and 97% humidity produces significant degradation of critical current density
Kim et. al.  measured the temperature dependence of the normal zone diffusion in Bi-2223 tapes over the range 10-40K. Their results showed that the propagation velocity of the normal zone is several orders of magnitude slower than in low temperature superconducting tapes. The propagation velocity of the normal zone was very slow, on the order of 1 cm/second for a transport current It = 65 A at 40K.
2.1.3. HTSC Applications to Magnetic Levitation
Various studies have been performed to evaluate the viability of application
of HTSC technology to EDS and
Goodall et. al.  has concluded that direct
control of HTSC magnets in an EMS Maglev environment should be straightforward.
Preliminary experimental results show that superconductor losses are minimal
and that system power dissipation is dominated by eddy currents in the iron
core. They suggest that an overall vehicle weight reduction of 5% may be
achieved by replacing copper magnets with HTSC coils. Goodall’s group has also
demonstrated a magnet used for controlled
Kalsi  considers the application of high temperature superconductors to the Grumman EMS Maglev design. The preliminary analysis suggests that a functional Maglev magnet could be constructed with either Bi-2212 or Bi-2223 and cooled with a cryocooler at 10K or higher.
Scholle and Schwartz  have examined the effects of using a high-Tc superconductor in an air-core EDS Maglev configuration. They performed simulations based on the Japanese MLU002 geometry to determine the strains, power dissipation, and temperature rise in the superconducting material. They concluded that vibration-induced strains in the HTSC coils due to ground-coil/superconductor interactions at select vehicle velocities may exceed several percent, hence significantly affecting the critical current density. They also concluded that the power dissipation and heat leak for the Maglev coils will be small enough so that the magnet may be run for extended periods of time before recooling.
Yokoyama et. al.  discuss design issues for a high-Tc Maglev magnet for the Japanese Maglev system. The superconducting coil is based on a Bi-2223 tape and is cooled by a refrigerator at 20K and is operated in persistent mode. Each coil is run at 590 kA-turns with a design limit at 20K of 800 kA-turns. They concluded that the temperature rise due to AC losses would be minimal and that the coil would be very stable to external disturbances.
Senba et. al.  built an attractive-type
magnetic levitation system with the levitated body being a mass of bulk YBCO
superconductor cooled with liquid nitrogen. The levitated body is a
demonstration of the Meissner effect. The group at the
2.1.4. AC Applications and AC Losses in HTSC
The subject of AC losses in high-temperature superconductors has become of interest due to possible new applications in Maglev, superconducting magnet energy storage (SMES), current leads for low-temperature superconducting magnets, and power distribution. Iwasa [8, 291, pp. 319] has concluded that while total AC losses in a HTSC magnet will be of the same order-of-magnitude as in a comparable LTSC magnet, the effect of AC losses is much reduced due to the increase in the energy density needed to initiate a magnet quench. Furthermore, refrigeration is easier at higher temperatures , with an energy cost of the order of 10 Watts of energy for every Watt of energy removed when operated at 77K. This compares to ~1000-2000 Watts/Watt at 4.2K.
Prior art over the past 20 years has focused on calculation and measurement of AC losses in low temperature superconductors. Hlasnik and Ito  discuss the use and limitations of low temperature multifilamentary composite superconductors in motors, transformers, and other machines up to 60 Hz. They discuss progress in increasing the critical current densities in AC applications by decreasing the size of the low temperature superconducting filaments.
Gomory [271, 272] discusses methods of measuring magnetization and AC losses in low temperature superconductors. Power loss is calculated by measuring magnet current and voltage and compensating for the reactive impedance of the coil.
Giese  discusses the possibility of using HTSC in generators, motors, transmission lines, SMES, transformers, and power electronics. He makes the point that since the energy (and power) of a superconducting machine or motor is proportional to its volume while heat leak is proportional to surface area, the cost of refrigeration favors large machines. If you take this line of thinking to its logical conclusion, it may be that HTSC will be cost effective for smaller machines than their LTSC counterparts.
Boggs  evaluated YBCO fiber as a possible candidate for power transmission, and generated scaling laws for AC losses in superconducting wires. Paasi et. al. [282, 283] evaluated AC losses in single layer coils of Bi-2223 at 4.2K and 77K at frequencies up to 100 Hz. At 50 Hz, 77K and with 1 Ampere peak sinusoidal current at 50 Hz, a power density of ~150 Watts/m3 was measured. It was also found that the AC losses do not have the I3 dependence on transport current which would be predicted by the critical state model. The losses at 77K were more than two orders of magnitude lower than the losses in a copper coil of similar geometry.
Herrmann et. al.  evaluated losses in a 5 kARMS/50kV 50 Hz AC current lead using BSCCO superconductor. It was predicted that a significant refrigeration load reduction could be achieved by using HTSC. Yasukawa et. al.  fabricated and tested a 2 kA HTSC current lead system which could carry current at 50 Hz. Ciszek et. al.  present the results of measurements on losses in Bi-2223 tapes under various operating conditions of transport current, frequency, and applied AC external field. All measurements were taken at liquid nitrogen temperature (77K). Their results show that the dominant losses are due to magnetic hysteresis.
2.2. Inductance Approximate Calculation Methods
In the design and analysis of our magnet and guideway structures, approximate techniques for the calculation of self and mutual inductances were used. Several early references were used, and the validity of filamentary and other approximations for our structures were verified by finite element analysis. In Maglev guideway design as well as the design of motors and transformers, a figure of merit for a coil is the L/R time constant; for a more efficient coil, it is necessary to maximize the inductance and minimize the winding resistance. Several references were found which allow approximate inductance calculations and derivation of scaling laws.
The works by
Lyle  developed a method in the early 1913 where the self-inductance of a circular coil of rectangular cross section may be calculated to an arbitrary level of accuracy by calculating the inductance of a filamentary ring with the filament placed at the geometric mean distance (G.M.D.) of the cross section. This method may be used with arbitrary accuracy by breaking up a complicated cross section into multiple filaments placed at the G.M.D.
Grover  builds on the seminal works of Maxwell, Lyle, Dwight, Butterworth, and others and presents compiled methods for the approximate calculation of inductors of arbitrary cross section. Although much of the material is dated due to the availability today of computers, there is an abundance of useful approximations, both for low and high frequency inductance calculations. The Radio Engineers’ Handbook, by F. Terman  also provides inductance calculations for many interesting winding shapes. Electrical Coils and Conductors by H. Dwight , Static and Dynamic Electricity by W. Smythe , and the skin effect reference by H. Wheeler  provide useful information on the calculation of skin and proximity effects in wires, and calculation of inductance in the high-frequency limit.
Hurley and Duffy  present a method by which Maxwell’s original equation for the mutual inductance of coaxial filamentary rings may be extended to coils with a finite cross section. The geometric mean distance method of Lyle was used to calculate self and mutual inductances. Experimental verification of their method is done for frequencies up to 100 MHz for planar coils above a ferrite substrate.
Murgatroyd  performed design studies in order to optimize the Q of toroidal air-core inductors. By using the calculus of variations, he calculated the ideal geometry of coil cross section which maximizes inductance for a given turn length. His methods are limited to toroidal cage coils, but may be extended to coils of other geometries.
2.3. Maglev System Design and Test Data
2.3.1. Elementary Theory of Magnetic Levitation
The literature is rich with references evaluating the performance of EDS magnetic suspensions, focusing primarily on problems which may be reduced to simple models with closed-form solutions. Theoretical work has focused on static equilibrium solutions. Boerdijk  in 1956 summarized state of the art in levitation technology and reported on an experiment where a piece of diamagnetic graphite was levitated over specially shaped permanent magnets. He also commented on the application of superconductors to levitation, and specifically to magnetic bearings.
Early workers analyzed simplifying cases which give insight into more complicated levitating geometries. Solutions have been calculated for eddy induced currents and resultant forces acting on a long straight wire moving with constant translational velocity over a conductor by Reitz  and Davis and Wilkie ; a permanent magnet moving over a thin sheet by Davis ; and a moving rectangular coil over a conductor by Langerholc , Lee and Menendez [105, 106], Ooi , Reitz , and Reitz and Davis .
In a later work, Hill  in 1990 considered the special case of a current sheet with a sinusoidal spatial dependence traveling over a conducting sheet. He calculated results in the thin and thick sheet limits. His results were verified by a test fixture consisting of permanent magnets suspended above a circular magnetic plate 88 cm in diameter.
Saslow  applied Maxwell’s theories to many different situations involving magnets, wires, and continuous sheets. One interesting example which he gives is the drag calculation for a magnet falling down a conducting tube. He shows that the falling time through the tube scales as ~m2 where m is the magnetic dipole strength. This result is entirely consistent with other Maglev drag force calculations. He also comments that recent advances in high strength rare-earth magnets makes the demonstration much more dramatic.
2.3.2. Maglev Early Works
Following is the summary of the early investigators of Maglev, including Powell
Magnetic levitation using eddy currents was first proposed in 1914 by the French scientist Bachelet who proposed using coils excited with AC currents by magnetic induction for levitation [217, pp. 15]. He built a prototype vehicle which carried a conducting aluminum plate on its bottom surface, and was levitated above a row of electromagnets. He found that for this system the power dissipation was prohibitive, requiring 15 kiloWatts to levitate a 15 kg mass at a height of 1 centimeter.
The first recorded demonstration of magnetic levitation using superconductors was by Arkadiev in 1945 who levitated a 15 millimeter wide bar over a superconducting lead plate [215, pp. 35]. Subsequent research in the 1950’s was done on levitated superconducting rotors for gyroscope applications. A method for levitating a moving vehicle over superconducting rails was proposed by Powell in 1963. This scheme was modified later and by Powell and Danby in 1966  who first proposed placing superconducting magnets on a moving vehicle, levitating the vehicle above a passive guideway where there are induced currents.
Guderjahn et. al. [138, 158, 159] and Coffey et. al.  in 1969 proposed using similar technology to levitate and propel high speed rockets. The Guderjahn design consisted of null-flux coils levitated over a thick aluminum sheet. The calculated lift/drag ratio of 10/1 at cruising speed was sufficient for a test rocket sled, but is not practical for a high-speed train.
Studies of baseline specifications for Maglev vehicles using low temperature
superconductors were done by Borcherts et. al.  and Thornton  in 1973 who proposed specifications
for vehicles capable of 300 miles/hour. Pioneering Japanese work was
2.3.3. Maglev System Specification and Design
In the heyday of Maglev EDS research in the 1970’s, a number of studies were done which specified Maglev system requirements and performance. Borcherts, Davis, Reitz, and Wilkie  in 1973 presented a baseline specification for an EDS train, with a cruising speed of 300 miles/hour. In this design, the train travels in a U-shaped guideway with separate lift and guidance magnets. Details of the cryostat design, as well as heat load were given.
Miericke and Urankar [210, 211] in 1973-74 developed exact analytical expressions for an EDS system utilizing null flux coils and a continuous sheet track. Results are compared to normal flux systems. They conclude that the continuous sheet track is superior with regard to construction costs and safety as compared to the closed loop guideway proposed by Powell and Danby.
Andriollo et. al.  present a method for the design optimization of the coil configurations for an EDS Maglev system. A number of design criteria were considered in the design study, including the amount of the levitation coil conductor, the levitation transient stability, ride comfort, and others. Over 700 different designs were considered and evaluated by computer, and designs were optimized for a given cost function.
Papers from workers at the Japanese National Railway [156, 157] discuss the design of the MLU002 prototypes, designed to operate up to 500 km/hour. The Japanese system has a non-linear vertical spring constant, and a nominal operating gap of approximately 20 cm. The papers give significant detail on the primary suspension, but secondary suspension and control is not discussed.
The United States Department of Transportation funded 4 system concept definition reports  in 1992. The separate studies considered baseline designs for Maglev vehicles, including suspension, guidance, guideway, and propulsion systems.
2.3.4. Maglev Circuit Modeling Techniques
The impedance-modeling technique is a method by which the electrodynamic effects in Maglev coils and guideway structures are reduced to lumped circuit models. The simplest circuit models allow calculation of average forces. Although the circuit modeling tends to obscure the details of the electrodynamic interactions, it is a powerful technique for evaluating Maglev systems.
The technique was first introduced by Guderjahn et. al.  in 1969 in an analysis of the use of magnetic levitation for a rocket sleds in an evacuated tube. In this technique, the energy of the entire levitated system is evaluated by measuring the inductance of the excited coils as position is varied. The force on the coils can be calculated if the gradient of the mutual inductance is found. Image methods were used to predict Maglev lift forces at high train speed.
Iwasa  applied the technique to the Magneplane Maglev system in 1972. The technique was extended to study the static stability of pitch and roll. The method was used by Ohno et. al.  in 1973 to predict pulsating forces in discrete-coil Maglev guideway geometries. The method was applied in 1974 by Atherton and Eastham  to Maglev geometries for various levitation and guidance schemes. In 1975, Howell et. al.  applied similar techniques to the Wolfson experimental Maglev vehicle, and evaluated dynamic stability, ignoring aerodynamic damping. They found that dynamic stability could be greatly improved by adding passive copper damping windings. In 1976, Atherton et. al.  applied the impedance modeling technique to Maglev systems with passive secondary suspensions. They claim that passive aluminum damper coils mounted on the underside of the sprung mass are an attractive alternative to mechanical or hydraulic dampers. Wong, Mulhall, and Rhodes  summarized the results of previous workers and further explained the use of transformer models for evaluating Maglev forces.
The technique was further expanded to include multiple-loop coils and guideways, with works by He, Rote and Coffey [48 - 50] and Ooi , among others. Methods of guideway inductance calculation were discussed by Mills [54 - 56], who summarizes some of the inductance calculation methods of Grover . An important simplification that is made when evaluating the null-flux topology is that the guideway conductors are large enough and far enough apart that the mutual inductance with adjacent coils is ignored. Multiple-loop structures require the computation of inductance and resistance matrices. The computations are simplified if a single-harmonic excitation is assumed.
Jain and Ooi  discuss the limitations of the impedance modeling technique. They show that the technique is valid in the high speed limit, but that the fundamental approximations break down in the low speed limit.
2.3.5. EDS Maglev Electromechanical Stability
Early studies of Maglev suspensions focused on the calculation and measurement of static forces and torques, rather than the dynamics of vehicle motion. The stability of Maglev train motion is of considerable interest due to its effects on passenger safety and structural requirements. The subject is very complicated and there is not as yet a definitive reference covering all aspects of Maglev stability. Many theoretical studies have been performed on simplified limiting cases.
Woods et. al.  considered the stability of a levitated superconducting current ring and evaluated passive damping techniques as well as active stabilization. In a related topic, Holmes  studied the stability of levitating forces on metal spheres suspended in A.C. magnetic fields, with application to induction heating of molten metals.
Davis and Wilkie  and Fink and Hobrecht  analyzed the motion of a long wire over a thin conducting plate, and found vertical and translational instabilities in the absence of air drag. They found that for a Maglev system the unstable longitudinal time constant is very long (~ several minutes) and that there is an underdamped vertical mode at approximately 2 Hz. These studies further showed that the vertical oscillation of the moving wire can produce a negative damping force depending on the wire speed.
Yamada et. al.  built an experimental facility to test the dynamics of EDS Maglev in 1973. A ferrite magnet was suspended and allowed to vibrate near a rotating aluminum drum. The damping behavior of the system was observed at various operating speeds, and it was found that negative damping exists for linear velocities above a critical velocity. For a full-scale train traveling over a sheet guideway, these results extrapolated to negative damping for train speeds higher than ~60 km/hour.
Iwasa  and later Iwamoto et. al.  and Ohsaki  applied the inductance-modeling method to the study of Maglev stability. Iwamoto predicts a negative damping coefficient for train speed over ~50 m/sec traveling over a trace with discrete loops. Iwamoto recommends using passive damping to achieve good ride quality. Nguyen et. al.  describe the design of a passive magnetic damper.
The most detailed study of instabilities in EDS Maglev has been performed by the Cai and Chen and the Maglev group at Argonne National Laboratories . Suspension instabilities of EDS systems with 3 and 5 degrees-of-freedom (D.O.F.) have been evaluated by computer simulation. Their results show that coupling effects among the 5 D.O.F. play an important role and that there are several potential instabilities. The instabilities depend on the equilibrium air gap, which in turn is determined by the vehicle mass, passenger load, and guideway design.
2.3.6. Maglev Control Systems
Several different schemes for active and passive control of vertical
dynamics have been proposed. They include active secondary air suspensions
, passive damping using aluminum or copper damping coils , and
hydraulic dampers . Active control of magnet currents is proposed for EMS
systems, where copper coils are used and superconducting magnet quenching is
not an issue General discussions of EMS control
systems were done by Goodall’s group in
For EDS systems using low temperature superconductors, active control of the magnet currents has not been implemented due to the deleterious effects of AC losses. Several studies show that the intrinsic damping of vertical dynamics is very low. Atherton, Eastham, and Sturgess  proposed secondary magnetic damping using short-circuited aluminum coils coupled to the linear synchronous motor. The use of the linear synchronous motor for active heave damping was demonstrated by Brown  in 1975 for the M.I.T. Magneplane project. Nagai, Mori, and Nakadai  built a small scale one degree-of-freedom EDS Maglev test fixture, with a resultant damping ratio without control of 0.5%. With active control, the damping ratio was increased to 20%.
Boldea  performed an analysis where it is shown that an EDS system with active control of magnet currents can theoretically provide good ride comfort at 100 m/sec without a secondary suspension system. Secondary control coils are allowed to have transient currents under active control. Performance of the discrete ladder and continuous-sheet guideways are compared. It was found that for the continuous sheet, for a full-scale Maglev system the drag peak will occur at approximately 40 m/sec, and a high speed lift-drag ratio of 14 is predicted. This is compared to a ladder guideway, where the drag peak occurs at 15 m/sec and a lift/drag ratio of 29 is predicted at cruising speed. Also, for the continuous sheet, skin effect is more pronounced due to the wide geometry of the sheet.
Modern control systems with control of multiple degrees of freedom for EDS systems are discussed by Nakadai, Nagai, Nonami, He, and Nishimura [67, 68].
2.3.7. Maglev Thermal Stability
Low temperature superconducting coils are susceptible to quenching due to AC
losses from magnetic, electrical, and mechanical disturbances. Pioneering work
on mechanical disturbances and its effect on LTSC coils was done by
2.3.8. Maglev Scale-Model Test Results
Several programs have been implemented to evaluate Maglev scale model systems. With the notable exception of a test fixture for evaluation of linear synchronous motors and null-flux suspension built by the Japanese National Railways in 1975 , work has concentrated on models of discrete-coil systems.
One of the earliest model tests was performed by Borcherts and Davis at Ford  in 1972. A 4.24 centimeter diameter low temperature superconducting coil was suspended in a cryostat above a rotating 61 centimeter diameter aluminum cylinder. The cylinder was rotated up to linear peripheral speeds of 483 kilometers/hour. The experimental results were used to compare to analytic results for a loop coil traveling over a continuous sheet guideway. A lift/drag ratio at high speed of 30-50 was predicted for a full scale train. Other early tests were done by the Siemens group in the early 1970s [185, 211, 212].
At M.I.T., 1/25 scale tests of the Magneplane system of Kolm, Thornton, Iwasa, Brown [183, 188, 189] and others was carried out in 1972-75. The 1 meter long, 14 kilogram test vehicle was propelled by a linear synchronous motor at 25 meters/second on a 116 meter long guideway. Active heave damping was provided by the linear synchronous motor. It was shown that the superconducting magnet vehicle was lighter than a similar design with permanent magnets, and that the linear synchronous motor could be used to damp heave oscillations.
A 550 meter test track was built and operated at the
Canadian Maglev studies have been carried out at the Universities of
Later rotating test fixtures have been operated at Argonne National
Laboratories by Mulcahy, He, Rote and Rossing , at Siemens Corporation
 and a smaller scale test at the
2.3.9. Other Issues Related to Maglev System Design
22.214.171.124. Magnetic Shielding
Magnetic shielding is of special importance in air-core Maglev designs such
as the Japanese MLU-series. The German EMS system has lower guideway field, and
the iron core design and iron rails guide the flux away from the passenger
cabin. Significant work has been done in
Passive shielding for Maglev was first discussed by Iwasa  in 1973. He found that a heavy iron plate 2 cm thick must be placed in the floor of the passenger cabin, adding 10,000 kg to the weight of a 100 passenger vehicle. An aluminum shield was recommended to attenuate A.C. fields due to propulsion windings. Later works [130, 132] result in designs which may be lighter.
An analysis of stray magnetic fields from a linear synchronous motor was
126.96.36.199. Guideway Design and Ride Comfort
The study of guideway design and ride comfort are important because of safety and system cost issues. The cost of a guideway structure is expected to be 60-80% of the overall initial capital investment . A more flexible guideway can be built at a lower cost, but there are complications due to vehicle/guideway interactions which may impact safety and ride quality. A Ph.D. thesis by Phelan  at M.I.T. discusses Maglev guideway structures.
Fearnsides et. al.  reviewed ride quality specifications. They used railroads as their test case, but the results are applicable to Maglev vehicles. Later, Jayawant and Sinha  studied low speed vehicle dynamics with specific application to EMS Maglev systems operating up to 50-70 km/hour. They built an experimental suspension test rig and determined that the optimum operating air gap for an attractive suspension is around 15 mm, if the passenger acceleration level was not to exceed 0.04g. This could be achieved without a secondary suspension.
In 1972, Yamada et. al.  performed a study comparing guideways with independent coils with a proposed ladder guideway systems. It was found that the ladder system has a higher lift-drag ratio at cruising speed, and that it is desirable to increase the number of guideway coils in order to reduce the pulsating forces acting on the train.
Cai. et. al.  and the group at Argonne National Laboratories have developed a model which consists of a rigid train consisting of multiple magnetic loads traveling over a flexible guideway. Their results show that less guideway deflections occur if the levitation magnets are distributed over the length of a vehicle. Although this is an intuitive result, their results are important as they quantitatively evaluate expected guideway deflections, which can be kept to a fraction of a centimeter by proper design.
In a U.S. Department of Transportation supported work, Zahn  discussed heating effects in steel rebars in Maglev guideways. In this study, transient electromagnetic effects due to the field from the passing train are analyzed for representative guideway structure.
2.4. Test Wheel Mechanical Design Issues
A short review of the literature in flywheel design was performed prior to the design of our Maglev test wheel. Of specific interest are material parameters of composite materials such as strength, cost, and thermal properties found in [228-231, 236]. Basic stress analysis for rotating discs is found in reference , and rotordynamics and calculation of rotating wheel resonances is found in references [245, 256].
Marc T. Thompson, Ph.D.
Thompson Consulting, Inc.