Brief History of Magnetic Levitation Essay
Brief History of Magnetic Levitation
In the early 1900s, Emile Bache let first conceived of a magnetic suspension using repulsive forces generated by alternating currents. Bache let’s ideas for EDS remained dormant until the 1960s when superconducting magnets became available, because his concept used too much power for conventional conductors. In 1922, Hermann Kemper in Germany pioneered attractive-mode (EMS) Maglev and received a patent for magnetic levitation of trains in 1934. In 1939-43, the Germans first worked on a real train at the ATE in Goettingen. The basic design for practical attractive-mode maglev was presented by Kemper in 1953. The Tran rapid (TR01) was built in 1969.
Maglev development in the U.S. began as a result of the the High-Speed Ground Transportation (HSGT) Act of 1965. This act authorized Federal funding for HSGT projects, including rail, air cushion vehicles, and Maglev. This government largesse gave the U.S. researchers an early advantage over their foreign counterparts. Americans pioneered the concept of superconducting magnetic levitation (EDS,) and they dominated early experimental research. As early as 1963, James Powell and Gordon Danby of Brookhaven National Laboratory realized that superconductivity could get around the problems of Bache let’s earlier concepts. In 1966, Powell and Danby presented their Maglev concept of using superconducting magnets in a vehicle and discrete coils on a guide way. Powell and Danby were awarded a patent in 1968, and their work was eventually adopted by the Japanese for use in their system. Powell and Danby were awarded the 2000 Benjamin Franklin Medal in Engineering by the Franklin Institute for their work on EDS Maglev.
In 1969, groups from Stanford, Atomics International and Sandia developed a continuous-sheet guide way (CSG) concept. In this system, the moving magnetic fields of the vehicle magnets induce currents in a continuous sheet of conducting material such as aluminum. Several groups, including MIT (Kolm and Thornton, MIT, 1972,) built 1/25th scale models and tested them at speeds up to 27 m/s (97.2 km/h.) The CSG concept is alive and well in 2001 with the Magplane. EDS systems were also being developed in the US in the early ’70s, including work by Rohr, Boeing, and Carnegie-Mellon University.
Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended above another object with no support other than magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force.
Experiment: Magnetic Levitation
Magnetic fields are actively excluded from superconductors (Eisner effect). If a small magnet is brought near a superconductor, it will be repelled because induced super currents will produce mirror images of each pole. If a small permanent magnet is placed above a superconductor, it can be levitated by this repulsive force. The black ceramic material is a sample of the yttrium based superconductor.
By tapping with a sharp instrument, the suspended magnet can be caused to oscillate or rotate. This motion is found to be damped, and will come to rest in a few seconds.
The Meissner effect in superconductors like this black ceramic yttrium based superconductor acts to exclude magnetic fields from the material. Since the electrical resistance is zero, super currents are generated in the material to exclude the magnetic fields from a magnet brought near it. The currents which cancel the external field produce magnetic poles which mirror the poles of the permanent magnet, repelling them to provide the lift to levitate the magnet.
The levitation process is quite remarkable. Since the levitating currents in the superconductor meet no resistance, they can adjust almost instantly to maintain the levitation. The suspended magnet can be moved, put into oscillation, or even spun rapidly and the levitation currents will adjust to keep it in suspension.
2. Levitating pyrolytic graphite
There are some materials that are more diamagnetic than bismuth. These include superconductors (which at this time require cryogenic temperatures to work), and similar materials that exhibit “giant diamagnetism” (also at very low temperatures).
But there is one material that is more diamagnetic than bismuth at room temperature, at least in one direction. That material is called pyrolytic graphite.
Pyrolytic graphite is a synthetic material, made by a process called chemical vapor deposition. To make pyrolytic graphite, methane gas at low pressure (about 1 Torr) is heated to 2000 degrees Celsius. Very slowly, (one thousandth of an inch per hour) a layer of graphite grows. The graphite made this way is very highly ordered, and the layers of carbon atoms form like a crystal of hexagonal sheets. These sheets lie on top of one another like sheets of mica. You can separate the layers with a sharp knife to make thinner sheets. Pyrolytic graphite is more diamagnetic than bismuth, but only in the direction perpendicular to the sheets of carbon. In other directions, it is still diamagnetic, but not as good as bismuth. Because the density of pyrolytic graphite is lower than bismuth, (the specific gravity is 2.1), it is light enough to be levitated above a sufficiently powerful magnet. A thick piece will still be too heavy, since the material above about a half of a millimeter does not contribute much to the lift. But if the piece is thin enough, it will simply slide right off of a strong magnet, and refuse to sit still on it. With a piece half a millimeter thick, using neodymium-iron-boron super magnets, you can see from the photos that the piece is levitating about a millimeter above the magnets. To make the pyrolytic graphite plate sit still above the magnet, we need a way to force it towards the center. We can do that by using four magnets. The poles of the magnets push on the diamagnetic material more strongly than other parts of the magnet. With four magnets, the four edges of the square of pyrolytic graphite will be pushed away from the four poles. If the square is slightly smaller than half the width of the four magnets (a little smaller than one magnet), then we can place it in the center, and it will be pushed to the middle and stay. Since diamagnetic materials are repelled by either pole, we can place the magnets with alternating north and south poles, and they will stick nicely to one another. I like to sit the whole array on a piece of sheet steel, so the magnets stay put. The pyrolytic graphite plate floats above the magnets and springs back when you push it down with a finger. Since pyrolytic graphite is a little more diamagnetic than bismuth, it makes a great substitute for bismuth in the levitating magnet project.
Place the blade carefully in the middle of the edge of the graphite. Slowly push the blade in with a slight rocking motion. The graphite will make a nice clean sound as it starts to split. Sometimes you will get one thin piece and one thicker piece after they are split. You can often split the thicker piece again, giving you three pieces. If you are very skilled, you can get four pieces, but you will break a few gaining that skill. Lastly, once the slices are very thin, you can cut them in half by rocking the sharp knife over the middle of each one. The pieces will snap and may fly some distance unless you put a finger over them to hold them down. The thick graphite is too heavy to float on the magnets. The nice thin sheets you split it into will float, and the thinnest ones will float highest.
How can you magnetically levitate objects?
Magnetism is fascinating, especially when it is used to cause objects to levitate or float or be suspended in the air, defying the gravity which keeps us on the ground. How can this be done? There are 10 ways to magnetically levitate objects:
1. Repulsion between like poles of permanent magnets or electromagnets. However, there needs to be a way to constrain the magnets so they don’t flip over and become attracted to each other. For example, floating donut magnets have the dowel rod in the center to keep them from flipping over.
2. Repulsion between a magnet and a metallic conductor induced by relative motion. However, the magnet needs to be restrained from moving in the same direction as the conductor, otherwise it will travel with the conductor.
3. Repulsion between a metallic conductor and an AC electromagnet. It is possible to shape the magnetic field to keep the conductor constrained in its motions; otherwise, a mechanical means is needed to keep the conductor in place. 4. Repulsion between a magnetic field and a diamagnetic substance. This is the case of the floating frog, and the floating magnet between two diamagnetic disks.
5. Repulsion between a magnet and a superconductor. No mechanical constraints are needed for this.
6. Attraction between unlike poles of permanent magnets or electromagnets. This will work as long as there is a mechanical method to constrain the magnets so they don’t touch.
7. Attraction between the open core of an electromagnetic solenoid and a piece of iron or a magnet. The iron or magnet will touch the inside surface of the solenoid.
8. Attraction between a permanent magnet or electromagnet and a piece of iron. Again, the iron needs to be constrained.
9. Attraction between an electromagnet and a piece of iron or a magnet, with sensors and active control of the current to the electromagnet used to maintain some distance between them.
10. Repulsion between and electromagnet and a magnet, with sensors and active control of the current to the electromagnet used to maintain some distance between them.
The stable levitation of magnets is forbidden by Earn Shaw’s theorem, which states
that no stationary object made of magnets in a fixed configuration can be held in
stable equilibrium by any combination of static magnetic or gravitational forces,.
Earn Shaw’s theorem can be viewed as a consequence of the Maxwell equations, which
do not allow the magnitude of a magnetic field in a free space to possess a maximum,
as required for stable equilibrium. Diamagnetism (which respond to magnetic fields with
mild repulsion) are known to flout the theorem, as their negative susceptibility results
in the requirement of a minimum rather than a maximum in the field’s magnitude,
Nevertheless, levitation of a magnet without using superconductors is widely thought
to be impossible. We find that the stable levitation of a magnet can be achieved using
the feeble diamagnetism of materials that are normally perceived as being
non-magnetic, so that even human fingers can keep a magnet hovering in mid-air
without touching it.
Earn Shaw Theorem
The proof of Earn Shaw’s theorem is very simple if you understand some basic vector calculus. The static force as a function of position F(x) acting on any body in vacuum due to gravitation, electrostatic and magneto static fields will always be divergence less. divF = 0. At a point of equilibrium the force is zero. If the equilibrium is stable the force must point in towards the point of equilibrium on some small sphere around the point. However, by Gauss’ theorem,
| F(x).dS = | divF dV
The integral of the radial component of the force over the surface must be equal to the integral of the divergence of the force over the volume inside which is zero. QED!
This theorem even applies to extended bodies which may even be flexible and conducting so long as they are not diamagnetic. They will always be unstable to lateral rigid displacements of the body in some direction about any position of equilibrium. You cannot get round it using any combination of fixed magnets with fixed pendulums or whatever.
There are not really exceptions to any theorem but there are ways around it which violate the assumptions. Here are some of them.
Quantum effects: Technically any body sitting on a surface is levitated a microscopic distance above it. This is due to electromagnetic intermolecular forces and is not what is really meant by the term “levitation”. Because of the small distances, quantum effects are significant but Earn Shaw’s theorem assumes that only classical physics is relevant.
Feedback: If you can detect the position of an object in space and feed it into a control system which can vary the strength of electromagnets which are acting on the object, it is not difficult to keep it levitated. You just have to program the system to weaken the strength of the magnet whenever the object approaches it and strengthen when it moves away. You could even do it with movable permanent magnets. These methods violate the assumption of Earn Shaw’s theorem that the magnets are fixed. Electromagnetic suspension is one system used in magnetic levitation trains (maglev) such as the one at Birmingham airport, England. It is also possible to buy gadgets which levitate objects in this way.
Diamagnetism: It is possible to levitate superconductors and other diamagnetic materials. This is also used in maglev trains. It has become common place to see the new high temperature superconducting materials levitated in this way. A superconductor is perfectly diamagnetic which means it expels a magnetic field. Other diamagnetic materials are common place and can also be levitated in a magnetic field if it is strong enough. Water droplets and even frogs have been levitated in this way at a magnetic laboratory in the Netherlands (Physics World, April 1997).
Earn Shaw’s theorem does not apply to diamagnetic as they behave like “anti-magnets”: they align ANTI-parallel to magnetic lines while the magnets meant in the theorem always try to align in parallel. In diamagnetic, electrons adjust their trajectories to compensate the influence of the external magnetic field and these results in an induced magnetic field which is directed in the opposite direction. It means that the induced magnetic moment is ant parallel to the external field. Superconductors are diamagnetic with the macroscopic change in trajectories (screening current at the surface). The frog is another example but the electron orbits are changed in every molecule of its body.
There are several methods to obtain magnetic levitation. The primary ones used in maglev trains are servo-stabilized electromagnetic suspension (EMS), electrodynamics suspension (EDS), and Induct rack.
If two magnets are mechanically constrained along a single vertical axis (a piece of string, for example), and arranged to repel each other strongly, this will act to levitate one of the magnets above the other. This is not considered true levitation, however, because there is still a mechanical contact. A popular toy based on this principle is the Revolution, invented by Gary Ritts and produced commercially by Carlisle Co. (U.S. Patent 5,182,533), which constrains repelling magnets against a piece of glass.
Direct diamagnetic levitation
A live frog levitates inside a 32 mm diameter vertical bore of a Bitter solenoid in a magnetic field of about 16 teslas at the Nijmegen High Field Magnet Laboratory.
A substance which is diamagnetic repels a magnetic field. Earn Shaw’s theorem does not apply to diamagnetism; they behave in the opposite manner of a typical magnet due to their relative permeability of μr < 1. All materials have diamagnetic properties, but the effect is very weak, and usually overcome by the object’s paramagnetic or ferromagnetic properties, which act in the opposite manner. Any material in which the diamagnetic component is strongest will be repelled by a magnet, though this force is not usually very large. Diamagnetic levitation can be used to levitate very light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this technique has been used to levitate water droplets and even live animals, such as a grasshopper and a frog; however, the magnetic fields required for this are very high, typically in the range of 16 teslas, and therefore create significant problems if ferromagnetic materials are nearby.
The minimum criterion for diamagnetic levitation is, where:
· χ is the magnetic susceptibility
· ρ is the density of the material
· g is the local gravitational acceleration (9.8 m/s2 on Earth)
· μ0 is the permeability of free space
· B is the magnetic fiel
· is the rate of change of the magnetic field along the vertical axis
· Assuming ideal conditions along the z-direction of solenoid magnet:
· Water levitates at
· Graphite levitates
Superconductors may be considered perfect diamagnetism (μr = 0), completely expelling magnetic fields due to the Meissner effect. The levitation of the magnet is stabilized due to flux pinning within the superconductor. This principle is exploited by EDS (electrodynamics suspension) magnetic levitation trains.
In trains where the weight of the large electromagnet is a major design issue (a very strong magnetic field is required to levitate a massive train) superconductors are used for the electromagnet, since they can produce a stronger magnetic field for the same weight.
Diamagnetic ally-stabilized levitation
A per magnet can be stably suspended by various configurations of strong permanent magnets and strong diamagnetism. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.
A magnet can be stabilized by spinning it in a field created by a ring of other magnets. However, it will only remain stable until the rate of precession slows below a critical threshold— the region of stability is quite narrow both spatially and in the required rate of precession. The first discovery of this principle was by Roy Harrigan, a Vermont inventor who patented a levitation device in 1983 several devices using rotational stabilization (such as the popular Levitron toy) have been developed citing this patent. Non-commercial devices have been created for university research laboratories, generally using magnets too powerful for safe public interaction.
Dynamically-stabilized magnetic levitation can be achieved by measuring the position and trajectory of the magnet being levitated, and continuously adjusting the local magnetic field to compensate for its motion.
This is the principle in place behind common tabletop levitation demonstrations, which use a beam of light to measure the position and velocity of an object. In simple systems, an electromagnet is above the object being levitated upwards; the electromagnet is turned off whenever the object gets too close, and turned back on when it falls further away. Such a simple system is not very robust; much more complicated and effective measurement, magnetic, and control systems are, however, possible.
This is also the principle upon which electromagnetic suspension (EMS) magnetic levitation trains are based: The train wraps around the track, and is pulled upwards from below. The servo controls keep it at a constant distance from the track.
Rotating conductors beneath magnets
If one rotates a base made of an electrical conductor beneath a magnet, a current will be induced in the conductor that will repel the magnet. At a sufficiently high rate of rotation of the conductive base, the suspended magnet will levitate. An especially technologically-interesting case of this comes when one uses a Halbach array instead of a single pole permanent magnet.
Halbach arrays are also well-suited to magnetic levitation of gyroscopes and electric motor and generator spindles.
High-frequency oscillating electromagnetic fields
A conductor can be levitated above an electromagnet with a high frequency alternating current flowing through it. This causes any regular conductor to behave like a diamagnetic, due to the eddy currents generated in the conductor. Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet.
This effect requires high frequencies and non-ferromagnetic conductive materials like aluminum or copper, as the ferromagnetic ones are also strongly attracted to the electromagnet. The effect can be used for stunts such as levitating a telephone book by concealing an aluminum plate within it.
Translational Halbach arrays and Induct rack
Moving Halbach arrays over a conductive loop will generate a current in the loop, which will in turn create an opposing magnetic field. At some critical velocity the induced magnetic field is strong enough to induce levitation over a series of such loops. The Halbach arrays can be placed in a stable configuration and installed in, for example, a train cart.
The Induct rack maglev train system avoids the problems inherent in both the EMS and EDS systems, especially failsafe suspension. It uses only permanent magnets — in a Halbach array mounted in the train cart — and empowered conductive loops installed in the track to provide levitation. The only requirement for levitation is that the train must already be moving at a few kilometers per hour (roughly the same as walking speed) to keep levitating.
The electric current induced in the loop conductors in the track drains energy from the motion of the train (called “magnetic drag”), but efficiency is still good, and no active electronics or cryogenics for superconductors are needed.
Thermodynamics subtype is electromagnetism and its further subtype leading to Magneto dynamics. As can be seen from this example: The interaction of the electromagnetic fields with various media (liquid and solid metals, liquid semiconductors, plasmas, electrolytes, Ferro fluids) occurs by means of various forces, including Lorentz, Kelvin, and diamagnetic forces. This allows to control, process, manipulate materials, and to affect their microstructure. Examples of the action of various forces include magnetic levitation of electrically conducting and non-conducting fluids, melting, stirring, pumping, stabilization of melts, free surfaces and interfaces, etc. EPM is involved in the production of metals and alloys (e.g. aluminum, steel, titanium and magnesium alloys), ceramics and glasses of highest purity, semiconductors (Si, GaAs, CdTe), and in efficient control of production of nano-scale metallic and ceramic powders, Ferro fluids for medical and engineering applications, laser welding, etc. Solidification occurs in a wide range of industrial applications, including crystal growth and casting. The understanding of the solidification processes heavily relies on thermodynamics for describing heat transfer and phase transition phenomena as well as on magneto hydrodynamics for accounting for fluid flows and the appearance of convective instabilities and turbulence. The goal is to better understand the parameters that affect solidification, in particular in relation to external electromagnetic fields or mechanical perturbations, the formation of the mushy zone, and its effect on the microstructure of materials. Fundamental studies on solidification include model experiments and numerical simulation. The goal is to improve the understanding of free surface and interface instabilities with the aim of controlling the behavior of surfaces of electrically conducting fluids. This includes modeling and experimental work on the stabilization of interfaces using external fields. The numerical description of levitation melting, in which a piece of metal is being simultaneously levitated and melted by the magnetic field generated by a high frequency current is also of particular interest.
· Diamagnetic ally stabilized magnet levitation
· US Patent 4382245, 1983-05-03.
· Moon, Francis C. (1994). Superconducting Levitation Applications to Bearings and Magnetic Transportation. Wiley-VCH. ISBN 0-471-55925 – 3.
· Braun beck, W. Free suspension of bodies in electric and magnetic fields, Zeitschrift für Physik, 112, 11, pp753-763 (1939)
Brandt, Science, Jan 1989
· New Physics by K.Ravi (O Level Pakistan 2000-2001 course in education for grade 10-11)
· How can you magnetically levitate objects?
· Instructions to build an optically triggered feedback maglev demonstration
· Spin-stabilized Magnetic Levitation: The History of a Discovery
· Nature 400, 323 – 324 (1999) © Macmillan Publishers Ltd.
Nature magazine, July 22,1999, p323
Magnet levitation at your fingertips
A. K. GEIM, M. D. SIMON, M. I. BOAMFA & L. O. HEFLINGER
· Earn Shaw, S., on the nature of the molecular forces which regulate the constitution of the luminferous ether. Trans. Camb. Phil. Soc., 7, pp 97-112 (1842)
B.V. Jayawant, “Electromagnetic Levitation and Suspension Systems”, Publishers: Edward Arnold, London, 1981
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Further reading: http://www.hfml.ru.nl/levitate.html