Magnetic levitation

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Template:Cleanup-date Magnetic levitation 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.

Earnshaw's theorem proved conclusively that it is not possible to levitate using static, macroscopic, "classical" electromagnetic fields. The forces acting on an object in any combination of gravitational, electrostatic, and magnetostatic fields will make the object's position unstable. However, several possibilities exist to make levitation viable, by violating the assumptions of the theorem.

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Methods

There are several methods to obtain magnetic levitation:

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(Mechanically-stabilized Levitation)

If one mechanically constrains a permanent magnet with either a string or plate along one axis, one can create a stable configuration in which the repulsion between the magnets creates a substantial levitation. This is not considered true levitation because there is mechanical contact, even though that constraint is usually perpendicular to the vertical levitation axis. A popular toy based on this principle is the [Revolution by Carlisle].

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Direct Diamagnetic Levitation

Image:Frog diamagnetic levitation.jpg A substance which is diamagnetic repels a magnetic field. Earnshaw's theorem does not apply to diamagnets since they behave in the opposite manner of a typical magnet (relative permeability μr < 1). All materials have diamagnetic properties, but the effect is very weak, and usually overcome by the object's paramagnetic or ferromagnetic properties. A material which is predominantly diamagnetic will be repelled by a magnet, although typical objects only feel a very small force. This can be used to levitate light pieces of pyrolytic graphite or bismuth above a moderately strong permanent magnet. As water is predominantly diamagnetic, this property has been used to levitate water droplets and even live animals, such as a grasshopper and a frog. The magnetic fields required for this are very high, however; in the range of 16 teslas, and create significant problems if ferromagnetic materials are nearby.

The minimum criteria for Diamagnetic Levitation is B * (dB/dz) = mu0 * rho * g / chi, where 

chi == magnetic susceptibility
rho == density of the material
g = local gravitational acceleration (9.8 m s^-2)
mu0 = permeability of free space
B = magnetic field
dB/dz = rate of change of the magnetic field along the vertical axis

(assuming ideal conditions along the z-direction of solenoid magnet)

H2O levitates at [B dB/dz] » 1400 T2/m Graphite levitates at [B dB/dz] » 375 T2/m

See also: Diamagnetic levitation


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Levitation Over a Superconductor

Superconductors may be considered perfect diamagnets (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 (electrodynamic suspension) in some magnetic levitation trains.

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Diamagnetically-Stabilized Levitation

A permanent magnet can be stably suspended at room temperature without either servo control or superconductors by various configurations of strong permanent magnets and strong diamagnets. When using superconducting magnets, the levitation of a permanent magnet can even be stabilized by the small diamagnetism of water in human fingers.

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Rotationally-Stabilized Levitation

Spinning a strong permanent magnet in a field created by a ring of other strong permanent magnets will stabilize it until the rate of precession slows below a critical threshold. This method of levitation was popularized by the Levitron toy. Although "stable", the region of stability is quite narrow both spatially and in the required rate of precession.

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Servo-Stabilized Electromagnetic Levitation

Dynamically-stabilized magnetic levitation can be achieved by measuring the position and trajectory of a permanent magnet to be levitated, and continuously adjusting the field of nearby electromagnets (or even the position of permanent magnets) feedback control systems to keep the levitated object in the desired position.

This is the principle in place behind common tabletop levitation demonstrations, which use a beam of light to measure the position of an object. The electromagnet (arranged to pull the ferromagnetic object upwards) is turned off whenever the beam of light is broken by the object, and turned back on when it falls beyond the beam. This is a very simple example, and not very robust. Much more complicated and effective measurement, magnetic, and control systems are possible.

This is also the principle upon which EMS (electromagnetic suspension) magnetic levitation trains are based. The train wraps around the track, and is pulled upwards from below.

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Rotating conductors beneath magnets

If one rotates a base made of an electrical conductor beneath a permanent magnet, a current will be induced in the conductor that will repel the permanent 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.

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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 diamagnet, 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 aluminium or copper, as the ferromagnetic ones are attracted to the electromagnet.

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Translational Halbach Arrays

Translating Halbach Arrays of NdFeB magnets over conductive loops generates a current in the loop which produces an opposing magnetic field. At some critical velocity the induced magnetic field is strong enough to induce levitation. The Halbach arrays can be placed in a stable configuration.

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Halbach arrays

Another way of stabilizing the repulsive effect is to use fields that move in space, rather than just time. This effect can be demonstrated with a rotating conductive disc and a permanent magnet, which will repel each other.

This is the principle of the Inductrack maglev train system, which avoids the problems inherent in both the EMS and EDS systems. It uses only permanent magnets (in a Halbach array) and unpowered conductors to provide levitation. The only restriction is that the train must already be moving at a few kilometers per hour (about human walking speed) to levitate. The energy for suspension comes entirely from forward motion, efficiency is good, and no extremely low temperature suspension magnets are required.

Halbach arrays are also well-suited to magnetic levitation of gyroscope, motor and generator spindles.

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See also

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External links

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Levitron

nl:Maglev

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