Magnetic levitation

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This article is about magnetic levitation. For trains based on this effect, see Maglev train.
Levitating pyrolytic carbon
Levitating pyrolytic carbon

Magnetic levitation, maglev, or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force.

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[edit] Stability

Earnshaw's theorem proved conclusively that it is not possible to levitate stably using only 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, for example, the use of electronic stabilization or diamagnetic materials.

[edit] Methods

There are several methods to obtain magnetic levitation. The primary ones used in maglev trains are servo-stabilized electromagnetic suspension (EMS), electrodynamic suspension (EDS), and (in the future) Inductrack.

[edit] Mechanical constraint

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 considered pseudo-levitation.

[edit] 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. Direct link to video
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. Direct link to video

A substance which is diamagnetic repels a magnetic field. 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.

Earnshaw's theorem does not apply to diamagnets. These behave in the opposite manner to normal magnets due to their relative permeability of μr < 1.

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 criteria for diamagnetic levitation is B \frac{dB}{dz} = \mu_0 \, \rho \, \frac{g}{\chi} , where:

Assuming ideal conditions along the z-direction of solenoid magnet:

See also: Diamagnetic levitation in the Diamagnetism article.

[edit] Superconductors

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) 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 sometimes proposed for use for the electromagnet, since they can produce a stronger magnetic field for the same weight.

[edit] Diamagnetically-stabilized levitation

A permanent magnet can be stably suspended 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.[1]

[edit] Rotational stabilization

Main article: Spin stabilized magnetic levitation

A magnet can be stabilized by spinning it in a field created by a ring of other magnet(s). 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 phenomenon was by Roy Harrigan, a Vermont inventor who patented a levitation device in 1983 based upon it.[2] 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.

[edit] Servomechanisms

The attraction from an electromagnet with a constant current flowing through it decreases with increased distance, and increases at close distance. This is termed 'unstable'. For a stable system, the opposite is needed, variations from a stable position should push it back to the target position.

Stable magnetic levitation can be achieved by measuring the position and trajectory of the object being levitated, and using a feedback loop to continuously adjusting the local magnetic field to compensate for its motion, thus forming a servomechanism.

Most systems use magnetic attraction pulling upwards against gravity for these kinds of systems as this gives some inherent lateral stability, but some use a combination of magnetic attraction and magnetic repulsion to push upwards.

This is termed Electromagnetic suspension (EMS).

For a very simple example, some tabletop levitation demonstrations use this principle, and the object cuts a beam of light to measure the position of the object. The electromagnet is above the object being levitated; 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; far more effective control systems exist, but this illustrates the basic idea.

EMS magnetic levitation trains are based on this kind of levitation: The train wraps around the track, and is pulled upwards from below. The servo controls keep it safely at a constant distance from the track.

[edit] Eddy currents

This is sometimes called ElectroDynamic Suspension (EDS).

[edit] Relative motion between conductors and magnets

If one moves a base made of a very good electrical conductor such as copper, aluminium or silver close to a magnet, an eddy current will be induced in the conductor that will repel the magnet. At a sufficiently high rate of movement, a suspended magnet will levitate on the metal, or vice versa with suspended metal.

An especially technologically-interesting case of this comes when one uses a Halbach array instead of a single pole permanent magnet, as this doubles the field strength.

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

[edit] Oscillating electromagnetic fields

A conductor can be levitated above an electromagnet with an alternating current flowing through it. This causes any regular conductor to behave like a diamagnet, due to the eddy currents generated in the conductor.[3][4] Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet.

This effect requires non-ferromagnetic but highly conductive materials like aluminium or copper, as the ferromagnetic ones are also strongly attracted to the electromagnet (although at high frequencies the field can still be expelled) and tend to have a higher resistivity giving lower eddy currents.

The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.

[edit] Translational Halbach arrays and Inductrack

Main article: Inductrack

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 on, for example, a train cart.

The Inductrack 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 unpowered 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.

The lift/drag ratio of these type of systems can be higher at sufficient speed than the lift/drag ratio of conventional aircraft, or even the weight/drag ratio of rubber wheels.

[edit] See also

[edit] References

  1. ^ Diamagnetically stabilized magnet levitation
  2. ^ US4,382,245 (PDF version) (1983-05-03) Roy M. Harrigan Levitation device 
  3. ^ Eddy current magnetic levitation, models and experiments by Marc T. Thompson
  4. ^ Levitated Ball-Levitating an 1cm aluminum sphere

[edit] External links