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Magnetic levitation,
maglev, or
magnetic suspension is a method by which an object is
levitation object with no support other than
magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force.
Stability
Earnshaw's theorem proved conclusively that it is not possible to levitate stably using only static, macroscopic,
classical electromagnetism. The forces acting on an object in any combination of gravitational field, electrostatic field, 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 — for example, the use of electronic stabilization or
diamagnetic materials.
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.
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.
Direct diamagnetic levitation
diameter vertical
bore of a Bitter solenoid in a magnetic field of about 16
tesla (unit) at the Nijmegen High Field Magnet Laboratory. Direct link to video
A substance which is diamagnetic repels a magnetic field. Earnshaw's theorem does not apply to diamagnets; they behave in the opposite manner of a typical magnet due to their relative
Permeability (electromagnetism) of μ
r < 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
Tesla (unit)s, 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:
- \chi is the magnetic susceptibility
- \rho is the density of the material
- g is the local gravitational acceleration (-9.8 metre/second² on Earth)
- \mu_0 is the permeability of free space
- B is the magnetic field
- \frac{dB}{dz} 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 B \frac{dB}{dz} \gg 1400\ \mathrm{T^2/m}
- Graphite levitates at B \frac{dB}{dz} \gg 375\ \mathrm{T^2/m}
See also: Diamagnetism#Diamagnetic levitation in the Diamagnetism article.
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 used for the electromagnet, since they can produce a stronger magnetic field for the same weight.
Diamagnetically-stabilized levitation
A permagnet 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. Diamagnetically stabilized magnet levitation
Rotational stabilization
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.
Servo stabilization
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
electrical generator spindles.
High-frequency oscillating electromagnetic fields
A electrical 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 also strongly attracted to the electromagnet. The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.
Translational Halbach arrays and 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 in, 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.
See also
References
battymanddodoloyuo
External links
- ShinyShack - UK supplier of Diamagnetic Levitation Kits
- Magnetic Levitation - Science is Fun
- Maglev video gallery
- How can you magnetically levitate objects?
- Levitated aluminum ball (oscillating field)
- Instructions to build an optically triggered feedback maglev demonstration
- Videos of diamagnetically levitated objects, including frogs and grasshoppers
- Larry Spring's Mendocino Brushless Magnetic Levitation Solar Motor
- Spin-stabilized Magnetic Levitation: The History of a Discovery
Magnetic levitation,
maglev, or
magnetic suspension is a method by which an object is levitation object with no support other than magnetic fields. The electromagnetic force is used to counteract the effects of the gravitational force.
Stability
Earnshaw's theorem proved conclusively that it is not possible to levitate stably using only static, macroscopic,
classical electromagnetism. The forces acting on an object in any combination of
gravitational field, electrostatic field, 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 — for example, the use of electronic stabilization or
diamagnetic materials.
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.
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.
Direct diamagnetic levitation
diameter vertical
bore of a Bitter solenoid in a magnetic field of about 16
tesla (unit) at the Nijmegen High Field Magnet Laboratory. Direct link to video
A substance which is diamagnetic repels a magnetic field. Earnshaw's theorem does not apply to diamagnets; they behave in the opposite manner of a typical magnet due to their relative Permeability (electromagnetism) of μ
r < 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
Tesla (unit)s, 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:
- Water levitates at B \frac{dB}{dz} \gg 1400\ \mathrm{T^2/m}
- Graphite levitates at B \frac{dB}{dz} \gg 375\ \mathrm{T^2/m}
See also: Diamagnetism#Diamagnetic levitation in the Diamagnetism article.
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 used for the electromagnet, since they can produce a stronger magnetic field for the same weight.
Diamagnetically-stabilized levitation
A permagnet 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. Diamagnetically stabilized magnet levitation
Rotational stabilization
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.
Servo stabilization
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 electrical generator
spindles.
High-frequency oscillating electromagnetic fields
A electrical 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 also strongly attracted to the electromagnet. The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it.
Translational Halbach arrays and 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 in, 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.
See also
References
battymanddodoloyuo
External links
- ShinyShack - UK supplier of Diamagnetic Levitation Kits
- Magnetic Levitation - Science is Fun
- Maglev video gallery
- How can you magnetically levitate objects?
- Levitated aluminum ball (oscillating field)
- Instructions to build an optically triggered feedback maglev demonstration
- Videos of diamagnetically levitated objects, including frogs and grasshoppers
- Larry Spring's Mendocino Brushless Magnetic Levitation Solar Motor
- Spin-stabilized Magnetic Levitation: The History of a Discovery
Magnetic Levitation
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Magnetic levitation research at the University of Nottingham, England.
Maglev (transport) - Wikipedia, the free encyclopedia
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