# Magnetic levitation

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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.

In some cases the lifting force is provided by magnetic levitation, but there is a mechanical support bearing little load that provides stability. This is termed pseudo-levitation.

Magnetic levitation is used for maglev trains, magnetic bearings and for product display purposes.

## Stability Edit

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.

## Methods Edit

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 (Pseudo-levitation)Edit

With a small amount of mechanical constraint for stability, pseudo-levitation is relatively straightforwardly achieved.

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.

Another example is the Zippe-type centrifuge where a cylinder is suspended under an attractive magnet, and stabilised by a needle bearing from below.

### Direct diamagnetic levitation Edit

A substance that is diamagnetic repels a magnetic field. All materials have diamagnetic properties, but the effect is very weak, and is 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 owing 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 criterion 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 m/s2 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 $B \frac{dB}{dz} \approx 1400\ \mathrm{T^2/m}$
• Graphite levitates at $B \frac{dB}{dz} \approx 375\ \mathrm{T^2/m}$

### Superconductors Edit

Superconductors may be considered perfect diamagnetsr = 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, superconducting bearings, flywheels, etc.

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.

### Diamagnetically-stabilized levitation Edit

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]

### Rotational stabilization Edit

Main article: Spin stabilized magnetic levitation

A magnet can be repulsively levitated when gyroscopically stabilized by spinning it in a toroidal field created by a ring of 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 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.

### Servomechanisms Edit

The attraction from a fixed strength magnet decreases with increased distance, and increases at closer distances. 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 speed of the object being levitated, and using a feedback loop to continuously adjusting one or more electromagnets to correct its motion, thus forming a servomechanism.

Many 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.

### Induced currents/Eddy currentsEdit

This is sometimes called ElectroDynamic Suspension (EDS).

#### Relative motion between conductors and magnets Edit

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 oppose the changes in the field and create an opposite field that will repel the magnet (Lenz's law). 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 almost doubles the field strength, which in turn almost doubles the strength of the eddy currents- the net effect is to more than triple the lift force. Using two opposed Halbach arrays increases the field even further.[3]

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

#### Oscillating electromagnetic fields Edit

A conductor can be levitated above an electromagnet (or vice versa) 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.[4][5] 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.

### Strong focusingEdit

Main article: Strong focusing

Earnshaw's theory strictly only applies to static fields. Alternating magnetic fields, even purely alternating attractive fields[6] can induce stability and confine a trajectory through a magnetic field to give a levitation effect.

This is used in particle accelerators to confine and lift charged particles, and has been proposed for maglev trains also.[6]

## Difficulties Edit

Template:Unreferencedsection Most of the levitation techniques have various complexities.

• Many of the active suspension techniques have a fairly narrow region of stability.
• Magnetic fields have no built-in damping. This can permit vibration modes to exist that can cause the item to leave the stable region. Eddy currents can be stabilising if a suitably shaped conductor is present in the field, and other mechanical or electronic damping techniques have been used in some cases.
• Power and current requirements can be very large to generate sufficiently strong magnetic fields using electromagnets to lift significant mass.
• Superconductors require very low temperatures to operate, often helium cooling is employed.