For successful levitation and control of all 6 axes (degrees of freedom; 3 translational and 3 rotational) a combination of permanent magnets and electromagnets or diamagnets or superconductors as well as attractive and repulsive fields can be used. From Earnshaw's theorem at least one stable axis must be present for the system to levitate successfully, but the other axes can be stabilized using ferromagnetism. The primary ones used in
maglev trains are servo-stabilized
electromagnetic suspension (EMS), electrodynamic suspension (EDS).
Mechanical constraint (pseudo-levitation) With a small amount of mechanical constraint for stability, achieving pseudo-levitation is a relatively straightforward process. If two
magnets are mechanically constrained along a single axis, for example, and arranged to repel each other strongly, this will act to levitate one of the magnets above the other. Another geometry is where the magnets are attracted, but prevented from touching by a tensile member, such as a string or cable. Another example is the
Zippe-type centrifuge where a cylinder is suspended under an attractive magnet, and stabilized by a needle bearing from below. Another configuration consists of an array of permanent magnets installed in a ferromagnetic U-shaped profile and coupled with a ferromagnetic rail. The magnetic flux crosses the rail in a direction transversal to the first axis and creates a closed-loop on the U-shaped profile. This configuration generates a stable equilibrium along the first axis that maintains the rail centered on the flux crossing point (minimum
magnetic reluctance) and allows to bear a load magnetically. On the other axis, the system is constrained and centered by mechanical means, such as wheels.
Servomechanisms system uses servomechanisms to pull the train up from underneath the track and maintains a constant gap while travelling at high speed The attraction from a fixed-strength magnet decreases with increased distance, and increases at closer distances. This is 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 which continuously adjusts one or more electromagnets to correct the object's motion, thus forming a
servomechanism. Many systems use magnetic attraction pulling upward 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 upward. Either system represents examples of ElectroMagnetic Suspension (EMS). For a very simple example, some tabletop levitation demonstrations use this principle, and the object cuts a beam of light or
Hall effect sensor method is used 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 upward from below. The
servo controls keep it safely at a constant distance from the track.
Induced currents These schemes work due to repulsion due to
Lenz's law. When a conductor is presented with a time-varying magnetic field, electrical currents are set up in the conductor which create a magnetic field that causes a repulsive effect. These kinds of systems typically show an inherent stability, although extra damping is sometimes required.
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 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.
Litz wire made of wire thinner than the
skin depth for the frequencies seen by the metal works much more efficiently than solid conductors. Figure-8 coils can be used to keep something aligned. Halbach arrays are also well-suited to magnetic levitation and stabilisation of
gyroscopes and spindles of
electric motors and
generators.
Oscillating electromagnetic fields 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. Since the eddy currents create their own fields which oppose the magnetic field, the conductive object is repelled from the electromagnet, and most of the field lines of the magnetic field will no longer penetrate the conductive object. 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. Again, litz wire gives the best results. The effect can be used for stunts such as levitating a telephone book by concealing an aluminium plate within it. At high frequencies (a few tens of kilohertz or so) and kilowatt powers small quantities of metals can be levitated and melted using
levitation melting without the risk of the metal being contaminated by the crucible. One source of oscillating magnetic field that is used is the
linear induction motor. This can be used to levitate as well as provide propulsion.
Diamagnetically stabilized levitation Earnshaw's theorem does not apply to
diamagnets. These behave in the opposite manner to normal magnets owing to their relative
permeability of (i.e. negative
magnetic susceptibility). Diamagnetic levitation can be inherently stable. 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.
Diamagnetic levitation Diamagnetism is the property of an object which causes it to create a magnetic field in opposition to an externally applied magnetic field, thus causing the material to be repelled by magnetic fields. Diamagnetic materials cause lines of
magnetic flux to curve away from the material. Specifically, an external magnetic field alters the orbital velocity of electrons around their nuclei, thus changing the
magnetic dipole moment. According to Lenz's law, this opposes the external field. Diamagnets are materials with a magnetic permeability less than μ0 (a relative permeability less than 1). Consequently, diamagnetism is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. It is generally quite a weak effect in most materials, although superconductors exhibit a strong effect.
Direct diamagnetic levitation diameter vertical bore of a
Bitter solenoid in a magnetic field of about 16
teslas 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 stronger will be repelled by a magnet. 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, frog and a mouse. 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. Operation of this electromagnet used in the frog levitation experiment required 4
MW (4000000 watts) of power. Several devices using rotational stabilization (such as the popular
Levitron branded levitating top 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.
Strong focusing Earnshaw's theory strictly only applies to static fields. Alternating magnetic fields, even purely alternating attractive fields, 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 as well. ==Uses==