Defying Gravity: Fascination of Levitation
Part 1 : Magnetic Levitation
1. General introduction
Levitation (from Latin levitas “lightness”) is a magical sort of phenomenon that has fascinated writers and philosophers through the ages. It is a process where an object is raised against gravity without any physical contact. The legend science fiction writer Arther C.Clarke once said that “any sufficiently advanced technology (e.g. levitation in the present context) is indistinguishable from magic”. The subtle difference between lifting and levitation is that the latter is associated with stable, free floatation. The invisible contact-free levitation technique has attracted attention of scientists as a means of eliminating friction, and has thus been upgraded in recent times from being pure science fiction to science fact.
The primary requirement for levitation on Earth is a vertical upward force that would counteract the downward drag of the gravitational pull and be stable enough to create a firm, durable levitation.
2. Levitation methods
A magnet with sufficiently strong magnetic field can exert enough concentrated force on an object to counteract downward pull of gravity. However, because magnetism is involved, such levitation would only work on objects that are magnetic. For non-magnetic, stable levitation could originate from sound (acoustic), optical, aerodynamic and electric fields.
Some of the levitation techniques have benefitted industrial sectors such as transportation (Maglev train, Hovercrafts) and pharmaceutical industries. The principles and commercial attractions of some of the levitation methods are considered with a discussion of magnetic levitation in the present article, followed by acoustic levitation in Part 2. Also, based on quantum theory, quantum levitation involving reversal Casimir force, although still in its infancy with possible application in nanotechnology, is finally briefly discussed in Part 3.
3. Magnetic Levitation
It is evident from the literature that magnetic levitation was known as long as in the 18th century when fictional floatation of magnetically levitated island of Laputa In Gulliver’s Travels (1726) was imagined to be capable of attaining heights of several kilometres. Historically, magnetic levitation was known for over 100 years when American scientists Robert Goddard and Emile Bachelet first conceived the idea of frictionless trains.
4. Magnetic properties
A simple understanding of magnetic levitation would require some basic knowledge of magnetic parameters such as magnetic permeability (μ expressed in N*A^-2 where N denotes force in Newton on an area A) and susceptibility (χ).
Magnetic permeability is defined as the ability of a material to become magnetized. Magnetic flux is allowed to move through metals such as iron and other ferromagnets easier with high μ than non-ferromagnetics with negligible μ such as animals, living cells and non-metallic materials namely wood, plastics etc.
When a metallic material is placed in a magnetic field of intensity B (Tesla T = N*A^-1*m^-1 where m denotes mass), the material becomes “magnetized” and acquires magnetization M (= A*m^-1). For many metals, M is proportional to B i.e. M = (χ/μo)*B where χ denotes magnetic susceptibility and is expressed as the ratio of the amount of magnetism induced in the sample to the amount generated by the magnetic field, and μ0 is the permeability of free space or vacuum (4*π*10^-7 or 1.257 * 10^-6 Henry/meter).
5. Problem with magnetic levitation
Magnetic levitation is related to magnetic field. It is well known that the magnetic fields of the north (N) and south (S) poles of magnets will always attract when placed against each other, but repel when faced with the same poles (N-N or S-S). Based on this simple magnetic phenomenon, it would be tempting to levitate one magnet over another using the force of attraction between opposite poles of two magnets placed on top of each other. The top magnet should attract and lift the bottom magnet upwards against the downward pull of gravitational force. The difficulty here is that the lower magnet cannot stay in this practically weightlessness condition for more than a fraction of a second before either jumping up to get stuck to the top magnet, or falling down to the ground.
The above example illustrates the difficulty of achieving stability in magnetic levitation. The levitated object (the bottom magnet) once displaced from its equilibrium position, should remain steady via restoration of force in all directions horizontally and vertically without any sideways slip. It is obvious that a delicate balance is required between the distance of the two magnets and the effective overall combined opposing forces of magnetic fields and gravity to achieve stable levitation of the object.
Perhaps, development of a suitable software programme could lower the strength of the magnetic field of the top magnet when the bottom magnet (object) approaches it, but raise the strength when the object moves away. However, before considering anything further, the speculation of levitating permanent magnets is an impossible dream according to the general laws of physics and Earnshaw‘s mathematical theorem in 1842. It is argued that static levitation with stable suspension of one magnet over another via magnetic attraction is theoretically impossible against the force of gravity. This instability of mid-air equilibrium of attraction (or repulsion) applies to most known forces such as magnetism, gravity and electrostatics which all obey physics’ inverse square law stipulating the intensity of a natural force (magnetic or gravitational) to die down in proportion to the inverse square of the distance from the source of the force i.e. force ≈ 1/(distance)^2 .
5.1. Diamagnetism provides solution
The above problem of magnetic levitation using permanent magnets was solved by considering diamagnetic materials that would provide conditions to flaunt Earnshaw’ s theorem. Diamagnetism was named and studied by Michael Faraday around 1846 without realising its considerable effect in physics later on, especially in magnetic levitation. Soon after Faraday’s study, and only a few years after Earnshaw’s theorem, Lord Kelvin in 1847 showed that diamagnetic substances could be theoretically levitated in a magnetic field.
Diamagnets, unlike the positive χ values of paramagnets and ferromagnets, are characterised by exceedingly low, negative χ values. A diamagnet is always repelled by the magnetic field of a permanent magnet as was in as early as 1778 by S.J.Brugmans (1778) in bismuth and antimony. This “anti-magnetic” behaviour allows diamagnets to circumvent Earnshaw’s theorem with possible levitatation above a permanent magnet. A subtle balance of the upward repulsive force exerted by a diamagnet over an underlying permanent magnet and the downward drag by gravity would make it possible for the diamagnetic object to levitate.
6. Diamagnetism and levitation
Diamagnets although million times weaker than the magnetic forces of permanent magnets such as ferromagnetic iron, could levitate under right conditions. Atoms of diamagnets have completely filled electronic shells which would mean that there is equal number of electrons with positive and negative spins so that the net magnetic moment is zero. As a result, diamagnets are not affected by magnetic fields. The electrons in a diamagnet are able to rearrange their orbits slightly so as to create a small persistent current that would oppose/ repel the externally applied magnetic field.
Most of the seemingly common, non-magnetic substances exhibit diamagnetism via readjustment of electron orbits in a magnetic field. Examples of diamagnetism include graphite, bismuth, quartz (SiO2), calcite (CaCO3), superconductors, protein, diamond, DNA, plastic, wood and many others including water. Also, other examples which constitute diamagnetic molecules namely live animals and humans, are made up of components such as bones, proteins and where two third of body fluid is water. Bismuth and graphite are the strongest diamagnetic elements (~ 20 times greater than water). Even for these elements, χ is very small and negative ranging from - 17*10^-5 for bismuth to - 41*10^-5 for pyrolytic graphite. These χ values are orders of magnitude lower than the positive values of paramagnets and ferromagnets.
6.1 Laboratory demonstration
Three basic demonstrations of magnetic levitation are described.
Type 1: Levitation of diamagnet in a magnetic field
In the presence of a powerful magnet, the tiny repulsive force of a diamagnet could be sufficient to levitate it with apparent weightlessness over a permanent magnet. A proper balance between the attraction of a permanent magnet and the repulsive force of a diamagnetic object can overcome gravitational pull on the individual atoms and molecules of the levitated object. Illustrations of diamagnets floating in a magnetic field under controlled magnetic force of a strong magnet are reported for a range of diamagnetic materials from simple metals (antimony and bismuth), polymers, organic liquids (propanol, acetone) to various everyday plants and living creatures such as frog, fish and mouse.
Magnetic field required for levitation of a diamagnet can be estimated from a knowledge of the ratio of magnetic susceptibility (χ) to material density (ρ). For great majority of diamagnetic materials, χ/ρ ratio is close to 10^-5 cubic centimetre per gram with graphite having the largest ratio of 8*10^-5 cm^3/g known for a diamagnet. Magnetic field with an intensity ~ 10 Tesla is estimated to be strong enough to levitate most diamagnetic materials with χ/ρ around 10^-5 cm^3/g. A worldwide attention of the wonder of diamagnetic levitation was drawn by Andre Geim and his group in 1997 by magnetically levitating a live frog in the bore of a 16 - 20 Tesla strong magnet such as Bitter magnet. Interestingly, it has been reported that levitation of a human body would possibly require a novel magnet design such as special racetrack magnet that could provide a magnetic field of about 40 Tesla with an expected consumption of about 1GW energy.
Type 2 : Levitation of magnet sandwiched between two diamagnets
The unstable levitation (sec.5) of a bottom magnet towards the opposite polarity of another magnet on top, can be stabilised by placing the bottom magnet between two diamagnets such as graphite plates or human fingertips (χ ~ - 10^ -5). If a magnet is held between two human fingers which are about 20 times less diamagnetic than graphite, a much larger magnet would be required at the top of the fingers. Levitation is possible because of the repulsion between a magnet and a diamagnet. Thus if the floating (bottom) magnet tends to drop off because of gravity, repulsive force of the diamagnet underneath would push it up without touching it. On the other hand, if the floating magnet tends to jump up towards the top magnet, it will be forced down by repulsion of the second diamagnet placed above it.
Type 3 : Levitation of superconductor(diamagnet) over magnet and vice versa
Superconductors can be considered as perfect diamagnets (χ = - 1) and are even more profoundly diamagnetic than bismuth and graphite. However, as such at room temperature they have no interesting magnetic or electrical properties. But once cooled down to a very low characteristic critical temperature Tc, e.g. -185 C for diamagnetic yttrium-barium-copper oxide ceramic, these materials become superconductors when they are able to conduct electricity at zero resistance, and hence with no energy loss.
There are two types of superconductors: Type – 1 : these are elements e.g. lead, aluminium, mercury, etc with very low Tc (highest is for lead at -266 C), and
Type – 2 : these are compounds with higher Tc (highest Tc has so far been + 77 C for Tl7Sn2Ba2MnCu10O20).
Superconductivity and magnetism do not like each other. Superconductors expel magnetic field, hence repel magnets. As a result, a superconductor on transition from normal non-conductive state to superconductivity below Tc, actively excludes magnetic field from its interior (Meissner effect). Once the repulsion becomes stronger than gravity, levitation would occur.
The Type - 2 superconductors, unlike pure metals of Type -1, are made up of several component elements, and consequently characterized by imperfect crystalline structures with vacancy defects/ voids that would allow some magnetic flux lines to pass through them. These few local flux lines become pinned/locked inside a superconductor known as flux pinning phenomenon. Thus despite dislike for magnetism, some of the lines of magnetic field in the form of tubes of magnetic flux could penetrate through a superconductor via weak areas of microscopic inhomogeneity in the material such as crystal lattice defects, grain boundaries or precipitation of a different phase. Superconductivity will be locally destroyed in these weak areas. Flux pinning, however, cannot occur in Type – 1 superconductors because of their homogeneous perfect crystal structures which lack weakness to allow magnetic fields to penetrate.
Levitation of superconductor
On placing a magnet over a Type-2 superconductor or vice versa, a balance is struck between the repulsive force of the superconductor and attraction of the magnet that can outweigh the pull of gravity. Under this condition, a superconductor or magnet as the case may be, would start to levitate. A stable levitation will have a continuous range of equilibrium positions or orientations that would allow levitation to be motionless as if it were stuck in sand. Apart from the necessity of a low working temperature i.e. below Tc to attain superconductivity, there are no other energy inputs for such levitation.
The local pinning of magnetic flux lines trapped in the superconductor serve as invisible threads holding the superconductor and magnet together at a certain distance. Thinner the superconductor disc, easier it is for the magnetic field to exploit the crystalline defects in the disc and thereby ensuring local threading to be effective enough to prevent the levitating disc from flying into air/space.
Quantum Levitation – clarification of terminology
The phenomenon of magnetic levitation of a superconductor due to local pinning/ locking of magnetic field is coined as quantum levitation by Tel Aviv University superconductor group because of link of superconductivity to quantum physics. However, the terminology is a misnomer. For an ideal quantum levitation to be discussed in the part 3, reversal Casimir force derived from quantum theory is involved.
7. Electromagnetism and levitation
Despite impressive laboratory demonstrations of magnetic levitation (sec.6.1), the magnetic field of a diamagnet is too weak to warrant any commercial interest. The feeble magnetic field can be made stronger by transforming the non-magnetic diamagnet (e.g. superconductor) or a conductor (like copper) to an electromagnet.
Basics of electromagnetism
An electromagnet is similar to a magnet in terms of attraction and repulsion properties. However, via principle of electromagnetism, magnetic field is created by passing electric current through a non-magnetic conductor such as a copper wire or a superconducting diamagnet. This can be demonstrated by connecting the ends of a copper wire to the positive and negative terminals of a battery. On applying the current, electrons i.e. electric charges will move along the wire generating a magnetic field that would attract metallic objects like paperclips. Thus the non-magnetic copper wire becomes an electromagnet with its magnetic field the strength directly proportional to the area of the wire and magnitude of the battery voltage hence the current.
Above demonstration indicates possible creation of a stronger magnetic field can be produced in a conductor like copper or a superconductor by simply increasing the applied current. The effect of producing “free” electromagnets will be specially pronounced in supercooled i.e. below Tc superconductors. This is because, unlike copper wire, superconductors have no resistance, thus allowing the current to flow through them virtually forever. A major advantage of an electromagnet over a permanent magnet is that the magnetic field can be rapidly manipulated over a wide range by controlling the input of electric current. The drawback of electromagnetism is the need for continuous supply of electrical energy to sustain magnetism and hence the magnetic field. Once the power is turned off by disconnecting from the battery, the magnetic field and hence electromagnetism will disappear and the paperclips will drop off the wire.
Application of the simple wire-and-battery concept of electromagnetism to a real operational system for magnetic levitation involves considerable technological innovation. Based on electromagnetism, commercial magnetic levitation namely Maglev (acronym for magnetic levitation) train has been developed in Germany and Japan primarily in the field of transportation.
8 . Commercial application of magnetic levitation - Maglev trains
Passenger air travel has revolutionized the transportation industry in the last century with the development of modern aircraft industry that provides the fastest way to travel hundreds and thousands of miles. Alternatives to air transport namely cars, buses, ships and conventional trains are too slow for today’s fast –paced society. Commercial propositions around that time when the first US Patent (No.1, 020,942) was awarded to Emile Bachelet in 1912 for his “Levitated Transmitted Apparatus”, were impractical because of either too high power consumption, unstable levitation or the weight that could be levitated was too small. Research has moved on since then with the first practical Maglev system proposed and published in 1966 in the USA.
There has been development of high-speed Maglev trains using electricity as the only main source of energy. It is now apparent that the modern advanced technology is likely to revolutionize transportation of the 21st century the way airplanes did in the 20th century. Besides speeding up transportation, Maglev technology is capable of counteracting the adverse effects of growing congestion on the roads and at airports, increasing fuel costs and environmental issues including increasing oil dependence.
8.1 Maglev and conventional trains
Maglev train is inconspicuous and does not have a traditional railway engine to pull compartments. Instead of fossil fuels in conventional train to pull the engine along the steel tracks, Maglev train is propelled by magnetic field. It does not require wheels, axles and bearings of conventional trains. This replacement of mechanical components with wear-free electronics in Maglev makes the system free of technical restrictions of wheel-on-rail technology.
Maglev trains float/levitate on a cushion of air above ground without any direct physical contact with the guidway/track, and thus avoid any friction normally involved in the movement of traditional trains. The lack of friction combined with trains’ aerodynamic designs allows Maglev trains to reach unprecedented ground speed of more than 310 mph (500km/h) which, for example, would mean that the travelling time from Paris to Rome would be just over two hours.
8.2 System evaluation
There are currently three known maglev systems : 1) electromagnetic levitation /suspension (EML/EMS), 2) electrodynamic levitation /suspension (EDL/EDS), and 3)Inductrack In order to avoid mixing up of terms such as levitation and suspension, the present text will adhere to EML and EDL terminologies only. Electrodynamic levitation lends its name from the dynamic activity using electromagnetic induction. Based on electromagnetism, both EML and EDL systems operate on the interaction of superconductors and magnets, while copper coils on the track underneath the train’s permanent magnets are used in Inductrack. Unlike EDL and EML, electromagnetism is not involved in Inductrack. EML is primarily developed in Germany, EDL in Japan and Inductrack in the USA.
The three primary functions in Maglev technology namely levitation, propulsion and guidance are all performed by magnetic fields/forces using magnets which are located within the vehicle and the guideway/track. Attractive and repulsive magnetic forces operate in EML and EDL systems respectively.
Guideway which traces the vehicle paths, is a structure constructed with concrete or steel girders. It supports the load of Maglev trains and provides guidance for the trains’ movement over it. Function of the guideway structure is basically to endure applied loads from the train and transfer them to the foundations.
The levitating magnets in both EDL and EML systems are mounted onto a number of “carriages” connected to the train body by a secondary suspension system of dampers and springs. Both systems have merits and drawbacks in terms of maintenance of coils, mechanical and electrical complexity and operational stability. Speeds of Maglev trains up to 552 km/h (343 mph) and 450km/h (280 mph)are reported in Japan and Germany respectively. In fact, speeds up to 361 mph (581 km/h) have been recorded in Japan.
8.2.1 EML levitation ( known as Transrapid after a German company’s name)
The wire-and-battery illustration of electromagnetism provides the basic idea for EML to create a magnetic field necessary to levitate a train over a guiding rail. The three major essentials in EML system are large electrical power source, metal coils lining the vehicle path (guideway) and electromagnets attached to the underside of the train for levitation and guidance.
Based on attractive forces of magnet, EML system uses powered electromagnets to levitate the train by about 1-2 cm above the guideway. Levitation or supporting magnets fixed on either side of train’s undercarriage are powered by batteries on board the train to convert them to electromagnets. They are directed up toward a stator attached to the underside of the concrete guideway. The stator is a pack of laminated conductors of ferromagnetic steel sheets and cable windings. When the attraction due to magnetic field between train’s levitation electromagnets and the stator exceeds the gravitational downward pull, the train is pulled upwards and begins to levitate over the guideway.
There are also guidance magnets attached to either side of train’s undercarriage, which generate magnetic force to guide the train along the guideway track. These magnets stop the train swaying side to side and thereby prevent the train from hitting the side of the track and thus avoid damage to the train. EML trains are virtually impossible to derail because of being wrapped around a T-shaped guideway.
The intensity of magnetic field inside passenger compartments in EML compared to EDS is quite small, comparable to earth’s magnetic field of 25-65 microtesla, and far below that of a hair dryer or an electric drill or a sewing machine. Passengers with pacemakers or carrying magnetic storage such as credit card or hard disk are thus safe to travel in EML than EDL maglev trains. However, drawback of EML system lies with its inherent instability due to the the narrow gap (1-2 cm) between the levitated train and guideway. Computerised position sensors and electronic feedback systems are used to maintain the required gap within ± 1 mm and also to prevent the train hitting the guidway.
8.2.2 EDL levitation (Japanese system)
Japanese engineers have developed a competing version of Maglev trains based on magnetic force of repulsion rather than attraction of the EML system. There are two aspects of EDL system: levitation and propulsion of levitated train. EDS utilizes the principle of electromagnetic induction briefly described next.
In 1831, Michael Faraday discovered that when a permanent magnet was dropped down a conductive coil/tube of say copper in close proximity, a voltage and hence a current was induced (called Eddy current) in the coil by the magnetic field of the magnet. Thus an electric current was detected in the coil by applying magnetic field only, and no batteries. According to Faraday’s electromagnetic induction law, movement of the magnet back and forth in the coil or vice versa, would induce current whose magnitude is proportional to the speed of the relative movement between the coil and magnet. For example, faster the magnet travels, the bigger the current produced. In EDL, electromagnet on board the train travels over the stationary conducting coils mounted on the sidewalls of guideway which will have induced Eddy current from the magnetic field of the electromagnet from the moving train.
Lenz’s law extends Faraday’s law by stipulating that the induced Eddy current will in turn generate a magnetic field in the coil that would oppose or counteract the original magnetic field of the magnet. This would lead to repulsion between the two fields.
In EDL, conductors on board the train are converted to electromagnets by passing current through them. The corresponding magnetic field would quickly die away if copper is used as the conductor because of its internal resistance. In contrast, a superconductor with no resistance would provide greater magnetic field. It would also allow the induced current and hence the accompanying magnetic field to sustain without dissipation even when the train containing the superconducting magnet stops moving.
Mechanics of EDL operation
In general, EDL system has a magnetic track that repels other magnets on board the train, allowing the train to levitate above the track. Superconductors converted to electromagnets by passing current through them after being cooled to cryogenic temperature, are placed on board the train. Conductive coils are mounted as a series of “8”-shaped coils on each side of the sidewalls of guideway. When the train with on-board superconducting magnets travels at a high speed about several centimetres below the centre of these coils, Eddy current is induced within the coils which then become electromagnets temporarily. It is estimated that the train would not induce magnetic field in the coils for levitation until it reaches a minimum speed ~ 50 mph (80 km/h).The magnetic field from the induced currents on the guidway walls interacts with the large magnetic field of the superconducting magnets of the passing train. Following Lenz’s law, this interaction produces repelling force which once becomes high enough to overcome the weight of the train, it would levitate the train above the guideway by up to 10 cm.
The “8” shaped levitation on either side of the guideway walls facing each other, are connected under the guideway, making a loop. An electric current induced in the loop by the running train helps to keep the train located at the centre of the guideway. Once the train is levitated, electric current is supplied to these coils to create a unique combination of magnetic fields that will pull and push the on-board superconducting magnets and propel the train along the guideway.
Unlike EML where the stability of a moving train levitating over a small air gap requires complicated feedback loop, the EDL system does not require such feedback control. The larger air gap in EDL is, however, continuously monitored and adjusted by computer to prevent the train hitting the guideway. The need for maintaining a low (liquid helium) temperature of ~ 4.2 k for superconducting magnetic coils results in costly electrically powered expensive, cryogenic equipment for EDL trains.
8.2.3 Inductrack (USA) This is another version of EDL using room-temperature permanent magnets to produce the magnetic fields instead of powered electromagnets (EML) or cooled superconducting magnets (EDL). Magnets are arranged on the underside of a train in a special way called “Halbach array” which makes the magnetic field on one side of the array stronger and cancelling the field to near zero on the other side. In this array, tracks made of copper coils are arranged like rungs in a ladder to produce magnetic fields that induce strong repulsive currents, similar to electromagnetic induction principle of EDL system. As the train moves, the generated induced magnetic field of the coils repels the fields from magnets mounted on train’s undercarriages. This repulsion causes lifting up/levitation of the train by several centimetres. As long as the train moves a few miles per hour, an Inductrack train will levitate nearly an inch above the track. When at rest, no levitation occurs. There is no commercial operation of Inductrack system as yet.
9. Final comments
The technology of “high speed” or “bullet” trains with speeds around 241 – 290 km/h (150 – 180 mph) has reached its final phase because of the limitation of speed imposed by the mechanical friction between railway wheels and metal tracks. In contrast, no friction is involved in Maglev trains. Although the concept is known for years, the technology has now advanced enough to encourage commercial interest primarily in transportation. As a result, Maglev system is becoming a popular application around the globe where the train is levitated by magnetic fields with no physical contact between the train and the track. It is incredible to think that a train can actually float 1-10 cm in the air while travelling at a speed around 500km/h (310 mph). The new technology can reduce air and motorway congestion, air pollution and petroleum use. All this achievement indicates a very bright future for Maglev. After all, fighting the forces of gravity and friction is what magnets do best.