Solar sail

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IKAROS spaceprobe with solar sail in flight (artist's depiction) showing a typical square sail configuration

Solar sails (also called light sails or photon sails) are a form of spacecraft propulsion using the radiation pressure (also called solar pressure) from stars to push large ultra-thin mirrors to high speeds. Light sails could also be driven by energy beams to extend their range of operations, which is strictly beam sailing rather than solar sailing.

Solar sail craft offer the possibility of low-cost operations combined with long operating lifetimes. Since they have few moving parts and use no propellant, they can potentially be used numerous times for delivery of payloads.

Solar sails use a phenomenon that has a proven, measured effect on spacecraft. Solar pressure affects all spacecraft, whether in interplanetary space or in orbit around a planet or small body. A typical spacecraft going to Mars, for example, will be displaced by thousands of kilometres by solar pressure, so the effects must be accounted for in trajectory planning, which has been done since the time of the earliest interplanetary spacecraft of the 1960s. Solar pressure also affects the attitude of a craft, a factor that must be included in spacecraft design.^[1]

The total force exerted on an 800 by 800 meter solar sail, for example, is about 5 newtons (1.1 lbf) at Earth's distance from Sol,^[2] making it a low-thrust propulsion system, similar to spacecraft propelled by electric engines.

History of concept

Johannes Kepler observed that comet tails point away from the Sun and suggested that the sun caused the effect. In a letter to Galileo in 1610, he wrote, "Provide ships or sails adapted to the heavenly breezes, and there will be some who will brave even that void." He might have had the comet tail phenomenon in mind when he wrote those words, although his publications on comet tails came several years later.^[3]

James Clerk Maxwell, in 1861–64, published his theory of electromagnetic fields and radiation, which shows that light has momentum and thus can exert pressure on objects. Maxwell's equations provide the theoretical foundation for sailing with light pressure. So by 1864, the physics community and beyond knew sunlight carried momentum that would exert a pressure on objects.

Jules Verne, in From the Earth to the Moon, published in 1865, wrote "there will some day appear velocities far greater than these [of the planets and the projectile], of which light or electricity will probably be the mechanical agent ... we shall one day travel to the moon, the planets, and the stars." This is possibly the first published recognition that light could move ships through space. Given the date of his publication and the widespread, permanent distribution of his work, it appears that he should be regarded as the originator of the concept of space sailing by light pressure, although he did not develop the concept further^{[original research?]}. Verne probably got the idea directly and immediately from Maxwell's 1864 theory (although it cannot be ruled out that Maxwell or an intermediary recognized the sailing potential and became the source for Verne).^[4]

Pyotr Lebedev was first to successfully demonstrate light pressure, which he did in 1899 with a torsional balance;^[5] Ernest Nichols and Gordon Hull conducted a similar independent experiment in 1901 using a Nichols radiometer.^[6]

Albert Einstein provided a different formalism by his recognizing the equivalence of mass and energy. He simply wrote p = E/c as the relationship between the momentum, the energy, and the speed of light.

Svante Arrhenius predicted in 1908 the possibility of solar radiation pressure distributing life spores across interstellar distances, the concept of panspermia. He apparently was the first scientist to state that light could move objects between stars.^[7]

Friedrich Zander (Tsander) published a technical paper that included technical analysis of solar sailing. Zander wrote of "using tremendous mirrors of very thin sheets" and "using the pressure of sunlight to attain cosmic velocities".^[8]

JBS Haldane speculated in 1927 the invention of tubular spaceships that would take humanity to space and how "wings of metallic foil of a square kilometre or more in area are spread out to catch the sun's radiation pressure".^[9]

J.D. Bernal wrote in 1929, "A form of space sailing might be developed which used the repulsive effect of the sun's rays instead of wind. A space vessel spreading its large, metallic wings, acres in extent, to the full, might be blown to the limit of Neptune's orbit. Then, to increase its speed, it would tack, close-hauled, down the gravitational field, spreading full sail again as it rushed past the sun."^[10]
The first formal technology and design effort for a solar sail began in 1976 at Jet Propulsion Laboratory for a proposed mission to rendezvous with Halley's Comet.^[2]

Physical principles

Solar radiation pressure

Solar radiation exerts a pressure on the sail due to reflection and a small fraction that is absorbed. The absorbed energy heats the sail, which re-radiates that energy from the front and rear surfaces.
The momentum of a photon or an entire flux is given by p = E/c,^[11][12] where E is the photon or flux energy, p is the momentum, and c is the speed of light. Solar radiation pressure is calculated on an irradiance (solar constant) value of 1361 W/m² at 1 AU (earth-sun distance), as revised in 2011:^[13]

perfect absorbance: F = 4.54 μN per square metre (4.54 μPa)
perfect reflectance: F = 9.08 μN per square metre (9.08 μPa)  (normal to surface)

A perfect sail is flat and has 100% specular reflection. An actual sail will have an overall efficiency of about 90%, about 8.25 μN/m²,^[14] due to curvature (billow), wrinkles, absorbance, re-radiation from front and back, non-specular effects, and other factors.

Force on a sail results from reflecting the photon flux

The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the sun (unless close to the sun^[15]), and by the square of the cosine of the angle between the sail force vector and the radial from the sun, so

F = F₀ cos² θ / R² (ideal sail)

where R is distance from the sun in AU. An actual square sail can be modeled as:

F = F₀ (0.349 + 0.662 cos 2θ − 0.011 cos 4θ) / R²

Note that the force and acceleration approach zero generally around θ = 60° rather than 90° as one might expect with an ideal sail.^[16]

Solar wind, the flux of charged particles blown out from the sun, exerts a nominal dynamic pressure of about 3 to 4 nPa, three orders of magnitude less than solar radiation pressure on a reflective sail.^[17]

Sail parameters

Sail loading (areal density) is an important parameter, which is the total mass divided by the sail area, expressed in g/m². It is represented by the Greek letter σ.

A sail craft has a characteristic acceleration, a_c, which it would experience at 1 AU when facing the sun. It is related to areal density by:

a_c = 8.25 / σ, in mm/s² (assuming 90% efficiency)

The lightness number, λ, is the dimensionless ratio of maximum vehicle acceleration divided by the sun's local gravity; using the values at 1 AU:

λ = a_c / 5.93

The table presents some example values. Payloads are not included. The first two are from the detailed design effort at JPL in the 1970s. The third, the lattice sailer, might represent about the best possible performance level.^[2] The dimensions for square and lattice sails are edges. The dimension for heliogyro is blade tip to blade tip.

Type	σ	ac	λ	Size
Square sail	5.27	1.56	0.26	820 m
Heliogyro	6.39	1.29	0.22	15 km
Lattice sailer	0.07	117	20	1 km

Attitude control

An active attitude control system (ACS) is essential for a sail craft to achieve and maintain a desired orientation. The required sail orientation changes slowly (often less than 1 degree per day) in interplanetary space, but much more rapidly in a planetary orbit. The ACS must be capable of meeting these orientation requirements.

Attitude control is achieved by a relative shift between the craft's center of pressure and its center of mass. This can be achieved with control vanes, movement of individual sails, movement of a control mass, or altering reflectivity.

Holding a constant attitude requires that the ACS maintain a net torque of zero on the craft. The total force and torque on a sail, or set of sails, is not constant along a trajectory. The force changes with solar distance and sail angle, which changes the billow in the sail and deflects some elements of the supporting structure, resulting in changes in the sail force and torque.

Sail temperature also changes with solar distance and sail angle, which changes sail dimensions. The radiant heat from the sail changes the temperature of the supporting structure. Both factors affect total force and torque.

To hold the desired attitude the ACS must compensate for all of these changes.^[18]

Constraints

In Earth orbit, solar pressure and drag pressure are typically equal at an altitude of about 800 km, which means that a sail craft would have to operate above that altitude. Sail craft must operate in orbits where their turn rates are compatible with the orbits, which is generally a concern only for spinning disk configurations.

Sail operating temperatures are a function of solar distance, sail angle, reflectivity, and front and back emissivities. A sail can be used only where its temperature is kept within its material limits. Generally, a sail can be used rather close to the sun, around 0.25 AU, or even closer if carefully designed for those conditions.^[2]

Applications

Potential applications for sail craft range throughout the solar system, from near the sun to the comet clouds beyond Neptune. The craft can make outbound voyages to deliver loads or to take up station keeping at the destination. They can be used to haul cargo and possibly also used for human travel.^[2]

Inner planets

For trips within the inner solar system, they can deliver loads and then return to Earth for subsequent voyages, operating as an interplanetary shuttle. For Mars in particular, the craft could provide economical means of routinely supplying operations on the planet.

Solar sail craft can approach the sun to deliver observation payloads or to take up station keeping orbits. They can operate at 0.25 AU or closer. They can reach high orbital inclinations, including polar.

Solar sails can travel to and from all of the inner planets. Trips to Mercury and Venus are for rendezvous and orbit entry for the payload. Trips to Mars could be either for rendezvous or swing-by with release of the payload for aerodynamic braking.^[2]

Outer planets

Minimum transfer times to the outer planets benefit from using an indirect transfer (solar swing-by). However, this method results in high arrival speeds. Slower transfers have lower arrival speeds.
The minimum transfer time to Jupiter for a_c of 1 mm/s² with no departure velocity relative to Earth is 2 years when using an indirect transfer (solar swing-by). The arrival speed (V_∞) is close to 17 km/s. For Saturn, the minimum trip time is 3.3 years, with an arrival speed of nearly 19 km/s.^[2]

Minimum times to the outer planets (a_c = 1 mm/s²)

	Jupiter	Saturn	Uranus	Neptune
Time, yr	2.0	3.3	5.8	8.5
Speed, km/s	17	19	20	20

Oort Cloud

A small team had initially proposed a beryllium inflated sail that would go down to 0.05 AU from the Sun in order to get an acceleration peaking at 36.4 m/s², reaching a speed of 0.00264c (about 950 km/s) in less than a day. Such proximity to the Sun could prove to be impractical in the near term due to the structural degradation of beryllium at high temperatures, diffusion of Hydrogen at high temperatures as well as an electrostatic gradient, generated by the ionization of beryllium due to the solar wind, posing a burst risk; thus a revised perihelion of 0.1 AU was proposed to reduce the aforementioned temperature and solar flux exposure.^[19] Such a sail would take "Two and a half years to reach the heliopause, six and a half years to get to the Sun’s inner gravitational focus (at about 550 AU, the point at which light is focused by gravity as it passes the sun^[20]), with arrival at the inner Oort Cloud in no more than thirty years." "Such a mission could perform useful astrophysical observations en route, explore gravitational focusing techniques, and image Oort Cloud objects while exploring particles and fields in that region that are of galactic rather than solar origin."

Satellites

Robert L. Forward pointed out that a solar sail could be used to modify the orbit of a satellite around the Earth. In the limit, a sail could be used to "hover" a satellite above one pole of the Earth.
Spacecraft fitted with solar sails could also be placed in close orbits about the Sun that are stationary with respect to either the Sun or the Earth, a type of satellite named by Forward a statite. This is possible because the propulsion provided by the sail offsets the gravitational potential of the Sun. Such an orbit could be useful for studying the properties of the Sun over long durations.^{[citation needed]}
Such a spacecraft could conceivably be placed directly over a pole of the Sun, and remain at that station for lengthy durations. Likewise a solar sail-equipped spacecraft could also remain on station nearly above the polar terminator of a planet such as the Earth by tilting the sail at the appropriate angle needed to just counteract the planet's gravity.^{[citation needed]}

In his book The Case for Mars, Robert Zubrin points out that the reflected sunlight from a large statite placed near the polar terminator of the planet Mars could be focused on one of the Martian polar ice caps to significantly warm the planet's atmosphere. Such a statite could be made from asteroid material.^{[citation needed]}

Trajectory corrections

The MESSENGER probe orbiting Mercury used light pressure on its solar panels to perform fine trajectory corrections on the way to Mercury.^[21] By changing the angle of the solar panels relative to the Sun, the amount of solar radiation pressure was varied to adjust the spacecraft trajectory more delicately than possible with thrusters. Minor errors are greatly amplified by gravity assist maneuvers, so using radiation pressure to make very small corrections saved large amounts of propellant.

Interstellar flight

In the 1970s, Robert Forward proposed two beam-powered propulsion schemes using either lasers or masers to push giant sails to a significant fraction of the speed of light.^[22]
In The Flight of the Dragonfly, Forward described a light sail propelled by super lasers. As the starship neared its destination, the outer portion of the sail would detach. The outer sail would then refocus and reflect the lasers back onto a smaller, inner sail. This would provide braking thrust to stop the ship in the destination star system.

Both methods pose monumental engineering challenges. The lasers would have to operate for years continuously at gigawatt strength. Forward's solution to this requires enormous solar panel arrays to be built at or near the planet Mercury. A planet-sized mirror or fresnel lens would be needed several dozen astronomical units from the Sun to keep the lasers focused on the sail. The giant braking sail would have to act as a precision mirror to focus the braking beam onto the inner "deceleration" sail.

A potentially easier approach would be to use a maser to drive a "solar sail" composed of a mesh of wires with the same spacing as the wavelength of the microwaves, since the manipulation of microwave radiation is somewhat easier than the manipulation of visible light. The hypothetical "Starwisp" interstellar probe design^[23][24] would use microwaves, rather than visible light, to push it. Masers spread out more rapidly than optical lasers owing to their longer wavelength, and so would not have as long an effective range.

Masers could also be used to power a painted solar sail, a conventional sail coated with a layer of chemicals designed to evaporate when struck by microwave radiation.^[25] The momentum generated by this evaporation could significantly increase the thrust generated by solar sails, as a form of lightweight ablative laser propulsion.

To further focus the energy on a distant solar sail, designs have considered the use of a large zone plate. This would be placed at a location between the laser or maser and the spacecraft.^[22]

Another more physically realistic approach would be to use the light from the sun to accelerate.^[26] The ship would first drop into an orbit making a close pass to the sun, to maximize the solar energy input on the sail, then the ship would begin to accelerate away from the system using the light from the sun to keep accelerating. Acceleration will drop approximately as the inverse square of the distance from the sun, and beyond some distance, the ship would no longer receive enough light to accelerate it significantly, but would maintain its course due to inertia. When nearing the target star, the ship could turn its sails toward it and begin to use the outward acceleration to decelerate. Additional forward and reverse thrust could be achieved with more conventional means of propulsion such as rockets.

Similar solar sailing launch and capture were suggested for directed panspermia to expand life in other solar systems. Velocities of 0.0005 c could be obtained by solar sails carrying 10 kg payloads, using thin solar sail vehicles with effective areal densities of 0.1 g/m² with thin sails of 0.1 µm thickness and sizes on the order of one square kilometer. Alternatively, swarms of 1 mm capsules can be launched on solar sails with radii of 42 cm, each carrying 10,000 capsules of a hundred million extremophile microorganism to seed life in diverse target environments.^[27][28]

Deorbiting artificial satellites

Small solar sails have been proposed to accelerate the deorbiting of small artificial satellites from Earth orbits. Satellites in low Earth orbit can use a combination of solar pressure on the sail and increased atmospheric drag to accelerate satellite reentry.^[29]

Sail configurations

NASA illustration of the unlit side of a half-kilometre solar sail, showing the struts stretching the sail.

An artist's depiction of a Cosmos 1-type spaceship in orbit

IKAROS, launched in 2010, has been the first practical solar sail vehicle. In 2012, it was still under thrust, proving the practicality of a solar sail for long-duration missions.^[30] It is spin-deployed, with tip-masses in the corners of its square sail. The sail is made of thin polyimide film, with evaporated aluminium on it. It steers with electrically-controlled liquid crystal panels. The sail slowly spins, and these panels turn on and off to control the attitude of the vehicle. When on, they diffuse light, reducing the momentum transfer to that part of the sail. When off, the sail reflects more light, transferring more momentum. In that way, they turn the sail.^[31] Thin-film solar cells are also integrated into the sail, powering the spacecraft. The design is very reliable, because spin deployment simplified the mechanisms to unfold the sail and the LCD panels have no moving parts.

Parachutes have very low mass, but a parachute is not a workable configuration for a solar sail. Analysis shows that a parachute configuration would collapse from the forces exerted by shroud lines, since radiation pressure does not behave like aerodynamic pressure, and would not act to keep the parachute open.^[32]

Eric Drexler^[33] proposed very high thrust-to-mass solar sails, and made prototypes of the sail material. His sail would use panels of thin aluminium film (30 to 100 nanometres thick) supported by a tensile structure. The sail would rotate and would have to be continually under thrust. He made and handled samples of the film in the laboratory, but the material was too delicate to survive folding, launch, and deployment. The design planned to rely on space-based production of the film panels, joining them to a deploy-able tension structure. Sails in this class would offer high area per unit mass and hence accelerations up to "fifty times higher" than designs based on deploy-able plastic films.^[33]

The highest thrust-to-mass designs for ground-assembled deploy-able structures are square sails with the masts and guy lines on the dark side of the sail. Usually there are four masts that spread the corners of the sail, and a mast in the center to hold guy-wires. One of the largest advantages is that there are no hot spots in the rigging from wrinkling or bagging, and the sail protects the structure from the Sun. This form can, therefore, go close to the Sun for maximum thrust. Most designs steer with small moving sails on the ends of the spars.^[34]

In the 1970s JPL studied many rotating blade and ring sails for a mission to rendezvous with Halley's Comet. The intention was to stiffen the structures using angular momentum, eliminating the need for struts, and saving mass. In all cases, surprisingly large amounts of tensile strength were needed to cope with dynamic loads. Weaker sails would ripple or oscillate when the sail's attitude changed, and the oscillations would add and cause structural failure. The difference in the thrust-to-mass ratio between practical designs was almost nil, and the static designs were easier to control.^[34]

JPL's reference design was called the "heliogyro". It had plastic-film blades deployed from rollers and held out by centrifugal forces as it rotated. The spacecraft's attitude and direction were to be completely controlled by changing the angle of the blades in various ways, similar to the cyclic and collective pitch of a helicopter. Although the design had no mass advantage over a square sail, it remained attractive because the method of deploying the sail was simpler than a strut-based design.^[34]

JPL also investigated "ring sails" (Spinning Disk Sail in the above diagram), panels attached to the edge of a rotating spacecraft. The panels would have slight gaps, about one to five percent of the total area. Lines would connect the edge of one sail to the other. Masses in the middles of these lines would pull the sails taut against the coning caused by the radiation pressure. JPL researchers said that this might be an attractive sail design for large manned structures. The inner ring, in particular, might be made to have artificial gravity roughly equal to the gravity on the surface of Mars.^[34]

A solar sail can serve a dual function as a high-gain antenna.^[35] Designs differ, but most modify the metalization pattern to create a holographic monochromatic lens or mirror in the radio frequencies of interest, including visible light.^[35]

Electric solar wind sail

Pekka Janhunen from FMI has invented a type of solar sail called the electric solar wind sail.^[36] Mechanically it has little in common with the traditional solar sail design. The sails are replaced with straightened conducting tethers (wires) placed radially around the host ship. The wires are electrically charged to create an electric field around the wires. The electric field extends a few tens of metres into the plasma of the surrounding solar wind. The solar electrons are reflected by the electric field (like the photons on a traditional solar sail). The radius of the sail is from the electric field rather than the actual wire itself, making the sail lighter. The craft can also be steered by regulating the electric charge of the wires. A practical electric sail would have 50–100 straightened wires with a length of about 20 km each.^{[citation needed]}
Electric solar wind sails can adjust their electrostatic fields and sail attitudes.

Magnetic sail

A magnetic sail would also employ the solar wind. However, the magnetic field deflects the electrically charged particles in the wind. It uses wire loops, and runs a static current through them instead of applying a static voltage.^[37]
All these designs maneuver, though the mechanisms are different.

Magnetic sails bend the path of the charged protons that are in the solar wind. By changing the sails' attitudes, and the size of the magnetic fields, they can change the amount and direction of the thrust.

Sail making

Materials

The material developed for the Drexler solar sail was a thin aluminium film with a baseline thickness of 0.1 µm, to be fabricated by vapor deposition in a space-based system. Drexler used a similar process to prepare films on the ground. As anticipated, these films demonstrated adequate strength and robustness for handling in the laboratory and for use in space, but not for folding, launch, and deployment.

The most common material in current designs is aluminized 2 µm Kapton film. It resists the heat of a pass close to the Sun and still remains reasonably strong. The aluminium reflecting film is on the Sun side. The sails of Cosmos 1 were made of aluminized PET film (Mylar).

Research by Dr. Geoffrey Landis in 1998–9, funded by the NASA Institute for Advanced Concepts, showed that various materials such as alumina for laser lightsails and carbon fiber for microwave pushed lightsails were superior sail materials to the previously standard aluminium or Kapton films.^[38]

In 2000, Energy Science Laboratories developed a new carbon fiber material that might be useful for solar sails.^[39] The material is over 200 times thicker than conventional solar sail designs, but it is so porous that it has the same mass. The rigidity and durability of this material could make solar sails that are significantly sturdier than plastic films. The material could self-deploy and should withstand higher temperatures.

There has been some theoretical speculation about using molecular manufacturing techniques to create advanced, strong, hyper-light sail material, based on nanotube mesh weaves, where the weave "spaces" are less than half the wavelength of light impinging on the sail. While such materials have so far only been produced in laboratory conditions, and the means for manufacturing such material on an industrial scale are not yet available, such materials could mass less than 0.1 g/m²,^[40] making them lighter than any current sail material by a factor of at least 30. For comparison, 5 micrometre thick Mylar sail material mass 7 g/m², aluminized Kapton films have a mass as much as 12 g/m²,^[34] and Energy Science Laboratories' new carbon fiber material masses 3 g/m².^[39]

The least dense metal is lithium, about 5 times less dense than aluminium. Fresh, unoxidized surfaces are reflective. At a thickness of 20 nm, lithium has an areal density of 0.011 g/m². A high-performance sail could be made of lithium alone at 20 nm (no emission layer). It would have to be fabricated in space and not used to approach the sun. In the limit, a sail craft might be constructed with a total areal density of around 0.02 g/m², giving it a lightness number of 67 and a_c of about 400 mm/s². Magnesium and beryllium are also potential materials for high-performance sails. These 3 metals can be alloyed with each other and with aluminium.^[2]

Reflection and emissivity layers

Aluminium is the common choice for the reflection layer. It typically has a thickness of at least 20 nm, with a reflectivity of 0.88 to 0.90. Chromium is a good choice for the emission layer on the face away from the sun. It can readily provide emissivity values of 0.63 to 0.73 for thicknesses from 5 to 20 nm on plastic film. Usable emissivity values are empirical because thin-film effects dominate; bulk emissivity values do not hold up in these cases because material thickness is much thinner than the emitted wavelengths.^[41]

Fabrication

Sails are fabricated on Earth on long tables where ribbons are unrolled and joined to create the sails.
These sails are packed, launched, and unfurled in space.

In the future, fabrication could take place in orbit inside large frames that support the sail. This would result in lower mass sails and elimination of the risk of deployment failure.

Operations

A solar sail can spiral inward or outward by setting the sail angle

Changing orbits

Sailing operations are simplest in interplanetary orbits, where attitude changes are done at low rates. For outward bound trajectories, the sail force vector is oriented forward of the Sun line, which increases orbital energy and angular momentum, resulting in the craft moving farther from the Sun. For inward trajectories, the sail force vector is oriented behind the Sun line, which decreases orbital energy and angular momentum, resulting in the craft moving in toward the Sun. It is worth noting that only the Sun's gravity pulls the craft toward the Sun—there is no analog to a sailboat's tacking to windward. To change orbital inclination, the force vector is turned out of the plane of the velocity vector.

In orbits around planets or other bodies, the sail is oriented so that its force vector has a component along the velocity vector, either in the direction of motion for an outward spiral, or against the direction of motion for an inward spiral.

Trajectory optimizations can often require intervals of reduced or zero thrust. This can be achieved by rolling the craft around the sun line with the sail set at an appropriate angle to reduce or remove the thrust.^[42]

Swing-by Maneuvers

A close solar passage can be used to increase a craft's energy. The increased radiation pressure combines with the efficacy of being deep in the sun's gravity well to substantially increase the energy for runs to the outer solar system. The optimal approach to the sun is done by increasing the orbital eccentricity while keeping the energy level as high as practical. The minimum approach distance is a function of sail angle, thermal properties of the sail and other structure, load effects on structure, and sail optical characteristics (reflectivity and emissivity). A close passage can result in substantial optical degradation. Required turn rates can increase substantially for a close passage. A sail craft arriving at a star can use a close passage to reduce energy, which also applies to a sail craft on a return trip from the outer solar system.

A lunar swing-by can have important benefits for trajectories leaving from or arriving at Earth. This can reduce trip times, especially in cases where the sail is heavily loaded. A swing-by can also be used to obtain favorable departure or arrival directions relative to Earth.

A planetary swing-by could also be employed similar to what is done with coasting spacecraft, but good alignments might not exist due to the requirements for overall optimization of the trajectory.^[43]

Smart lines

A smart line could be a critical element of sailing operations. As with maritime ships, lines are essential for a wide range of uses. One difference is that some lines may be very long and need to be self-guiding. The lines could extend from and retract into the sail craft.

A maneuverable grappling device can be used at the end of a line to place or pick up payload containers, to secure a ship to a structure such as a station, to pick up samples from an asteroid or comet, or to engage in towing. The maneuvering unit is like a small spacecraft, with many of the same sensors and control systems. It could draw power from and communicate with the sail craft through the line. These operations could be done autonomously.

Lines a few hundred kilometers long may be used to move a ship from a space station to an orbit farther out where it could begin sailing.^[44]

Towing

Smart lines can enable towing operations by being able to attach to or release objects at the remote end of the line. Attached objects might be pulled in to the body of the sailer or remain at the end of the deployed line. Objects to be towed may have attachment points that allow multiple sail craft to engage in the towing. Towing operations can include deflecting large bodies that pose a hazard to Earth, bringing natural bodies to Earth or other sites for resource recovery, and transporting disabled spacecraft or other structures.

To tow or deflect a large body, poles can be inserted on the spin axis of the body. Sail craft can attach to the embedded poles using smart lines. Slip rings enable the craft to tow without the lines getting wrapped up as a result of rotation of the body.^[45][46]

Projects operating or completed

IKAROS 2010

The model of IKAROS at the 61st International Astronautical Congress in 2010

On 21 May 2010, Japan Aerospace Exploration Agency (Jaxa) launched the world's first interplanetary solar sail spacecraft "IKAROS" (Interplanetary Kite-craft Accelerated by Radiation Of the Sun) to Venus.^[47]

Japan's JAXA successfully tested IKAROS in 2010. The goal was to deploy and control the sail and for the first time determining the minute orbit perturbations caused by light pressure. Orbit determination was done by the nearby AKATSUKI probe from which IKAROS detached after both had been brought into a transfer orbit to Venus. The total effect over the six month' flight was 100 m/s.^[48]

Until 2010, no solar sails had been successfully used in space as primary propulsion systems. On 21 May 2010, the Japan Aerospace Exploration Agency (JAXA) launched the IKAROS (Interplanetary Kite-craft Accelerated by Radiation Of the Sun) spacecraft, which deployed a 200 m² polyimide experimental solar sail on June 10.^[49][50][51] In July, the next phase for the demonstration of acceleration by radiation began. On 9 July 2010, it was verified that IKAROS collected radiation from the Sun and began photon acceleration by the orbit determination of IKAROS by range-and-range-rate (RARR) that is newly calculated in addition to the data of the relativization accelerating speed of IKAROS between IKAROS and the Earth that has been taken since before the Doppler effect was utilized.^[52] The data showed that IKAROS appears to have been solar-sailing since 3 June when it deployed the sail.

IKAROS has a diagonal spinning square sail 20 m (66 ft) made of a 7.5-micrometre (0.0075 mm) thick sheet of polyimide. The polyimide sheet had a mass of about 10 grams per square metre. A thin-film solar array is embedded in the sail. Eight LCD panels are embedded in the sail, whose reflectance can be adjusted for attitude control.^[53][54] IKAROS spent six months traveling to Venus, and then began a three-year journey to the far side of the Sun.^[55]

Attitude (orientation) control

Both the Mariner 10 mission, which flew by the planets Mercury and Venus, and the MESSENGER mission to Mercury demonstrated the use of solar pressure as a method of attitude control in order to conserve attitude-control propellant.

Hayabusa also used solar pressure as a method of attitude control to compensate for broken reaction wheels and chemical thruster.

Sail deployment tests

NASA has successfully tested deployment technologies on small scale sails in vacuum chambers.^[56]
On February 4, 1993, the Znamya 2, a 20-meter wide aluminized-mylar reflector, was successfully deployed from the Russian Mir space station. Although the deployment succeeded, propulsion was not demonstrated. A second test, Znamya 2.5, failed to deploy properly.

In 1999, a full-scale deployment of a solar sail was tested on the ground at DLR/ESA in Cologne.^[57]

On August 9, 2004, the Japanese ISAS successfully deployed two prototype solar sails from a sounding rocket. A clover-shaped sail was deployed at 122 km altitude and a fan-shaped sail was deployed at 169 km altitude. Both sails used 7.5-micrometer film. The experiment purely tested the deployment mechanisms, not propulsion.^[58]

Solar sail propulsion attempts

NanoSail-D of LightSail-1 with sail deployed

A joint private project between Planetary Society, Cosmos Studios and Russian Academy of Science made two sail testing attempts: in 2001 a suborbital prototype test failed because of rocket failure; and in June 21, 2005, Cosmos 1 launched from a submarine in the Barents Sea, but the Volna rocket failed, and the spacecraft failed to reach orbit. They intended to use the sail to gradually raise the spacecraft to a higher Earth orbit over a mission duration of one month. On Carl Sagan's 75th birthday (November 9, 2009) the same group announced plans^[59] to make three further attempts, dubbed LightSail-1, -2, and -3.^[60] The new design will use a 32-square-meter Mylar sail, deployed in four triangular segments like NanoSail-D.^[60] The launch configuration is that of three adjacent CubeSats, and as of 2011 was waiting for a piggyback launch opportunity.^[61]

A 15-meter-diameter solar sail (SSP, solar sail sub payload, soraseiru sabupeiro-do) was launched together with ASTRO-F on a M-V rocket on February 21, 2006, and made it to orbit. It deployed from the stage, but opened incompletely.^[62]

NanoSail-D 2010

A team from the NASA Marshall Space Flight Center (Marshall), along with a team from the NASA Ames Research Center, developed a solar sail mission called NanoSail-D, which was lost in a launch failure aboard a Falcon 1 rocket on 3 August 2008.^[63][64] The second backup version, NanoSail-D2, also sometimes called simply NanoSail-D,^[65] was launched with FASTSAT on a Minotaur IV on November 19, 2010, becoming NASA's first solar sail deployed in low earth orbit. The objectives of the mission were to test sail deployment technologies, and to gather data about the use of solar sails as a simple, "passive" means of de-orbiting dead satellites and space debris.^[66] The NanoSail-D structure was made of aluminium and plastic, with the spacecraft massing less than 10 pounds (4.5 kg). The sail has about 100 square feet (9.3 m²) of light-catching surface. After some initial problems with deployment, the solar sail was deployed and over the course of its 240 day mission reportedly produced a "wealth of data" concerning the use of solar sails as passive deorbit devices.^[67]NASA launched the second NanoSail-D unit stowed inside the FASTSAT satellite on the Minotaur IV on November 19, 2010. The ejection date from the FASTSAT microsatellite was planned for December 6, 2010, but deployment only occurred on January 20, 2011.^[68]

Projects in development or proposed

Despite the losses of Cosmos 1 and NanoSail-D (which were due to failure of their launchers), scientists and engineers around the world remain encouraged and continue to work on solar sails.
While most direct applications created so far intend to use the sails as inexpensive modes of cargo transport, some scientists are investigating the possibility of using solar sails as a means of transporting humans. This goal is strongly related to the management of very large (i.e. well above 1 km²) surfaces in space and the sail making advancements. Thus, in the near/medium term, solar sail propulsion is aimed chiefly at accomplishing a very high number of non-crewed missions in any part of the solar system and beyond.^{[citation needed]} Manned space flight utilizing solar sails is still in the development state of infancy.

Sunjammer 2015

A technology demonstration sail craft, dubbed Sunjammer, was in development with the intent to prove the viability and value of sailing technology.^[69] Sunjammer had a square sail, 124 feet (38 meters) wide on each side (total area 13,000 sq ft or 1,208 sq m). It would have traveled from the Sun-Earth L₁ Lagrangian point 900,000 miles from Earth (1.5 million km) to a distance of 1,864,114 miles (3 million kilometers).^[70] The demonstration was expected to launch on a Falcon 9 in 2015.^[71] It would have been a secondary payload, released after the placement of the DSCOVR climate satellite at the L1 point.^[71]

LightSail-1

The Planetary Society's solar sail project. A ground-based deployment test was successfully done at Stellar Exploration in San Luis Obispo, California on March 4, 2011,^[72] with hardware and software adjustments leading to further tests. The configuration has four sail panels supported by four diagonal booms.
The Planetary Society of the United States plans to launch an artificial satellite "LightSail-1" onto the Earth's orbit in 2011.^[73]

Gossamer deorbit sail

As of December 2013^[update], the European Space Agency (ESA) has a proposed deorbit sail, named "Gossamer", that would be intended to be used to accelerate the deorbiting of small (less than 700 kilograms (1,500 lb)) artificial satellites from low-Earth orbits. The launch mass is 2 kilograms (4.4 lb) with a launch volume of only 15×15×25 centimetres (0.49×0.49×0.82 ft). Once deployed, the sail would expand to 5 by 5 metres (16 ft × 16 ft) and would use a combination of solar pressure on the sail and increased atmospheric drag to accelerate satellite reentry.^[29]

In science fiction

The earliest reference to solar sailing was in Jules Verne's 1865 novel From the Earth to the Moon, coming only a year after Maxwell's equations were published. The next known publication came more than 20 years later when Georges Le Faure and Henri De Graffigny published a four-volume science fiction novel in 1889, The Extraordinary Adventures of a Russian Scientist, which included a spacecraft propelled by solar pressure. B. Krasnogorskii published On the Waves of the Ether in 1913. In his story backed by technical calculations, a small, bullet-shaped capsule is surrounded by a circular mirror 35 meters in diameter. It travels through space by means of solar pressure on the mirror.

One of the earliest American stories about light sails is "The Lady Who Sailed the Soul" by Cordwainer Smith, which was published in 1960. In it, a tragedy results from the slowness of interstellar travel by this method. Another example is the 1962 story "Gateway to Strangeness" (also known as "Sail 25") by Jack Vance, in which the outward direction of propulsion poses a life-threatening dilemma. Also in early 20th century literature, Pierre Boulle's Planet of the Apes novel starts with a couple floating in space on a ship propelled and maneuvered by light sails. In Larry Niven and Jerry Pournelle's The Mote in God's Eye, a sail is used as a brake and a weapon. Author and scientist Arthur C. Clarke depicted a "yacht race" between solar sail spacecraft in the 1964 short story "Sunjammer". In "The Flight of the Dragonfly", Robert Forward (who also proposed the microwave-pushed Starwisp design) described an interstellar journey using a light driven propulsion system, wherein a part of the sail was broken off and used as a reflector to slow the main spacecraft as it approached its destination. Forward's ideas were developed further in Charles Stross's novel Accelerando.^[74] In the 1982 film Tron, a "Solar Sailer" was an inner spacecraft with butterfly like sails moved along focused beam of light. The 1983 episode "Enlightenment" of Doctor Who featured sailing ships in space that used solar wind to fly. In the episode "Explorers" of Star Trek: Deep Space Nine that aired in 1995, a reconstructed, "ancient" Bajoran "light ship" was featured. It was designed to use solar wind to fly out of a solar system with no engine. In the film Star Wars Episode II: Attack of the Clones one is used by Count Dooku to propel himself across space. A solar sail was also used in James Cameron's Avatar. In the Disney film Treasure Planet, solar sails are used literally as sails for interstellar travel as well as serving for the photovoltaic gathering of energy for the jet propulsion of a steampunk-styled masted sailing ship capable of traveling through space.

Magnetism

From Wikipedia, the free encyclopedia

A magnetic quadrupole

Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the fundamental magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. All materials are influenced to some extent by a magnetic field. The most familiar effect is on permanent magnets, which have persistent magnetic moments caused by ferromagnetism. Most materials do not have permanent moments. Some are attracted to a magnetic field (paramagnetism); others are repulsed by a magnetic field (diamagnetism); others have a much more complex relationship with an applied magnetic field (spin glass behavior and antiferromagnetism). Substances that are negligibly affected by magnetic fields are known as non-magnetic substances. They include copper, aluminium, gases, and plastic. Pure oxygen exhibits magnetic properties when cooled to a liquid state.

The magnetic state (or phase) of a material depends on temperature (and other variables such as pressure and the applied magnetic field) so that a material may exhibit more than one form of magnetism depending on its temperature, etc.

History

Drawing of a medical treatment using magnetic brushes. Charles Jacque 1843, France.

Aristotle attributed the first of what could be called a scientific discussion on magnetism to Thales of Miletus, who lived from about 625 BC to about 545 BC.^[1] Around the same time, in ancient India, the Indian surgeon, Sushruta, was the first to make use of the magnet for surgical purposes.^[2]

In ancient China, the earliest literary reference to magnetism lies in a 4th-century BC book named after its author, The Master of Demon Valley (鬼谷子): "The lodestone makes iron come or it attracts it."^[3] The earliest mention of the attraction of a needle appears in a work composed between AD 20 and 100 (Louen-heng): "A lodestone attracts a needle."^[4] The Chinese scientist Shen Kuo (1031–1095) was the first person to write of the magnetic needle compass and that it improved the accuracy of navigation by employing the astronomical concept of true north (Dream Pool Essays, AD 1088), and by the 12th century the Chinese were known to use the lodestone compass for navigation. They sculpted a directional spoon from lodestone in such a way that the handle of the spoon always pointed south.

Alexander Neckam, by 1187, was the first in Europe to describe the compass and its use for navigation. In 1269, Peter Peregrinus de Maricourt wrote the Epistola de magnete, the first extant treatise describing the properties of magnets. In 1282, the properties of magnets and the dry compass were discussed by Al-Ashraf, a Yemeni physicist, astronomer, and geographer.^[5]

Michael Faraday, 1842

In 1600, William Gilbert published his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth). In this work he describes many of his experiments with his model earth called the terrella. From his experiments, he concluded that the Earth was itself magnetic and that this was the reason compasses pointed north (previously, some believed that it was the pole star (Polaris) or a large magnetic island on the north pole that attracted the compass).

An understanding of the relationship between electricity and magnetism began in 1819 with work by Hans Christian Ørsted, a professor at the University of Copenhagen, who discovered more or less by accident that an electric current could influence a compass needle. This landmark experiment is known as Ørsted's Experiment. Several other experiments followed, with André-Marie Ampère, who in 1820 discovered that the magnetic field circulating in a closed-path was related to the current flowing through the perimeter of the path; Carl Friedrich Gauss; Jean-Baptiste Biot and Félix Savart, both of whom in 1820 came up with the Biot–Savart law giving an equation for the magnetic field from a current-carrying wire; Michael Faraday, who in 1831 found that a time-varying magnetic flux through a loop of wire induced a voltage, and others finding further links between magnetism and electricity. James Clerk Maxwell synthesized and expanded these insights into Maxwell's equations, unifying electricity, magnetism, and optics into the field of electromagnetism. In 1905, Einstein used these laws in motivating his theory of special relativity,^[6] requiring that the laws held true in all inertial reference frames.

Electromagnetism has continued to develop into the 21st century, being incorporated into the more fundamental theories of gauge theory, quantum electrodynamics, electroweak theory, and finally the standard model.

Sources of magnetism

Magnetism, at its root, arises from two sources:

1. Electric current (see electron magnetic dipole moment).
2. Nuclear magnetic moments of atomic nuclei. These moments are typically thousands of times smaller than the electrons' magnetic moments, so they are negligible in the context of the magnetization of materials. Nuclear magnetic moments are very important in other contexts, particularly in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

Ordinarily, the enormous number of electrons in a material are arranged such that their magnetic moments (both orbital and intrinsic) cancel out. This is due, to some extent, to electrons combining into pairs with opposite intrinsic magnetic moments as a result of the Pauli exclusion principle (see electron configuration), or combining into filled subshells with zero net orbital motion. In both cases, the electron arrangement is so as to exactly cancel the magnetic moments from each electron.
Moreover, even when the electron configuration is such that there are unpaired electrons and/or non-filled subshells, it is often the case that the various electrons in the solid will contribute magnetic moments that point in different, random directions, so that the material will not be magnetic.

However, sometimes—either spontaneously, or owing to an applied external magnetic field—each of the electron magnetic moments will be, on average, lined up. Then the material can produce a net total magnetic field, which can potentially be quite strong.

The magnetic behavior of a material depends on its structure, particularly its electron configuration, for the reasons mentioned above, and also on the temperature. At high temperatures, random thermal motion makes it more difficult for the electrons to maintain alignment.

Topics

Hierarchy of types of magnetism.^[7]

Diamagnetism

Diamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates.^[8] Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understood classically as follows:

When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to their Coulomb attraction to the nucleus, a Lorentz force from the magnetic field. Depending on which direction the electron is orbiting, this force may increase the centripetal force on the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect systematically increases the orbital magnetic moments that were aligned opposite the field, and decreases the ones aligned parallel to the field (in accordance with Lenz's law). This results in a small bulk magnetic moment, with an opposite direction to the applied field.

Note that this description is meant only as an heuristic; a proper understanding requires a quantum-mechanical description.

Note that all materials undergo this orbital response. However, in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effects caused by the unpaired electrons.

Paramagnetism

In a paramagnetic material there are unpaired electrons, i.e. atomic or molecular orbitals with exactly one electron in them. While paired electrons are required by the Pauli exclusion principle to have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it.

Ferromagnetism

A permanent magnet holding up several coins

A ferromagnet, like a paramagnetic substance, has unpaired electrons. However, in addition to the electrons' intrinsic magnetic moment's tendency to be parallel to an applied field, there is also in these materials a tendency for these magnetic moments to orient parallel to each other to maintain a lowered-energy state. Thus, even in the absence of an applied field, the magnetic moments of the electrons in the material spontaneously line up parallel to one another.

Every ferromagnetic substance has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy-lowering due to ferromagnetic order.

Ferromagnetism only occurs in a few substances; the common ones are iron, nickel, cobalt, their alloys, and some alloys of rare earth metals.

Magnetic domains

Magnetic domains boundaries (white lines) in ferromagnetic material (black rectangle).

The magnetic moment of atoms in a ferromagnetic material cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment called magnetic domains or Weiss domains. Magnetic domains can be observed with a magnetic force microscope to reveal magnetic domain boundaries that resemble white lines in the sketch. There are many scientific experiments that can physically show magnetic fields.

Effect of a magnet on the domains.

When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right.

When exposed to a magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure (dotted yellow area) as shown at the left. When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet.

When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material is magnetically saturated. When a magnetized ferromagnetic material is heated to the Curie point temperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns, in a manner roughly analogous to how a liquid can freeze into a crystalline solid.

Antiferromagnetism

Antiferromagnetic ordering

In an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point in opposite directions. When all atoms are arranged in a substance so that each neighbor is 'anti-aligned', the substance is antiferromagnetic.
Antiferromagnets have a zero net magnetic moment, meaning no field is produced by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.

In some materials, neighboring electrons want to point in opposite directions, but there is no geometrical arrangement in which each pair of neighbors is anti-aligned. This is called a spin glass, and is an example of geometrical frustration.

Ferrimagnetism

Ferrimagnetic ordering

Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins like to point in opposite directions. These two properties are not contradictory, because in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons that point in one direction, than from the sublattice that points in the opposite direction.

Most ferrites are ferrimagnetic. The first discovered magnetic substance, magnetite, is a ferrite and was originally believed to be a ferromagnet; Louis Néel disproved this, however, after discovering ferrimagnetism.

Superparamagnetism

When a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is subject to Brownian motion. Its response to a magnetic field is qualitatively similar to the response of a paramagnet, but much larger.

Electromagnet

An electromagnet is a type of magnet whose magnetism is produced by the flow of electric current. The magnetic field disappears when the current ceases.

Electromagnets attracts paper clips when current is applied creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.

Other types of magnetism

• Molecular magnet
• Metamagnetism
• Molecule-based magnet
• Spin glass

Magnetism, electricity, and special relativity

Magnetism from length-contraction.

As a consequence of Einstein's theory of special relativity, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity.^[6][9] In particular, a phenomenon that appears purely electric or purely magnetic to one observer may be a mix of both to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how relativity "mixes" space and time into spacetime.

All observations on electromagnetism apply to what might be considered to be primarily magnetism, e.g. perturbations in the magnetic field are necessarily accompanied by a nonzero electric field, and propagate at the speed of light.

Magnetic fields in a material

where μ₀ is the vacuum permeability.
In a material,

The quantity μ₀M is called magnetic polarization.

If the field H is small, the response of the magnetization M in a diamagnet or paramagnet is approximately linear:

the constant of proportionality being called the magnetic susceptibility. If so,

In a hard magnet such as a ferromagnet, M is not proportional to the field and is generally nonzero even when H is zero (see Remanence).

Magnetic force

Magnetic lines of force of a bar magnet shown by iron filings on paper

The phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.

Maxwell's equations, which simplify to the Biot–Savart law in the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically charged particles are in motion—for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum-mechanical spin.

The same situations that create magnetic fields—charge moving in a current or in an atom, and intrinsic magnetic dipoles—are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.

When a charged particle moves through a magnetic field B, it feels a Lorentz force F given by the cross product:^[10]

where

is the electric charge of the particle, and

v is the velocity vector of the particle

Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is

where is the angle between v and B.

One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively.

Magnetic dipoles

A very common source of magnetic field shown in nature is a dipole, with a "South pole" and a "North pole", terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the north pole of a magnet is attracted to the south pole of another magnet. The Earth's North Magnetic Pole (currently in the Arctic Ocean, north of Canada) is physically a south pole, as it attracts the north pole of a compass. A magnetic field contains energy, and physical systems move toward configurations with lower energy. When diamagnetic material is placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby lowering the net field strength. When ferromagnetic material is placed within a magnetic field, the magnetic dipoles align to the applied field, thus expanding the domain walls of the magnetic domains.

Magnetic monopoles

Since a bar magnet gets its ferromagnetism from electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole—if such a thing exists—would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. 

Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, as of 2010^[update], they have never been observed, and could very well not exist.^[11]
Nevertheless, some theoretical physics models predict the existence of these magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge—that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.

Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). The initial results of using these models to estimate the number of monopoles created in the big bang contradicted cosmological observations—the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.^[12]

Quantum-mechanical origin of magnetism

In principle all kinds of magnetism originate (similar to superconductivity)^{[clarification needed]} from specific quantum-mechanical phenomena (e.g. Mathematical formulation of quantum mechanics, in particular the chapters on spin and on the Pauli principle). A successful model was developed already in 1927, by Walter Heitler and Fritz London, who derived quantum-mechanically, how hydrogen molecules are formed from hydrogen atoms, i.e. from the atomic hydrogen orbitals and centered at the nuclei A and B, see below. That this leads to magnetism is not at all obvious, but will be explained in the following.

According to the Heitler-London theory, so-called two-body molecular -orbitals are formed, namely the resulting orbital is:

Here the last product means that a first electron, r₁, is in an atomic hydrogen-orbital centered at the second nucleus, whereas the second electron runs around the first nucleus. This "exchange" phenomenon is an expression for the quantum-mechanical property that particles with identical properties cannot be distinguished. It is specific not only for the formation of chemical bonds, but as we will see, also for magnetism, i.e. in this connection the term exchange interaction arises, a term which is essential for the origin of magnetism, and which is stronger, roughly by factors 100 and even by 1000, than the energies arising from the electrodynamic dipole-dipole interaction.

As for the spin function , which is responsible for the magnetism, we have the already mentioned Pauli's principle, namely that a symmetric orbital (i.e. with the + sign as above) must be multiplied with an antisymmetric spin function (i.e. with a − sign), and vice versa. Thus:

,

I.e., not only and must be substituted by α and β, respectively (the first entity means "spin up", the second one "spin down"), but also the sign + by the − sign, and finally r_i by the discrete values s_i (= ±½); thereby we have and . The "singlet state", i.e. the − sign, means: the spins are antiparallel, i.e. for the solid we have antiferromagnetism, and for two-atomic molecules one has diamagnetism. The tendency to form a (homoeopolar) chemical bond (this means: the formation of a symmetric molecular orbital, i.e. with the + sign) results through the Pauli principle automatically in an antisymmetric spin state (i.e. with the − sign). In contrast, the Coulomb repulsion of the electrons, i.e. the tendency that they try to avoid each other by this repulsion, would lead to an antisymmetric orbital function (i.e. with the − sign) of these two particles, and complementary to a symmetric spin function (i.e. with the + sign, one of the so-called "triplet functions"). Thus, now the spins would be parallel (ferromagnetism in a solid, paramagnetism in two-atomic gases).

The last-mentioned tendency dominates in the metals iron, cobalt and nickel, and in some rare earths, which are ferromagnetic. Most of the other metals, where the first-mentioned tendency dominates, are nonmagnetic (e.g. sodium, aluminium, and magnesium) or antiferromagnetic (e.g. manganese). Diatomic gases are also almost exclusively diamagnetic, and not paramagnetic. However, the oxygen molecule, because of the involvement of π-orbitals, is an exception important for the life-sciences.

The Heitler-London considerations can be generalized to the Heisenberg model of magnetism (Heisenberg 1928).

The explanation of the phenomena is thus essentially based on all subtleties of quantum mechanics, whereas the electrodynamics covers mainly the phenomenology.

Units of electromagnetism

SI units related to magnetism

Main article: Ferrimagnetismlectromagnetism units

Symbol[13]	Name of quantity	Derived units	Conversion of international to SI base units
I	Electric current	ampere (SI base unit)
q	Electric charge	coulomb
	Potential difference; Electromotive force	volt
	Electric resistance; Impedance; Reactance	ohm
	Resistivity	ohm metre
	Electric power	watt
	Capacitance	farad
	Electric field strength	volt per metre
	Electric displacement field	Coulomb per square metre
	Permittivity	farad per metre
	Electric susceptibility	Dimensionless
	Conductance; Admittance; Susceptance	siemens
	Conductivity	siemens per metre
	Magnetic flux density, Magnetic induction	tesla
	Magnetic flux	weber
	Magnetic field strength	ampere per metre
	Inductance	henry
	Permeability	henry per metre
	Magnetic susceptibility	Dimensionless

Other units

• gauss – The gauss is the centimeter-gram-second (CGS) unit of magnetic field (denoted B).
• oersted – The oersted is the CGS unit of magnetizing field (denoted H).
• maxwell – The maxwell is the CGS unit for magnetic flux.
• gamma – is a unit of magnetic flux density that was commonly used before the tesla came into use (1.0 gamma = 1.0 nanotesla)
• μ₀ – common symbol for the permeability of free space (4π×10⁻⁷ newton/(ampere-turn)²).

Living things

Some organisms can detect magnetic fields, a phenomenon known as magnetoception. Magnetobiology studies magnetic fields as a medical treatment; fields naturally produced by an organism are known as biomagnetism.