Alfvén wave
Encyclopedia
An Alfvén wave, named after Hannes Alfvén
, is a type of magnetohydrodynamic
wave
.
is a low-frequency (compared to the ion
cyclotron frequency) travelling oscillation
of the ions and the magnetic field
. The ion mass density provides the inertia
and the magnetic field line tension provides the restoring force.
The wave propagates in the direction of the magnetic field, although waves exist at oblique incidence and smoothly change into the magnetosonic wave
when the propagation is perpendicular to the magnetic field.
The motion of the ions and the perturbation of the magnetic field are in the same direction and transverse
to the direction of propagation. The wave is dispersionless
.
The low-frequency permittivity
of a magnetized plasma is given by
where
is the magnetic field strength, 
is the speed of light, 
is the permeability
of the vacuum, and
is the total mass density of the charged plasma particles. Here,
goes over all plasma species, both electrons and (few types of) ions.
Therefore, the velocity of an electromagnetic wave in such a medium is
or
where
is the Alfvén velocity. If
, then 
. On the other hand, when 
, then 
. That is, at high field or low density, the velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.
Neglecting the contribution of the electrons to the mass density and assuming that there is a single ion species, we get
in SI
in CGS
where
is the ion number density and 
is the ion mass.
is an important timescale for wave phenomena. It is related to the Alfvén velocity by:
where
denotes the characteristic scale of the system, for example 
is the minor radius of the torus in a tokamak
.
where
is the total energy density of plasma particles, 
is the total plasma pressure, and 
is the magnetic field pressure. In the non-relativistic limit 
, and we immediately get the expression from the previous section.
Hannes Alfvén
Hannes Olof Gösta Alfvén was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics . He described the class of MHD waves now known as Alfvén waves...
, is a type of magnetohydrodynamic
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
.
Definition
An Alfvén wave in a plasmaPlasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
is a low-frequency (compared to the ion
Ion
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
cyclotron frequency) travelling oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
of the ions and the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
. The ion mass density provides the inertia
Inertia
Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...
and the magnetic field line tension provides the restoring force.
The wave propagates in the direction of the magnetic field, although waves exist at oblique incidence and smoothly change into the magnetosonic wave
Magnetosonic wave
A magnetosonic wave is a longitudinal wave of ions in a magnetized plasma propagating perpendicular to the stationary magnetic field...
when the propagation is perpendicular to the magnetic field.
The motion of the ions and the perturbation of the magnetic field are in the same direction and transverse
Transverse wave
A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...
to the direction of propagation. The wave is dispersionless
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....
.
Alfvén velocity
The low-frequency permittivity
Permittivity
In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...
of a magnetized plasma is given bywhere
is the magnetic field strength, is the speed of light, is the permeabilityPermeability (electromagnetism)
In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. In other words, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically...
of the vacuum, and
is the total mass density of the charged plasma particles. Here,
goes over all plasma species, both electrons and (few types of) ions.Therefore, the velocity of an electromagnetic wave in such a medium is
or
where
is the Alfvén velocity. If
, then . On the other hand, when , then . That is, at high field or low density, the velocity of the Alfvén wave approaches the speed of light, and the Alfvén wave becomes an ordinary electromagnetic wave.Neglecting the contribution of the electrons to the mass density and assuming that there is a single ion species, we get
in SI in CGSwhere
is the ion number density and is the ion mass.Alfvén time
In plasma physics, the Alfvén time is an important timescale for wave phenomena. It is related to the Alfvén velocity by:where
denotes the characteristic scale of the system, for example is the minor radius of the torus in a tokamakTokamak
A tokamak is a device using a magnetic field to confine a plasma in the shape of a torus . Achieving a stable plasma equilibrium requires magnetic field lines that move around the torus in a helical shape...
.
Relativistic case
The general Alfvén wave velocity is defined by Gedalin (1993):where
is the total energy density of plasma particles, is the total plasma pressure, and is the magnetic field pressure. In the non-relativistic limit , and we immediately get the expression from the previous section.History
How this phenomenon became understood- 1942: Alfvén suggests the existence of electromagnetic-hydromagnetic waves in a paper published in Nature.
- 1949: Laboratory experiments by S. Lundquist produce such waves in magnetized mercury, with a velocity that approximated Alfvén's formula.
- 1949: Enrico FermiEnrico FermiEnrico Fermi was an Italian-born, naturalized American physicist particularly known for his work on the development of the first nuclear reactor, Chicago Pile-1, and for his contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics...
uses Alfvén waves in his theory of cosmic rayCosmic rayCosmic rays are energetic charged subatomic particles, originating from outer space. They may produce secondary particles that penetrate the Earth's atmosphere and surface. The term ray is historical as cosmic rays were thought to be electromagnetic radiation...
s. According to Alex Dessler in a 1970 Science journal article, Fermi had heard a lecture at the University of Chicago, Fermi nodded his head exclaiming "of course" and the next day, the physics world said "of course". - 1950: Alfvén publishes the first edition of his book, Cosmical Electrodynamics, detailing hydromagnetic waves, and discussing their application to both laboratory and space plasmas.
- 1952: Additional confirmation appears in experiments by Winston Bostick and Morton Levine with ionized helium
- 1954: Bo Lehnert produces Alfvén waves in liquid sodium
- 1958: Eugene ParkerEugene ParkerEugene N. Parker is an American solar astrophysicist who received his B.S. degree in physics from Michigan State University in 1948 and Ph.D. from Caltech in 1951. In the mid 1950s Parker developed the theory on the supersonic solar wind and predicted the Parker spiral shape of the solar magnetic...
suggests hydromagnetic waves in the interstellar mediumInterstellar mediumIn astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space... - 1958: Berthold, Harris, and Hope detect Alfvén waves in the ionosphere after the ArgusOperation ArgusOperation Argus was a series of nuclear weapons tests and missile tests secretly conducted during August and September 1958 over the South Atlantic Ocean by the United States's Defense Nuclear Agency, in conjunction with the Explorer 4 space mission. Operation Argus was conducted between the...
nuclear test, generated by the explosion, and traveling at speeds predicted by Alfvén formula. - 1958: Eugene Parker suggests hydromagnetic waves in the Solar corona extending into the Solar windSolar windThe solar wind is a stream of charged particles ejected from the upper atmosphere of the Sun. It mostly consists of electrons and protons with energies usually between 1.5 and 10 keV. The stream of particles varies in temperature and speed over time...
. - 1959: D. F. Jephcott produces Alfvén waves in a gas discharge
- 1959: C. H. Kelley and J. Yenser produce Alfvén waves in the ambient atmosphere.
- 1960: Coleman, et al., report the measurement of Alfvén waves by the magnetometerMagnetometerA magnetometer is a measuring instrument used to measure the strength or direction of a magnetic field either produced in the laboratory or existing in nature...
aboard the Pioneer and Explorer satellites - 1960: Sugiura suggests evidence of hydromagnetic waves in the Earth's magnetic field
- 1966: R.O.Motz generates and observes Alfven waves in mercury
- 1970 Hannes Alfvén wins the 1970 Nobel Prize in physicsNobel Prize in PhysicsThe Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
for "fundamental work and discoveries in magneto-hydrodynamicsMagnetohydrodynamicsMagnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
with fruitful applications in different parts of plasma physics" - 1973: Eugene Parker suggests hydromagnetic waves in the intergalactic medium
- 1974: Hollweg suggests the existence of hydromagnetic waves in interplanetary space
- 1974: Ip and Mendis suggests the existence of hydromagnetic waves in the coma of Comet KohoutekComet KohoutekComet Kohoutek, formally designated C/1973 E1, 1973 XII, and 1973f, was first sighted on 7 March 1973 by Czech astronomer Luboš Kohoutek. It attained perihelion on 28 December that same year....
. - 1999: Aschwanden, et al. and Nakariakov, et al. report the detection of damped transverse oscillations of solar coronal loops observed with the EUVExtreme ultravioletExtreme Ultraviolet radiation is high-energy ultraviolet radiation, generally defined to be electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths from 120 nm down to 10 nm, and therefore having photons with energies from 10 eV up to 124 eV...
imager on board the Transition Region And Coronal Explorer (TRACETRACETRACE was a NASA space telescope designed to investigate the connections between fine-scale magnetic fields and the associated plasma structures on the Sun by providing high resolution images and observation of the solar photosphere and transition region to the corona...
), interpreted as standing kink (or "Alfvénic") oscillations of the loops. - 2007: Tomczyk, et al., report the detection of Alfvénic waves in images of the solar corona with the Coronal Multi-Channel Polarimeter (CoMP) instrument at the National Solar ObservatoryNational Solar ObservatoryThe mission of the National Solar Observatory is to advance knowledge of the Sun, both as an astronomical object and as the dominant external influence on Earth, by providing forefront observational opportunities to the research community...
, New Mexico. These waves were interpreted as propagating kink waves by Van Doorsselaere et al. (2008) - 2007: Alfvén wave discoveries appear in articles by Jonathan Cirtain and colleagues, Takenori J. Okamoto and colleagues, and Bart De Pontieu and colleagues. De Pontieu’s team also shows that the energy associated with the waves is sufficient to heat the coronaCoronaA corona is a type of plasma "atmosphere" of the Sun or other celestial body, extending millions of kilometers into space, most easily seen during a total solar eclipse, but also observable in a coronagraph...
and accelerate the solar windSolar windThe solar wind is a stream of charged particles ejected from the upper atmosphere of the Sun. It mostly consists of electrons and protons with energies usually between 1.5 and 10 keV. The stream of particles varies in temperature and speed over time...
. These results appear in a special collection of 10 articles, by scientists in JapanJapanJapan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
, EuropeEuropeEurope is, by convention, one of the world's seven continents. Comprising the westernmost peninsula of Eurasia, Europe is generally 'divided' from Asia to its east by the watershed divides of the Ural and Caucasus Mountains, the Ural River, the Caspian and Black Seas, and the waterways connecting...
and the United StatesUnited StatesThe United States of America is a federal constitutional republic comprising fifty states and a federal district...
, in the 7 December issue of the journal ScienceScience (journal)Science is the academic journal of the American Association for the Advancement of Science and is one of the world's top scientific journals....
. It was demonstrated that those waves should be interpreted in terms of kink waves of coronal plasma structures by Van Doorsselaere, et al. (2008); Ofman and Wang (2008); and Vasheghani Farahani, et al. (2009).
See also
- ElectrohydrodynamicsElectrohydrodynamicsElectrohydrodynamics , also known as electro-fluid-dynamics or electrokinetics, is the study of the dynamics of electrically charged fluids. It is the study of the motions of ionised particles or molecules and their interactions with electric fields and the surrounding fluid...
- Plasma stabilityPlasma stabilityAn important field of plasma physics is the stability of the plasma. It usually only makes sense to analyze the stability of a plasma once it has been established that the plasma is in equilibrium. "Equilibrium" asks whether there are net forces that will accelerate any part of the plasma...
- Shocks and discontinuities (magnetohydrodynamics)
- Computational magnetohydrodynamicsComputational MagnetohydrodynamicsComputational magnetohydrodynamics is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electrically conducting fluids. Most of the methods used in CMHD are borrowed from the well established techniques...
- FerrofluidFerrofluidA ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field.Ferrofluids are colloidal liquids made of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid . Each tiny particle is thoroughly coated with a surfactant to inhibit clumping...
- MHD generatorMHD generatorThe MHD generator or dynamo transforms thermal energy or kinetic energy directly into electricity. MHD generators are different from traditional electric generators in that they can operate at high temperatures without moving parts...
- MHD sensorMHD sensorMHD sensors are used for precision measurements of angular velocities in inertial navigation systems such as in aerospace engineering). Accuracy improves with the size of the sensor....
- Magnetic flow meterMagnetic flow meterThe third most common flowmeter behind differential pressure and positive displacement flow meters, is the magnetic flow meter, also technically an electromagnetic flow meter or more commonly just called a mag meter. A magnetic field is applied to the metering tube, which results in a potential...
- Magnetohydrodynamic turbulenceMagnetohydrodynamic turbulenceMagnetohydrodynamics deals with what is a quasi-neutral fluid with very high conductivity. The fluid approximation implies that the we focus at macro length and time scales which are much larger than the collision length and collision time respectively...
- Molten saltMolten saltMolten salt refers to a salt that is in the liquid phase that is normally a solid at standard temperature and pressure . A salt which is normally liquid at STP is usually called a room temperature ionic liquid, although technically molten salts are a class of ionic liquids.-Uses:Molten salts have...
- Electromagnetic pumpElectromagnetic pumpAn electromagnetic pump is a pump that moves liquid metal using electromagnetism. A magnetic field is set at right angles to the direction the liquid moves in, and a current is passed through it. This causes an electromagnetic force that moves the liquid.Applications include pumping liquid metal...
- List of plasma (physics) applications articles