Magnetohydrodynamics
Encyclopedia
Magnetohydrodynamics (MHD) (magneto fluid dynamics or hydromagnetics) is an academic discipline
which studies the dynamics
of electrically conducting fluid
s. Examples of such fluids include plasmas
, liquid metals, and salt water
or electrolyte
s. The word magnetohydrodynamics (MHD) is derived from magneto- meaning magnetic field
, and hydro- meaning liquid
, and -dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén
, for which he received the Nobel Prize
in Physics in 1970.
The fundamental concept behind MHD is that magnetic fields can induce
currents in a moving conductive fluid, which in turn creates forces on the fluid and also changes the magnetic field itself. The set of equations which describe MHD are a combination of the Navier-Stokes equations
of fluid dynamics
and Maxwell's equations
of electromagnetism
. These differential equation
s have to be solved simultaneously, either analytically or numerically
.
The first recorded use of the word magnetohydrodynamics is by Hannes Alfvén
in 1942:
The ebbing salty water flowing past London's Waterloo Bridge
interacts with the Earth's magnetic field
to produce a potential difference between the two river-banks. Michael Faraday
tried this experiment in 1832 but the current was too small to measure with the equipment at the time, and the river bed contributed to short-circuit the signal. However, by the same process, Dr. William Hyde Wollaston
was able to measure the voltage induced by the tide in the English Channel in 1851.
The simplest form of MHD, Ideal MHD, assumes that the fluid has so little resistivity
that it can be treated as a perfect conductor
. This is the limit of infinite magnetic Reynolds number
. In ideal MHD, Lenz's law
dictates that the fluid is in a sense tied to the magnetic field lines. To explain, in ideal MHD a small rope-like volume of fluid surrounding a field line will continue to lie along a magnetic field line,
even as it is twisted and distorted by fluid flows in the system.
The connection between magnetic field lines and fluid in ideal MHD fixes the topology
of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection
that releases the stored energy from the magnetic field.
, the momentum equation
, Ampere's Law
neglecting displacement current, and a temperature evolution equation
. As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation. This is often accomplished with approximations to the heat flux through a condition of adiabaticity
or isothermality
.
In the following,
is the magnetic field, 
is the electric field, 
is the bulk plasma velocity, 
is the current density, 
is the mass density, 
is the plasma pressure, and 
is time. The continuity equation is
The momentum equation is
The Lorentz force term
can be expanded to give
where the first term on the right hand side is the magnetic tension force and the second term is the magnetic pressure
force.
The ideal Ohm's law for a plasma is given by
Faraday's law is
The low-frequency Ampere's law neglects displacement current and is given by
The magnetic divergence constraint is
The energy equation is given by
where
is the ratio of specific heats for an adiabatic equation of state.
Even in physical systems which are large and conductive enough that simple estimates of the Lundquist number
suggest that we can ignore the resistivity, resistivity may still be important: many instabilities
exist that can increase the effective resistivity of the plasma by factors of more than a billion. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic turbulence, introducing small spatial scales into the system over which ideal MHD is broken and magnetic diffusion can occur quickly. When this happens, magnetic reconnection may occur in the plasma to release stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration
, and heat.
Magnetic reconnection in highly conductive systems is important because it concentrates energy in time and space, so that gentle forces applied to a plasma for long periods of time can cause violent explosions and bursts of radiation.
When the fluid cannot be considered as completely conductive, but the other conditions for ideal MHD are satisfied, it is possible to use an extended model called resistive MHD. This includes an extra term in Ampere's Law which models the collisional resistivity. Generally MHD computer simulations are at least somewhat resistive because their computational grid introduces a numerical resistivity.
Effects which are essentially kinetic and not captured by fluid models include double layers
, Landau damping
, a wide range of instabilities, chemical separation in space plasmas and electron runaway.
In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheet
s. These can divide the fluid into magnetic domains, inside of which the currents are relatively weak. Current sheets in
the solar corona are thought to be between a few meters and a few kilometers in thickness, which is quite thin compared to the magnetic domains (which are thousands to hundreds of thousands of kilometers across). Another example is in the Earth's magnetosphere
, where current sheets separate topologically distinct domains, isolating most of the Earth's ionosphere
from the solar wind
.
All these waves have constant phase velocities for all frequencies, and hence there is no dispersion. At the limits when the angle between the wave propagation vector k and magnetic field B is either 0 (180) or 90 degrees, the wave modes are called:
The MHD oscillations will be damped if the fluid is not perfectly conducting but has a finite conductivity, or if viscous effects are present.
MHD waves and oscillations are a popular tool for the remote diagnostics of laboratory and astrophysical plasmas, e.g. the corona
of the Sun (Coronal seismology
).
). This diffusivity leads to a breaking in the magnetic topology; magnetic field lines can 'reconnect' when they collide. Usually this term is small and reconnections can be handled by thinking of them as not dissimilar to shocks; this process has been shown to be important in the Earth-Solar magnetic interactions.
. As a result, the electron and ion momenta must be treated separately. This description is more closely tied to Maxwell's equations as an evolution equation for the electric field exists.
.
Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior. After running the simulations for thousands of years in virtual time, the changes in Earth's magnetic field can be studied. The simulation results are in good agreement with the observations as the simulations have correctly predicted that the Earth's magnetic field flips every few thousands of years. During the flips, the magnetic field doesn't vanish altogether - it just gets more complicated.
since over 99% of baryonic matter content of the Universe is made up of plasma, including stars, the interplanetary medium
(space between the planets), the interstellar medium
(space between the stars), nebulae and jets
. Many astrophysical systems are not in local thermal equilibrium, and therefore require an additional kinematic treatment to describe all the phenomena within the system (see Astrophysical plasma
).
Sunspot
s are caused by the Sun's magnetic fields, as Joseph Larmor
theorized in 1919. The solar wind
is also governed by MHD. The differential solar rotation
may be the long term effect of magnetic drag at the poles of the Sun, an MHD phenomenon due to the Parker spiral
shape assumed by the extended magnetic field of the Sun.
Previously, theories describing the formation of the Sun and planets could not explain how the Sun has 99.87% of the mass, yet only 0.54% of the angular momentum
in the solar system
. In a closed system
such as the cloud of gas and dust from which the Sun was formed, mass and angular momentum are both conserved
. That conservation would imply that as the mass concentrated in the center of the cloud to form the Sun, it would spin up, much like a skater pulling their arms in. The high speed of rotation predicted by early theories would have flung the proto-Sun apart before it could have formed. However, magnetohydrodynamic effects transfer the Sun's angular momentum into the outer solar system, slowing its rotation.
Breakdown of ideal MHD (in the form of magnetic reconnection) is known to be the cause of solar flare
s, the largest explosions in the solar system. The magnetic field in a solar active region over a sunspot can become quite stressed over time, storing energy that is released suddenly as a burst of motion, X-ray
s, and radiation
when the main current sheet collapses, reconnecting the field.
, liquid-metal cooling of nuclear reactor
s, and electromagnetic
casting (among others).
The first prototype of this kind of propulsion was built and tested in 1965 by Steward Way, a professor of mechanical engineering at the University of California, Santa Barbara
. Way, on leave from his job at Westinghouse Electric
, assigned his senior year undergraduate students to develop a submarine with this new propulsion system. In early 1990s, Mitsubishi
built a boat, the 'Yamato
,' which uses a magnetohydrodynamic drive
, is driven by a liquid helium
-cooled superconductor, and can travel at 15 km/h.
MHD power generation fueled by potassium-seeded coal combustion gas showed potential for more efficient energy conversion (the absence of solid moving parts allows operation at higher temperatures), but failed due to cost prohibitive technical difficulties.
In microfluidic devices, the MHD pump is so far the most effective for producing a continuous, nonpulsating flow in a complex microchannel design. It was used to implement a PCR protocol.
Academic discipline
An academic discipline, or field of study, is a branch of knowledge that is taught and researched at the college or university level. Disciplines are defined , and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to...
which studies the dynamics
Dynamics (mechanics)
In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...
of electrically conducting fluid
Fluid
In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....
s. Examples of such fluids include plasmas
Plasma (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...
, liquid metals, and salt water
Brine
Brine is water, saturated or nearly saturated with salt .Brine is used to preserve vegetables, fruit, fish, and meat, in a process known as brining . Brine is also commonly used to age Halloumi and Feta cheeses, or for pickling foodstuffs, as a means of preserving them...
or electrolyte
Electrolyte
In chemistry, an electrolyte is any substance containing free ions that make the substance electrically conductive. The most typical electrolyte is an ionic solution, but molten electrolytes and solid electrolytes are also possible....
s. The word magnetohydrodynamics (MHD) is derived from magneto- meaning 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;...
, and hydro- meaning liquid
Liquid
Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...
, and -dynamics meaning movement. The field of MHD was initiated by Hannes Alfvén
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...
, for which he received the Nobel Prize
Nobel Prize
The Nobel Prizes are annual international awards bestowed by Scandinavian committees in recognition of cultural and scientific advances. The will of the Swedish chemist Alfred Nobel, the inventor of dynamite, established the prizes in 1895...
in Physics in 1970.
The fundamental concept behind MHD is that magnetic fields can induce
Electromagnetic induction
Electromagnetic induction is the production of an electric current across a conductor moving through a magnetic field. It underlies the operation of generators, transformers, induction motors, electric motors, synchronous motors, and solenoids....
currents in a moving conductive fluid, which in turn creates forces on the fluid and also changes the magnetic field itself. The set of equations which describe MHD are a combination of the Navier-Stokes equations
Navier-Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous...
of fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
and Maxwell's equations
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
of electromagnetism
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
. These differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s have to be solved simultaneously, either analytically or numerically
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
.
History
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...
in 1942:
- "At last some remarks are made about the transfer of momentum from the Sun to the planets, which is fundamental to the theory (§11). The importance of the magnetohydrodynamic waves in this respect are pointed out."
The ebbing salty water flowing past London's Waterloo Bridge
Waterloo Bridge
Waterloo Bridge is a road and foot traffic bridge crossing the River Thames in London, England between Blackfriars Bridge and Hungerford Bridge. The name of the bridge is in memory of the British victory at the Battle of Waterloo in 1815...
interacts with the Earth's magnetic field
Earth's magnetic field
Earth's magnetic field is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun...
to produce a potential difference between the two river-banks. Michael Faraday
Michael Faraday
Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....
tried this experiment in 1832 but the current was too small to measure with the equipment at the time, and the river bed contributed to short-circuit the signal. However, by the same process, Dr. William Hyde Wollaston
William Hyde Wollaston
William Hyde Wollaston FRS was an English chemist and physicist who is famous for discovering two chemical elements and for developing a way to process platinum ore.-Biography:...
was able to measure the voltage induced by the tide in the English Channel in 1851.
Ideal and resistive MHD
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
that it can be treated as a perfect conductor
Perfect conductor
A perfect conductor is an electrical conductor with no resistivity. The concept is used to model systems in which the electrical resistance or resistivity is negligible compared to other effects. One such model is ideal magnetohydrodynamics, the study of perfectly conductive fluids...
. This is the limit of infinite magnetic Reynolds number
Magnetic Reynolds number
The Magnetic Reynolds number is a dimensionless group thatoccurs in magnetohydrodynamics. It gives an estimate of the effects of magnetic advection to magnetic diffusion, and is typically defined by:where* U is a typical velocity scale of the flow...
. In ideal MHD, Lenz's law
Lenz's law
Lenz's law is a common way of understanding how electromagnetic circuits must always obey Newton's third law and The Law of Conservation of Energy...
dictates that the fluid is in a sense tied to the magnetic field lines. To explain, in ideal MHD a small rope-like volume of fluid surrounding a field line will continue to lie along a magnetic field line,
even as it is twisted and distorted by fluid flows in the system.
The connection between magnetic field lines and fluid in ideal MHD fixes the topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
of the magnetic field in the fluid—for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection
Magnetic reconnection
Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration...
that releases the stored energy from the magnetic field.
Ideal MHD equations
The ideal MHD equations consist of the continuity equationContinuity equation
A continuity equation in physics is a differential equation that describes the transport of a conserved quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described...
, the momentum equation
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
, Ampere's Law
Ampère's law
In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop...
neglecting displacement current, and a temperature evolution equation
Conservation of energy
The nineteenth century law of conservation of energy is a law of physics. It states that the total amount of energy in an isolated system remains constant over time. The total energy is said to be conserved over time...
. As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation. This is often accomplished with approximations to the heat flux through a condition of adiabaticity
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
or isothermality
Isothermal process
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir...
.
In the following,
is the magnetic field, is the electric field, is the bulk plasma velocity, is the current density, is the mass density, is the plasma pressure, and is time. The continuity equation isThe momentum equation is
The Lorentz force term
can be expanded to givewhere the first term on the right hand side is the magnetic tension force and the second term is the magnetic pressure
Magnetic pressure
Magnetic pressure is an energy density associated with the magnetic field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than kinetic energy of the gas molecules. Interplay between magnetic pressure and ordinary gas pressure is important to...
force.
The ideal Ohm's law for a plasma is given by
Faraday's law is
The low-frequency Ampere's law neglects displacement current and is given by
The magnetic divergence constraint is
The energy equation is given by
where
is the ratio of specific heats for an adiabatic equation of state.Applicability of ideal MHD to plasmas
Ideal MHD is only strictly applicable when:- The plasma is strongly collisional, so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are therefore close to Maxwellian.
- The resistivity due to these collisions is small. In particular, the typical magnetic diffusion times over any scale length present in the system must be longer than any time scale of interest.
- We are interested in length scales much longer than the ion skin depth and Larmor radius perpendicular to the field, long enough along the field to ignore Landau dampingLandau dampingIn physics, Landau damping, named after its discoverer, the eminent Soviet physicist Lev Davidovich Landau, is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in...
, and time scales much longer than the ion gyration time (system is smooth and slowly evolving).
Importance of resistivity
In an imperfectly conducting fluid the magnetic field can generally move through the fluid following a diffusion law with the resistivity of the plasma serving as a diffusion constant. This means that solutions to the ideal MHD equations are only applicable for a limited time for a region of a given size before diffusion becomes too important to ignore. One can estimate the diffusion time across a solar active region (from collisional resistivity) to be hundreds to thousands of years, much longer than the actual lifetime of a sunspot—so it would seem reasonable to ignore the resistivity. By contrast, a meter-sized volume of seawater has a magnetic diffusion time measured in milliseconds.Even in physical systems which are large and conductive enough that simple estimates of the Lundquist number
Lundquist number
In plasma physics, the Lundquist number is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale...
suggest that we can ignore the resistivity, resistivity may still be important: many instabilities
Instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...
exist that can increase the effective resistivity of the plasma by factors of more than a billion. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic turbulence, introducing small spatial scales into the system over which ideal MHD is broken and magnetic diffusion can occur quickly. When this happens, magnetic reconnection may occur in the plasma to release stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration
Particle acceleration
In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector...
, and heat.
Magnetic reconnection in highly conductive systems is important because it concentrates energy in time and space, so that gentle forces applied to a plasma for long periods of time can cause violent explosions and bursts of radiation.
When the fluid cannot be considered as completely conductive, but the other conditions for ideal MHD are satisfied, it is possible to use an extended model called resistive MHD. This includes an extra term in Ampere's Law which models the collisional resistivity. Generally MHD computer simulations are at least somewhat resistive because their computational grid introduces a numerical resistivity.
Importance of kinetic effects
Another limitation of MHD (and fluid theories in general) is that they depend on the assumption that the plasma is strongly collisional (this is the first criterion listed above), so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are Maxwellian. This is usually not the case in fusion, space and astrophysical plasmas. When this is not the case, or we are interested in smaller spatial scales, it may be necessary to use a kinetic model which properly accounts for the non-Maxwellian shape of the distribution function. However, because MHD is relatively simple and captures many of the important properties of plasma dynamics it is often qualitatively accurate and is almost invariably the first model tried.Effects which are essentially kinetic and not captured by fluid models include double layers
Double layer (plasma)
A double layer is a structure in a plasma and consists of two parallel layers with opposite electrical charge. The sheets of charge cause a strong electric field and a correspondingly sharp change in voltage across the double layer. Ions and electrons which enter the double layer are accelerated,...
, Landau damping
Landau damping
In physics, Landau damping, named after its discoverer, the eminent Soviet physicist Lev Davidovich Landau, is the effect of damping of longitudinal space charge waves in plasma or a similar environment. This phenomenon prevents an instability from developing, and creates a region of stability in...
, a wide range of instabilities, chemical separation in space plasmas and electron runaway.
Structures in MHD systems
Current sheet
A current sheet is an electric current that is confined to a surface, rather than being spread through a volume of space. Current sheets feature in magnetohydrodynamics , the study of the behavior of electrically conductive fluids: if there is an electric current through part of the volume of such...
s. These can divide the fluid into magnetic domains, inside of which the currents are relatively weak. Current sheets in
the solar corona are thought to be between a few meters and a few kilometers in thickness, which is quite thin compared to the magnetic domains (which are thousands to hundreds of thousands of kilometers across). Another example is in the Earth's magnetosphere
Magnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
, where current sheets separate topologically distinct domains, isolating most of the Earth's ionosphere
Ionosphere
The ionosphere is a part of the upper atmosphere, comprising portions of the mesosphere, thermosphere and exosphere, distinguished because it is ionized by solar radiation. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere...
from the solar wind
Solar wind
The 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...
.
MHD waves
The wave modes derived using MHD plasma theory are called magnetohydrodynamic waves or MHD waves. In general there are three MHD wave modes:- Pure (or oblique) Alfvén wave
- Slow MHD wave
- Fast MHD wave
All these waves have constant phase velocities for all frequencies, and hence there is no dispersion. At the limits when the angle between the wave propagation vector k and magnetic field B is either 0 (180) or 90 degrees, the wave modes are called:
| name | type | propagation | phase velocity | association | medium | other names |
|---|---|---|---|---|---|---|
| Sound wave | longitudinal | adiabatic sound velocity | none | compressible, nonconducting fluid | ||
| Alfvén wave Alfvén wave An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field... |
transverse | Alfvén velocity |  |
shear Alfvén wave, the slow Alfvén wave, torsional Alfvén wave | ||
| Magnetosonic wave Magnetosonic wave A magnetosonic wave is a longitudinal wave of ions in a magnetized plasma propagating perpendicular to the stationary magnetic field... |
longitudinal |  |
 ,  |
compressional Alfvén wave, fast Alfvén wave, magnetoacoustic wave |
The MHD oscillations will be damped if the fluid is not perfectly conducting but has a finite conductivity, or if viscous effects are present.
MHD waves and oscillations are a popular tool for the remote diagnostics of laboratory and astrophysical plasmas, e.g. the corona
Corona
A 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...
of the Sun (Coronal seismology
Coronal seismology
Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid is the coronal plasma. Observed properties of the waves...
).
Resistive MHD
Resistive MHD describes magnetized fluids with finite electron diffusivity (). This diffusivity leads to a breaking in the magnetic topology; magnetic field lines can 'reconnect' when they collide. Usually this term is small and reconnections can be handled by thinking of them as not dissimilar to shocks; this process has been shown to be important in the Earth-Solar magnetic interactions.Extended MHD
Extended MHD describes a class of phenomena in plasmas that are higher order than resistive MHD, but which can adequately be treated with a single fluid description. These include the effects of Hall physics, electron pressure gradients, finite Larmor Radii in the particle gyromotion, and electron inertia.Two-Fluid MHD
Two-Fluid MHD describes plasmas that include a non-negligible Hall electric fieldElectric field
In physics, an electric field surrounds electrically charged particles and time-varying magnetic fields. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding...
. As a result, the electron and ion momenta must be treated separately. This description is more closely tied to Maxwell's equations as an evolution equation for the electric field exists.
Hall MHD
In 1960, M. J. Lighthill criticized the applicability of ideal or resistive MHD theory for plasmas. It concerned the neglect of the "Hall current term", a frequent simplification made in magnetic fusion theory. Hall-magnetohydrodynamics (HMHD) takes into account this electric field description of magnetohydrodynamics. The most important difference is that in the absence of field line breaking, the magnetic field is tied to the electrons and not to the bulk fluid.Collisionless MHD
MHD is also often used for collisionless plasmas. In that case the MHD equations are derived from the Vlasov equationVlasov equation
The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction...
.
Geophysics
Beneath the Earth's mantle, lies the core which is made up of two parts - the solid inner core and liquid outer core - both have significant quantities of iron. The liquid outer core moves in the presence of the magnetic field and eddies are set up into the same due to the Coriolis effect. These eddies develop a magnetic field which boosts Earth's original magnetic field - a process which is self-sustaining and is called as the geomagnetic dynamo.Based on the MHD equations, Glatzmaier and Paul Roberts have made a supercomputer model of the Earth's interior. After running the simulations for thousands of years in virtual time, the changes in Earth's magnetic field can be studied. The simulation results are in good agreement with the observations as the simulations have correctly predicted that the Earth's magnetic field flips every few thousands of years. During the flips, the magnetic field doesn't vanish altogether - it just gets more complicated.
Astrophysics
MHD applies quite well to astrophysicsAstrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
since over 99% of baryonic matter content of the Universe is made up of plasma, including stars, the interplanetary medium
Interplanetary medium
The interplanetary medium is the material which fills the solar system and through which all the larger solar system bodies such as planets, asteroids and comets move.-Composition and physical characteristics:...
(space between the planets), the interstellar medium
Interstellar medium
In 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...
(space between the stars), nebulae and jets
Relativistic jet
Relativistic jets are extremely powerful jets of plasma which emerge from presumed massive objects at the centers of some active galaxies, notably radio galaxies and quasars. Their lengths can reach several thousand or even hundreds of thousands of light years...
. Many astrophysical systems are not in local thermal equilibrium, and therefore require an additional kinematic treatment to describe all the phenomena within the system (see Astrophysical plasma
Astrophysical plasma
An astrophysical plasma is a plasma the physical properties of which are studied as part of astrophysics. Much of the baryonic matter of the universe is thought to consist of plasma, a state of matter in which atoms and molecules are so hot, that they have ionized by breaking up into their...
).
Sunspot
Sunspot
Sunspots are temporary phenomena on the photosphere of the Sun that appear visibly as dark spots compared to surrounding regions. They are caused by intense magnetic activity, which inhibits convection by an effect comparable to the eddy current brake, forming areas of reduced surface temperature....
s are caused by the Sun's magnetic fields, as Joseph Larmor
Joseph Larmor
Sir Joseph Larmor , a physicist and mathematician who made innovations in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter...
theorized in 1919. The solar wind
Solar wind
The 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...
is also governed by MHD. The differential solar rotation
Solar rotation
Solar rotation is able to vary with latitude because the Sun is composed of a gaseous plasma. The rate of rotation is observed to be fastest at the equator , and to decrease as latitude increases...
may be the long term effect of magnetic drag at the poles of the Sun, an MHD phenomenon due to the Parker spiral
Parker spiral
The Parker spiral is the shape of the Sun's magnetic field as it extends through the solar system. Unlike the familiar shape of the field from a bar magnet, the Sun's extended field is twisted into an arithmetic spiral by the magnetohydrodynamic influence of the solar wind...
shape assumed by the extended magnetic field of the Sun.
Previously, theories describing the formation of the Sun and planets could not explain how the Sun has 99.87% of the mass, yet only 0.54% of the angular momentum
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...
in the solar system
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
. In a closed system
Closed system
-In physics:In thermodynamics, a closed system can exchange energy , but not matter, with its surroundings.In contrast, an isolated system cannot exchange any of heat, work, or matter with the surroundings, while an open system can exchange all of heat, work and matter.For a simple system, with...
such as the cloud of gas and dust from which the Sun was formed, mass and angular momentum are both conserved
Conservation law
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves....
. That conservation would imply that as the mass concentrated in the center of the cloud to form the Sun, it would spin up, much like a skater pulling their arms in. The high speed of rotation predicted by early theories would have flung the proto-Sun apart before it could have formed. However, magnetohydrodynamic effects transfer the Sun's angular momentum into the outer solar system, slowing its rotation.
Breakdown of ideal MHD (in the form of magnetic reconnection) is known to be the cause of solar flare
Solar flare
A solar flare is a sudden brightening observed over the Sun surface or the solar limb, which is interpreted as a large energy release of up to 6 × 1025 joules of energy . The flare ejects clouds of electrons, ions, and atoms through the corona into space. These clouds typically reach Earth a day...
s, the largest explosions in the solar system. The magnetic field in a solar active region over a sunspot can become quite stressed over time, storing energy that is released suddenly as a burst of motion, X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s, and radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
when the main current sheet collapses, reconnecting the field.
Engineering
MHD is related to engineering problems such as plasma confinementFusion power
Fusion power is the power generated by nuclear fusion processes. In fusion reactions two light atomic nuclei fuse together to form a heavier nucleus . In doing so they release a comparatively large amount of energy arising from the binding energy due to the strong nuclear force which is manifested...
, liquid-metal cooling of nuclear reactor
Nuclear reactor
A nuclear reactor is a device to initiate and control a sustained nuclear chain reaction. Most commonly they are used for generating electricity and for the propulsion of ships. Usually heat from nuclear fission is passed to a working fluid , which runs through turbines that power either ship's...
s, and electromagnetic
Electromagnetism
Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...
casting (among others).
The first prototype of this kind of propulsion was built and tested in 1965 by Steward Way, a professor of mechanical engineering at the University of California, Santa Barbara
University of California, Santa Barbara
The University of California, Santa Barbara, commonly known as UCSB or UC Santa Barbara, is a public research university and one of the 10 general campuses of the University of California system. The main campus is located on a site in Goleta, California, from Santa Barbara and northwest of Los...
. Way, on leave from his job at Westinghouse Electric
Westinghouse Electric (1886)
Westinghouse Electric was an American manufacturing company. It was founded in 1886 as Westinghouse Electric Company and later renamed Westinghouse Electric Corporation by George Westinghouse. The company purchased CBS in 1995 and became CBS Corporation in 1997...
, assigned his senior year undergraduate students to develop a submarine with this new propulsion system. In early 1990s, Mitsubishi
Mitsubishi
The Mitsubishi Group , Mitsubishi Group of Companies, or Mitsubishi Companies is a Japanese multinational conglomerate company that consists of a range of autonomous businesses which share the Mitsubishi brand, trademark and legacy...
built a boat, the 'Yamato
Yamato 1
Yamato 1 is a boat built in the early 1990s by Japanese conglomerate "The Mitsubishi Group" through their subsidiary company Mitsubishi Heavy Industries, Ltd at Wadasaki-cho Hyogo-ku, Kobe. It uses a MagnetoHydrodynamic Drive , driven by a liquid helium-cooled superconductor, and can travel at 15...
,' which uses a magnetohydrodynamic drive
Magnetohydrodynamic drive
A magnetohydrodynamic drive or MHD propulsor is a method for propelling seagoing vessels using only electric and magnetic fields with no moving parts, using magnetohydrodynamics. The working principle involves electrification of the propellant which can then be directed by a magnetic field,...
, is driven by a liquid helium
Helium
Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...
-cooled superconductor, and can travel at 15 km/h.
MHD power generation fueled by potassium-seeded coal combustion gas showed potential for more efficient energy conversion (the absence of solid moving parts allows operation at higher temperatures), but failed due to cost prohibitive technical difficulties.
In microfluidic devices, the MHD pump is so far the most effective for producing a continuous, nonpulsating flow in a complex microchannel design. It was used to implement a PCR protocol.
Magnetic Drug Targeting
Latest research on cancer is partly focused on localized delivery of cancer medicine to the affected part of the body. To achieve the same the medicine is bound to magnetic particles (e.g. ferrofluids) which are biologically compatible. For targeting the same permanent magnets can be used by positioning them at suitable locations of the external body. To study the interaction between the magnetic fluid particles passing through the blood with the external magnetic field, magnetohydrodynamic equations and finite element analysis are used. Thus the efficacy of such treatments can be estimated.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