![The sun is an MHD system that is not well understood- 2013-04-9 14-29](https://upload.wikimedia.org/wikipedia/commons/8/8e/The_sun_is_an_MHD_system_that_is_not_well_understood-_2013-04-9_14-29.jpg)
Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of
electrically conducting
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
s. Examples of such magnetofluids include
plasmas,
liquid metal
A liquid metal is a metal or a metal alloy which is liquid at or near room temperature.
The only stable liquid elemental metal at room temperature is Mercury (element), mercury (Hg), which is molten above −38.8 °C (234.3 K, −37.9&nbs ...
s,
salt water
Saline water (more commonly known as salt water) is water that contains a high concentration of dissolved salts (mainly sodium chloride). On the United States Geological Survey (USGS) salinity scale, saline water is saltier than brackish water, ...
, and
electrolyte
An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electrons. This includes most soluble salts, acids, and bases dissolved in a polar solvent, such as water. Upon dis ...
s. The word ''magnetohydrodynamics'' is derived from ' meaning
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, ' meaning water, and ' meaning movement. The field of MHD was initiated by
Hannes Alfvén
Hannes Olof Gösta Alfvén (; 30 May 1908 – 2 April 1995) was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics (MHD). He described the class of MHD waves now ...
, for which he received the
Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfr ...
in Physics in 1970.
The fundamental concept behind MHD is that magnetic fields can
induce currents in a moving conductive fluid, which in turn polarizes the fluid and reciprocally changes the magnetic field itself. The set of equations that describe MHD are a combination of the
Navier–Stokes equations
In physics, the Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematician Geo ...
of
fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) an ...
and
Maxwell’s equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
Th ...
of
electromagnetism. These
differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s must be solved
simultaneously
Simultaneity may refer to:
* Relativity of simultaneity, a concept in special relativity.
* Simultaneity (music), more than one complete musical texture occurring at the same time, rather than in succession
* Simultaneity, a concept in Endogene ...
, either analytically or
numerically.
History
![M Faraday Th Phillips oil 1842](https://upload.wikimedia.org/wikipedia/commons/8/88/M_Faraday_Th_Phillips_oil_1842.jpg)
The first recorded use of the word ''magnetohydrodynamics'' is by
Hannes Alfvén
Hannes Olof Gösta Alfvén (; 30 May 1908 – 2 April 1995) was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics (MHD). He described the class of MHD waves now ...
in 1942:
The ebbing salty water flowing past London's
Waterloo Bridge
Waterloo Bridge () is a road and foot traffic bridge crossing the River Thames in London, between Blackfriars Bridge and Hungerford Bridge and Golden Jubilee Bridges. Its name commemorates the victory of the British, Dutch and Prussians at the ...
interacts with the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
to produce a potential difference between the two river-banks.
Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
called this effect "magneto-electric induction" and 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 a similar process the voltage induced by the tide in the English Channel was measured in 1851.
Faraday carefully omitted the term of hydrodynamics in this work.
Ideal and resistive MHD
![T3e troy](https://upload.wikimedia.org/wikipedia/commons/2/2f/T3e_troy.jpg)
The simplest form of MHD, Ideal MHD, assumes that the fluid has so little
resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
that it can be treated as a
perfect conductor
A perfect conductor or perfect electric conductor (PEC) is an idealized material exhibiting infinite electrical conductivity or, equivalently, zero resistivity (cf. perfect dielectric). While perfect electrical conductors do not exist in nature, t ...
. This is the limit of infinite
magnetic Reynolds number
In magnetohydrodynamics, the magnetic Reynolds number (Rm) is a dimensionless quantity that estimates the relative effects of advection or induction of a magnetic field by the motion of a conducting medium to the magnetic diffusion. It is the mag ...
. In ideal MHD,
Lenz's law
Lenz's law states that the direction of the electric current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in the initial magnetic field. It is named after p ...
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. This is sometimes referred to as the magnetic field lines being
"frozen" in the fluid. The connection between magnetic field lines and fluid in ideal MHD fixes the
topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
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 is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnectio ...
that releases the stored energy from the magnetic field.
Ideal MHD equations
![Magnetohydrodynamic Flow Simulation](https://upload.wikimedia.org/wikipedia/commons/7/77/Magnetohydrodynamic_Flow_Simulation.jpg)
The ideal MHD equations consist of the
continuity equation
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
, the
Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum.
Main equation
In convective (or Lagrangian) form the Cauchy momentum equation is ...
,
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.
The main quantities which characterize the electrically conducting fluid are the bulk plasma
velocity field
In continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the f ...
, the
current density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
, the
mass density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
, and the plasma
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
. The flowing electric charge in the plasma is the source of a
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
and
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
. All quantities generally vary with time .
Vector operator
A vector operator is a differential operator used in vector calculus. Vector operators are defined in terms of del, and include the gradient, divergence, and Curl (mathematics), curl:
:\begin
\operatorname &\equiv \nabla \\
\operatorname &\equiv ...
notation will be used, in particular is
gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...
, is
divergence
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the ...
, and is
curl
cURL (pronounced like "curl", UK: , US: ) is a computer software project providing a library (libcurl) and command-line tool (curl) for transferring data using various network protocols. The name stands for "Client URL".
History
cURL was fi ...
.
The mass
continuity equation
A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
is
:
The
Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum.
Main equation
In convective (or Lagrangian) form the Cauchy momentum equation is ...
is
:
The
Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
term can be expanded using
Ampère's law and the
vector calculus identity
The following are important identities involving derivatives and integrals in vector calculus.
Operator notation
Gradient
For a function f(x, y, z) in three-dimensional Cartesian coordinate variables, the gradient is the vector field:
\o ...
:
to give
:
where the first term on the right hand side is the
magnetic tension force
In physics, magnetic tension is a restoring force with units of force density that acts to straighten bent magnetic field lines. In SI units, the force density \mathbf_T exerted perpendicular to a magnetic field \mathbf can be expressed as
:\mat ...
and the second term is the
magnetic pressure
In physics, magnetic pressure is an energy density associated with a magnetic field. In SI units, the energy density P_B of a magnetic field with strength B can be expressed as
:P_B = \frac
where \mu_0 is the vacuum permeability.
Any magnetic fiel ...
force.
The ideal
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equat ...
for a plasma is given by
:
Faraday's law is
:
The low-frequency Ampère'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 heat
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
s for an
adiabatic equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
. This energy equation is only applicable in the absence of shocks or heat conduction as it assumes that the entropy of a fluid element does not change.
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.
# Interest in length scales much longer than the ion
skin depth
Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the con ...
and
Larmor radius The gyroradius (also known as radius of gyration, Larmor radius or cyclotron radius) is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the non-relativistic gyroradius is given by
:r_ ...
perpendicular to the field, long enough along the field to ignore
Landau damping In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited a ...
, 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
Fick's laws of diffusion describe diffusion and were derived by Adolf Fick in 1855. They can be used to solve for the diffusion coefficient, . Fick's first law can be used to derive his second law which in turn is identical to the diffusion equ ...
. 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 In plasma physics, the Lundquist number (denoted by S) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the magnetic Reynolds number when the Alfvén ...
suggest that the resistivity can be ignored—resistivity may still be important: many
instabilities exist that can increase the effective resistivity of the plasma by factors of more than 10
9. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic
turbulence
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
, 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
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 (symbol: ''a'') is def ...
, 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 Ohm's Law which models the collisional resistivity. Generally MHD computer simulations are at least somewhat resistive because their computational grid introduces a
numerical resistivity
Numerical resistivity is a problem in computer simulations of ideal magnetohydrodynamics (MHD). It is a form of numerical diffusion. In near-ideal MHD systems, the magnetic field can diffuse only very slowly through the plasma or fluid of the sys ...
.
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 the interest is 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 therefore often the first model tried.
Effects which are essentially kinetic and not captured by fluid models include
double layers,
Landau damping In physics, Landau damping, named after its discoverer,Landau, L. "On the vibration of the electronic plasma". ''JETP'' 16 (1946), 574. English translation in ''J. Phys. (USSR)'' 10 (1946), 25. Reproduced in Collected papers of L.D. Landau, edited a ...
, a wide range of instabilities, chemical separation in space plasmas and electron runaway. In the case of ultra-high intensity laser interactions, the incredibly short timescales of energy deposition mean that hydrodynamic codes fail to capture the essential physics.
Structures in MHD systems
![Currents](https://upload.wikimedia.org/wikipedia/commons/0/0f/Currents.jpg)
In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed
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 (MHD), the study of the behavior of electrically conductive fluids: if ther ...
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
In astronomy and planetary science, a magnetosphere is a region of space surrounding an astronomical object in which charged particles are affected by that object's magnetic field. It is created by a celestial body with an active interior dynam ...
, where current sheets separate topologically distinct domains, isolating most of the Earth's
ionosphere
The ionosphere () is the ionized part of the upper atmosphere of Earth, from about to above sea level, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an ...
from the
solar wind
The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
.
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 and magnetic field is either 0° (180°) or 90°, the wave modes are called:
The phase velocity depends on the angle between the wave vector and the magnetic field . An MHD wave propagating at an arbitrary angle with respect to the time independent or bulk field will satisfy the dispersion relation
:
where
:
is the Alfvén speed. This branch corresponds to the shear Alfvén mode. Additionally the dispersion equation gives
:
where
:
is the ideal gas speed of sound. The plus branch corresponds to the fast-MHD wave mode and the minus branch corresponds to the slow-MHD wave mode.
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, for example, the
corona
Corona (from the Latin for 'crown') most commonly refers to:
* Stellar corona, the outer atmosphere of the Sun or another star
* Corona (beer), a Mexican beer
* Corona, informal term for the coronavirus SARS-CoV-2, which causes the COVID-19 di ...
of the Sun (
Coronal seismology
Coronal seismology is a technique of studying the plasma of the Sun's corona with the use of magnetohydrodynamic (MHD) waves and oscillations. Magnetohydrodynamics studies the dynamics of electrically conducting fluids - in this case the fluid is ...
).
Extensions
; Resistive
: 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
: 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
: Two-fluid MHD describes plasmas that include a non-negligible Hall
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
. 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
: 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.
; Electron MHD
: Electron Magnetohydrodynamics (EMHD) describes small scales plasmas when electron motion is much faster than the ion one. The main effects are changes in conservation laws, additional resistivity, importance of electron inertia. Many effects of Electron MHD are similar to effects of the Two fluid MHD and the Hall MHD. EMHD is especially important for
z-pinch
In fusion power research, the Z-pinch (zeta pinch) is a type of plasma confinement system that uses an electric current in the plasma to generate a magnetic field that compresses it (see pinch). These systems were originally referred to simply ...
,
magnetic reconnection
Magnetic reconnection is a physical process occurring in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnectio ...
,
ion thrusters
An ion thruster, ion drive, or ion engine is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating ions using electricity.
An ion thruster ionizes a neutral gas by extracting some electrons out of a ...
,
neutron stars
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
, and plasma switches.
; Collisionless
: MHD is also often used for collisionless plasmas. In that case the MHD equations are derived from the
Vlasov equation The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulo ...
.
[W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997]
; Reduced
: By using a
multiscale analysis the (resistive) MHD equations can be reduced to a set of four closed scalar equations. This allows for, amongst other things, more efficient numerical calculations.
Applications
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
Iron () is a chemical element with symbol Fe (from la, ferrum) and atomic number 26. It is a metal that belongs to the first transition series and group 8 of the periodic table. It is, by mass, the most common element on Earth, right in f ...
. 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
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
. These eddies develop a magnetic field which boosts Earth's original magnetic field—a process which is self-sustaining and is called the geomagnetic dynamo.
[NOVA , Magnetic Storm , What Drives Earth's Magnetic Field? , PBS](_blank)
/ref>
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 hundred thousand years. During the flips, the magnetic field does not vanish altogether—it just gets more complex.[Earth's Inconstant Magnetic Field – NASA Science](_blank)
/ref>
Earthquakes
Some monitoring stations have reported that earthquakes
An earthquake (also known as a quake, tremor or temblor) is the shaking of the surface of the Earth resulting from a sudden release of energy in the Earth's lithosphere that creates seismic waves. Earthquakes can range in intensity, from ...
are sometimes preceded by a spike in ultra low frequency
Ultra low frequency (ULF) is the ITU designation for the frequency range of electromagnetic waves between 300 hertz and 3 kilohertz, corresponding to wavelengths between 1,000 to 100 km. In magnetosphere science and seismology, alternative defin ...
(ULF) activity. A remarkable example of this occurred before the 1989 Loma Prieta earthquake
The 1989 Loma Prieta earthquake occurred on California's Central Coast on October 17 at local time. The shock was centered in The Forest of Nisene Marks State Park in Santa Cruz County, approximately northeast of Santa Cruz on a section of t ...
in California
California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territori ...
, although a subsequent study indicates that this was little more than a sensor malfunction. On December 9, 2010, geoscientists announced that the DEMETER
In ancient Greek religion and mythology, Demeter (; Attic: ''Dēmḗtēr'' ; Doric: ''Dāmā́tēr'') is the Olympian goddess of the harvest and agriculture, presiding over crops, grains, food, and the fertility of the earth. Although s ...
satellite observed a dramatic increase in ULF radio waves over Haiti
Haiti (; ht, Ayiti ; French: ), officially the Republic of Haiti (); ) and formerly known as Hayti, is a country located on the island of Hispaniola in the Greater Antilles archipelago of the Caribbean Sea, east of Cuba and Jamaica, and ...
in the month before the magnitude 7.0 Mw 2010 earthquake
Earthquakes in 2010 resulted in nearly 165,000 fatalities. Most of these were due to the 2010 Haiti earthquake, which caused an estimated 160,000 deaths, making it the 11th deadliest earthquake in recorded history. Other deadly quakes occurred i ...
. Researchers are attempting to learn more about this correlation to find out whether this method can be used as part of an early warning system for earthquakes.
Astrophysics
MHD applies to astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
, including stars, the interplanetary medium
The interplanetary medium (IPM) or interplanetary space consists of the mass and energy which fills the Solar System, and through which all the larger Solar System bodies, such as planets, dwarf planets, asteroids, and comets, move. The IPM sto ...
(space between the planets), and possibly within the interstellar medium
In astronomy, the interstellar medium is the matter and radiation that exist in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and cosmic rays. It fills interstella ...
(space between the stars) and jets. Most 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 is plasma outside of the Solar System. It is studied as part of astrophysics and is commonly observed in space. The accepted view of scientists is that much of the baryonic matter in the universe exists in this state.
Whe ...
).
Sunspot
Sunspots are phenomena on the Sun's photosphere that appear as temporary spots that are darker than the surrounding areas. They are regions of reduced surface temperature caused by concentrations of magnetic flux that inhibit convection. Sun ...
s are caused by the Sun's magnetic fields, as Joseph Larmor
Sir Joseph Larmor (11 July 1857 – 19 May 1942) was an Irish and British physicist and mathematician who made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter. His most influent ...
theorized in 1919. The solar wind
The solar wind is a stream of charged particles released from the upper atmosphere of the Sun, called the corona. This plasma mostly consists of electrons, protons and alpha particles with kinetic energy between . The composition of the sola ...
is also governed by MHD. The differential solar rotation
Solar rotation varies with latitude. The Sun is not a solid body, but is composed of a gaseous plasma. Different latitudes rotate at different periods. The source of this differential rotation is an area of current research in solar astronomy. ...
may be the long-term effect of magnetic drag at the poles of the Sun, an MHD phenomenon due to the Parker spiral
The heliospheric current sheet, or interplanetary current sheet, is a surface separating regions of the heliosphere where the interplanetary magnetic field points toward and away from the Sun. A small electrical current with a current density of ...
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 physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
in the Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
. In a closed system
A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed.
In ...
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 faster, 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 likely cause of solar flare
A solar flare is an intense localized eruption of electromagnetic radiation in the Sun's atmosphere. Flares occur in active regions and are often, but not always, accompanied by coronal mass ejections, solar particle events, and other solar phe ...
s. The magnetic field in a solar active region
An active region is a temporary region in the Sun's atmosphere characterized by a strong and complex magnetic field. They are often associated with sunspots and are commonly the source of violent eruptions such as coronal mass ejections and solar ...
over a sunspot can store energy that is released suddenly as a burst of motion, X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
s, and radiation
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. This includes:
* ''electromagnetic radiation'', such as radio waves, microwaves, infrared, visi ...
when the main current sheet collapses, reconnecting the field.
Sensors
Magnetohydrodynamic sensors are used for precision measurements of angular velocities in inertial navigation system
An inertial navigation system (INS) is a navigation device that uses motion sensors (accelerometers), rotation sensors ( gyroscopes) and a computer to continuously calculate by dead reckoning the position, the orientation, and the velocity (dire ...
s such as in aerospace engineering
Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is si ...
. Accuracy improves with the size of the sensor. The sensor is capable of surviving in harsh environments.
Engineering
MHD is related to engineering problems such as plasma confinement
In plasma physics, plasma confinement refers to the act of maintaining a plasma in a discrete volume. Confining plasma is required in order to achieve fusion power. There are two major approaches to confinement: magnetic confinement
Magnetic co ...
, liquid-metal cooling of nuclear reactor
A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nu ...
s, and electromagnetic
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
casting (among others).
A magnetohydrodynamic drive
A magnetohydrodynamic drive or MHD accelerator is a method for propelling vehicles using only electric and magnetic fields with no moving parts, accelerating an electrically conductive propellant ( liquid or gas) with magnetohydrodynamics. The ...
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 (gas or water) which can then be directed by a magnetic field, pushing the vehicle in the opposite direction. Although some working prototypes exist, MHD drives remain impractical.
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
The University of California, Santa Barbara (UC Santa Barbara or UCSB) is a Public university, public Land-grant university, land-grant research university in Santa Barbara County, California, Santa Barbara, California with 23,196 undergraduate ...
. Way, on leave from his job at Westinghouse Electric
The Westinghouse Electric Corporation was an American manufacturing company founded in 1886 by George Westinghouse. It was originally named "Westinghouse Electric & Manufacturing Company" and was renamed "Westinghouse Electric Corporation" in ...
, assigned his senior-year undergraduate students to develop a submarine with this new propulsion system. In the early 1990s, a foundation in Japan (Ship & Ocean Foundation (Minato-ku, Tokyo)) built an experimental boat, the '' Yamato-1'', which used a magnetohydrodynamic drive incorporating a superconductor cooled by liquid helium
Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity.
At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temp ...
, and could travel at 15 km/h.[Setsuo Takezawa et al. (March 1995) ''Operation of the Thruster for Superconducting Electromagnetohydrodynamic Propu1sion Ship YAMATO 1'']
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. One major engineering problem was the failure of the wall of the primary-coal combustion chamber due to abrasion.
In microfluidics
Microfluidics refers to the behavior, precise control, and manipulation of fluids that are geometrically constrained to a small scale (typically sub-millimeter) at which surface forces dominate volumetric forces. It is a multidisciplinary field tha ...
, MHD is studied as a fluid pump for producing a continuous, nonpulsating flow in a complex microchannel design.
MHD can be implemented in the continuous casting
Continuous casting, also called strand casting, is the process whereby molten metal is solidified into a "semifinished" billet, bloom, or slab for subsequent rolling in the finishing mills. Prior to the introduction of continuous casting in the ...
process of metals to suppress instabilities and control the flow.
Industrial MHD problems can be modeled using the open-source software EOF-Library. Two simulation examples are 3D MHD with a free surface for electromagnetic levitation
Magnetic levitation (maglev) or magnetic suspension is a method by which an object is suspended with no support other than magnetic fields. Magnetic force is used to counteract the effects of the gravitational force and any other forces.
The ...
melting, and liquid metal stirring by rotating permanent magnets.
Magnetic drug targeting
An important task in cancer research is developing more precise methods for delivery of medicine to affected areas. One method involves the binding of medicine to biologically compatible magnetic particles (such as ferrofluids), which are guided to the target via careful placement of permanent magnets on the external body. Magnetohydrodynamic equations and finite element analysis are used to study the interaction between the magnetic fluid particles in the bloodstream and the external magnetic field.
See also
* Computational magnetohydrodynamics Computational magnetohydrodynamics (CMHD) 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 a ...
* Electrohydrodynamics
Electrohydrodynamics (EHD), also known as electro-fluid-dynamics (EFD) or electrokinetics, is the study of the dynamics of electrically charged fluids. It is the study of the motions of ionized particles or molecules and their interactions with ...
* Electromagnetic pump
An electromagnetic pump is a pump that moves liquid metal, molten salt, brine, or other electrically conductive liquid using electromagnetism.
A magnetic field is set at right angles to the direction the liquid moves in, and a current is passed ...
* Ferrofluid
Ferrofluid is a liquid that is attracted to the poles of a magnet. It is a colloidal liquid made of nanoscale ferromagnetic or ferrimagnetic particles suspended in a carrier fluid (usually an organic solvent or water). Each magnetic particle ...
* List of plasma physics articles
This is a list of plasma physics topics.
A
* Ablation
* Abradable coating
* Abraham–Lorentz force
* Absorption band
* Accretion disk
* Active galactic nucleus
* Adiabatic invariant
* ADITYA (tokamak)
* Aeronomy
* Afterglow plasma
* Air ...
* Lorentz force velocity meter
* Magnetic flow meter
A ''magnetic flow meter'' (mag meter, electromagnetic flow meter) is a transducer that measures fluid flow by the voltage induced across the liquid by its flow through a magnetic field. A magnetic field is applied to the metering tube, which resu ...
* Magnetohydrodynamic generator A magnetohydrodynamic generator (MHD generator) is a magnetohydrodynamic converter that transforms thermal energy and kinetic energy directly into electricity. An MHD generator, like a conventional generator, relies on moving a conductor through a m ...
* Magnetohydrodynamic turbulence Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number. Magnetohydrodynamics (MHD) deals with what is a quasi-neutral fluid with very high conductivity. The fluid approximation implies that the focu ...
* Molten salt
Molten salt is salt which is solid at standard temperature and pressure but enters the liquid phase due to elevated temperature. Regular table salt has a melting point of 801 °C (1474°F) and a heat of fusion of 520 J/g.[< ...]
* Plasma stability
The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. ...
* Shocks and discontinuities (magnetohydrodynamics)
In magnetohydrodynamics (MHD), shocks and discontinuities are transition layers where properties of a plasma change from one equilibrium state to another. The relation between the plasma properties on both sides of a shock or a discontinuity can b ...
Notes
References
* Bansal, J. L. (1994) ''Magnetofluiddynamics of Viscous Fluids'' Jaipur Publishing House, Jaipur, India,
*
* Biskamp, Dieter. ''Nonlinear Magnetohydrodynamics''. Cambridge, England: Cambridge University Press, 1993. 378 p.
* Calvert, James B. (20 October 2002
"Magnetohydrodynamics: The dynamics of conducting fluids in an electromagnetic field"
(self published by an Associate Professor Emeritus of Engineering, University of Denver, U.S.A.)
* Davidson, Peter Alan (May 2001) ''An Introduction to Magnetohydrodynamics'' Cambridge University Press, Cambridge, England,
* Faraday, M. (1832). "Experimental Researches in Electricity." First Series, ''Philosophical Transactions of the Royal Society,'' pp. 125–162.
* Ferraro, Vincenzo Consolato Antonio and Plumpton, Charles. ''An Introduction to Magneto-Fluid Mechanics'', 2nd ed.
* Galtier, Sebastien
"Introduction to Modern Magnetohydrodynamics"
Cambridge University Press, Cambridge, England, 2016. 288 p.
*
* Haverkort, J.W. (2009) ''Magnetohydrodynamics'' short introduction for fluid dynamicists
Magnetohydrodynamics
* Hughes, William F. and Young, Frederick J. (1966) ''The Electromagnetodynamics of Fluids'' John Wiley, New York,
*
*
*
* Kulikovskiy, Andreĭ G. and Lyubimov, Grigoriĭ A. (1965)''Magnetohydrodynamics''. Addison-Wesley, Reading, Massachusetts,
* Lorrain, Paul ; Lorrain, François and Houle, Stéphane (2006) ''Magneto-fluid dynamics: fundamentals and case studies of natural phenomena'' Springer, New York,
* Pai, Shih-I (1962) ''Magnetogasdynamics and Plasma Dynamics'' Springer-Verlag, Vienna,
*
* Roberts, Paul H. (1967) ''An Introduction to Magnetohydrodynamics'' Longmans Green, London,
* Rosa, Richard J. (1987) ''Magnetohydrodynamic Energy Conversion'' (2nd edition) Hemisphere Publishing, Washington, D.C.,
* Sritharan, S. S. and Sundar, P. (1999) "The stochastic magneto-hydrodynamic system" ''Infinite Dimensional Analysis, Quantum Probability and Related Topics'' (e-journal) 2(2): pp. 241–265.
* Stern, David P
''In'' Stern, David P. ''The Great Magnet, the Earth'' United States National Aeronautics and Space Administration
* Sutton, George W., and Sherman, Arthur (1965) ''Engineering Magnetohydrodynamics'', McGraw-Hill Book Company, New York,
*
* Van Wie, D. M. (2005
Future Technologies – Application of Plasma Devices for Vehicle Systems
The Johns Hopkins University, Applied Physics Laboratory – Laurel, Maryland, USA – NATO
The North Atlantic Treaty Organization (NATO, ; french: Organisation du traité de l'Atlantique nord, ), also called the North Atlantic Alliance, is an intergovernmental military alliance between 30 member states – 28 European and two No ...
Document
*
"Magnetohydrodynamics"
''In'' Zumerchik, John (editor) (2001) ''Macmillan Encyclopedia of Energy'' Macmillan Reference USA, New York,
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Plasma physics