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.
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.
 Limitations 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.
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
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 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.
This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field.
“ Equations In MHD, motion in the fluid is described using linear combinations of the mean motions of the individual species: the current density and the center of mass
: 6 A fundamental concept underlying ideal MHD is the frozen-in flux theorem which states that the bulk fluid and embedded magnetic field are constrained to move together
such that one can be said to be “tied” or “frozen” to the other.
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 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.
In particular, the typical magnetic diffusion times over any scale length present in the system must be longer than any time scale of interest.
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.
: 25 The connection between the fluid and magnetic field 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 has negligible resistivity.
In a given fluid, each species has a number density , mass , electric charge , and a mean velocity .
Even in physical systems—which are large and conductive enough that simple estimates of the Lundquist number 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.
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
 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).
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 tokamak experiments, the equilibrium during each discharge is routinely calculated and reconstructed, which provides information on the shape and position of the plasma
controlled by currents in external coils.
The magnetic field in a solar active region over a sunspot can store energy that is released suddenly as a burst of motion, X-rays, and radiation when the main current sheet
collapses, reconnecting the field.
Researchers have developed global models using MHD to simulate phenomena within Earth’s magnetosphere, such as the location of Earth’s magnetopause (the boundary between
the Earth’s magnetic field and the solar wind), the formation of the ring current, auroral electrojets, and geomagnetically induced currents.
 Alfvén initially referred to these waves as “electromagnetic–hydrodynamic waves”; however, in a later paper he noted, “As the term ‘electromagnetic–hydrodynamic waves’
is somewhat complicated, it may be convenient to call this phenomenon ‘magneto–hydrodynamic’ waves.
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.
Two-fluid Two-fluid MHD describes plasmas that include a non-negligible Hall electric field.
As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation.
 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.
 Consequently, processes in ideal MHD that convert magnetic energy into kinetic energy, referred to as ideal processes, cannot generate heat and raise entropy.
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.
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
There are three MHD wave modes that can be derived from the linearized ideal-MHD equations for a fluid with a uniform and constant magnetic field: • Alfvén waves • Slow magnetosonic
waves • Fast magnetosonic waves Phase velocity plotted with respect to θ These modes have phase velocities that are independent of the magnitude of the wavevector, so they experience no dispersion.
When this happens, magnetic reconnection may occur in the plasma to release stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration,
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.
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.
After running the simulations for thousands of years in virtual time, the changes in Earth’s magnetic field can be studied.
Breakdown of ideal MHD (in the form of magnetic reconnection) is known to be the likely cause of solar flares.
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
History The MHD description of electrically conducting fluids was first developed by Hannes Alfvén in a 1942 paper published in Nature titled “Existence of Electromagnetic–Hydrodynamic
Waves” which outlined his discovery of what are now referred to as Alfvén waves.
Additionally the dispersion equation gives where is the ideal gas speed of sound.
However, magnetohydrodynamic effects transfer the Sun’s angular momentum into the outer solar system, slowing its rotation.
It is primarily concerned with the low-frequency, large-scale, magnetic behavior in plasmas and liquid metals and has applications in numerous fields including geophysics,
astrophysics, and engineering.
Structures in MHD systems In many MHD systems most of the electric current is compressed into thin nearly-two-dimensional ribbons termed current sheets.
Therefore, any two points that move with the bulk fluid velocity and lie on the same magnetic field line will continue to lie on the same field line even as the points are
advected by fluid flows in the system.
Magnetohydrodynamic equations and finite element analysis are used to study the interaction between the magnetic fluid particles in the bloodstream and the external magnetic
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.
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