Editing Magnetohydrodynamics (section)

== 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.<ref>{{cite web | url=https://www.livescience.com/39780-magnetic-field-pushes-earth-core.html | title=Why Earth's Inner and Outer Cores Rotate in Opposite Directions | website=[[Live Science]] | date=19 September 2013 }}</ref><ref>{{cite web | url=https://www.pnas.org/post/journal-club/earths-contrasting-inner-core-rotation-and-magnetic-field-rotation-linked | title=Earth's contrasting inner core rotation and magnetic field rotation linked | date=7 October 2013 }}</ref> 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]].<ref>{{cite web | url=http://ffden-2.phys.uaf.edu/webproj/647_fall_2019/Stefan_Awender/GFDwebsite/fluid_dynamics_core.html | title=Geodynamo }}</ref> 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.<ref name = "pbs">[https://www.pbs.org/wgbh/nova/magnetic/reve-drives.html NOVA | Magnetic Storm | What Drives Earth's Magnetic Field? | PBS<!-- Bot generated title -->]</ref>

[[File:NASA 54559main comparison1 strip.gif|thumb|center|350px|Reversals of [[Earth's magnetic field]]]]

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.<ref name = "glatz">[https://science.nasa.gov/science-news/science-at-nasa/2003/29dec_magneticfield/ Earth's Inconstant Magnetic Field – NASA Science<!-- Bot generated title -->]</ref>

====Earthquakes====
Some monitoring stations have reported that [[earthquakes]] are sometimes preceded by a spike in [[ultra low frequency]] (ULF) activity.  A remarkable example of this occurred before the [[1989 Loma Prieta earthquake]] in [[California]],<ref>{{cite journal |first1=Antony C. |last1=Fraser-Smith |first2=A. |last2=Bernardi |first3=P. R. |last3=McGill |first4=M. E. |last4=Ladd |first5=R. A. |last5=Helliwell |first6=O. G. |last6=Villard Jr. |date=August 1990 |title=Low-Frequency Magnetic Field Measurements Near the Epicenter of the M<sub>s</sub> 7.1 Loma Prieta Earthquake |journal=[[Geophysical Research Letters]] |volume=17 |issue=9 |pages=1465–1468 |issn=0094-8276 |oclc=1795290 |access-date=December 18, 2010 |url=http://ee.stanford.edu/~acfs/LomaPrietaPaper.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://ee.stanford.edu/~acfs/LomaPrietaPaper.pdf |archive-date=2022-10-09 |url-status=live |doi=10.1029/GL017i009p01465 |bibcode=1990GeoRL..17.1465F}}</ref> although a subsequent study indicates that this was little more than a sensor malfunction.<ref>{{Cite journal | last1 = Thomas | first1 = J. N. | last2 = Love | first2 = J. J. | last3 = Johnston | first3 = M. J. S. | title = On the reported magnetic precursor of the 1989 Loma Prieta earthquake | doi = 10.1016/j.pepi.2008.11.014 | journal = Physics of the Earth and Planetary Interiors | volume = 173 | issue = 3–4 | pages = 207–215 |date=April 2009 | bibcode=2009PEPI..173..207T}}</ref> On December 9, 2010, geoscientists announced that the [[Demeter (satellite)|DEMETER]] satellite observed a dramatic increase in ULF radio waves over [[Haiti]] in the month before the magnitude 7.0&nbsp;M<sub>w</sub> [[2010 Haiti earthquake|2010 earthquake]].<ref>{{cite web|url=http://www.technologyreview.com/blog/arxiv/26114/|title=Spacecraft Saw ULF Radio Emissions over Haiti before January Quake|author=KentuckyFC <!-- blogger's legitimate nom de plume -->|date=December 9, 2010|website=Physics arXiv Blog|publisher=[[TechnologyReview.com]]|location=[[Cambridge, Massachusetts]]|access-date=December 18, 2010}}  {{Cite journal|last1=Athanasiou|first1=M|last2=Anagnostopoulos|first2=G|last3=Iliopoulos|first3=A|last4=Pavlos|first4=G|last5=David|first5=K|year=2010|title=Enhanced ULF radiation observed by DEMETER two months around the strong 2010 Haiti earthquake|journal=Natural Hazards and Earth System Sciences|volume=11|issue=4|pages=1091|arxiv=1012.1533|doi=10.5194/nhess-11-1091-2011|bibcode=2011NHESS..11.1091A|s2cid=53456663|doi-access=free}}</ref> 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.

=== Space Physics ===
The study of space plasmas near [[Earth]] and throughout the [[Solar System]] is known as [[space physics]]. Areas researched within space physics encompass a large number of topics, ranging from the [[ionosphere]] to [[Aurora|auroras]], Earth's [[magnetosphere]], the [[Solar wind]], and [[Coronal mass ejection|coronal mass ejections]]. 

MHD forms the framework for understanding how populations of plasma interact within the local geospace environment. Researchers have developed global models using MHD to simulate phenomena within Earth's magnetosphere, such as the location of Earth's [[magnetopause]]<ref>{{Cite journal |last1=Mukhopadhyay |first1=Agnit |last2=Jia |first2=Xianzhe |last3=Welling |first3=Daniel T. |last4=Liemohn |first4=Michael W. |date=2021 |title=Global Magnetohydrodynamic Simulations: Performance Quantification of Magnetopause Distances and Convection Potential Predictions |journal=Frontiers in Astronomy and Space Sciences |volume=8 |page=45 |doi=10.3389/fspas.2021.637197 |bibcode=2021FrASS...8...45M |issn=2296-987X |doi-access=free }}</ref> (the boundary between the Earth's magnetic field and the solar wind), the formation of the [[ring current]], [[Electrojet|auroral electrojets]],<ref>{{Cite journal |last1=Wiltberger |first1=M. |last2=Lyon |first2=J. G. |last3=Goodrich |first3=C. C. |date=2003-07-01 |title=Results from the Lyon–Fedder–Mobarry global magnetospheric model for the electrojet challenge |url=https://www.sciencedirect.com/science/article/pii/S1364682603001718 |journal=Journal of Atmospheric and Solar-Terrestrial Physics |language=en |volume=65 |issue=11 |pages=1213–1222 |doi=10.1016/j.jastp.2003.08.003 |bibcode=2003JASTP..65.1213W |issn=1364-6826}}</ref> and [[Geomagnetically induced current|geomagnetically induced currents]].<ref>{{Citation |last=Welling |first=Daniel |title=Geomagnetically Induced Currents from the Sun to the Power Grid |chapter=Magnetohydrodynamic Models of B and Their Use in GIC Estimates |date=2019-09-25 |chapter-url=https://onlinelibrary.wiley.com/doi/10.1002/9781119434412.ch3 |series=Geophysical Monograph Series |pages=43–65 |editor-last=Gannon |editor-first=Jennifer L. |access-date=2023-03-10 |edition=1 |publisher=Wiley |language=en |doi=10.1002/9781119434412.ch3 |isbn=978-1-119-43434-4 |s2cid=204194812 |editor2-last=Swidinsky |editor2-first=Andrei |editor3-last=Xu |editor3-first=Zhonghua}}</ref> 

One prominent use of global MHD models is in [[space weather]] forecasting. [[List of solar storms|Intense solar storms]] have the potential to cause extensive damage to satellites<ref>{{Cite web |title=What is Space Weather ? - Space Weather |url=https://swe.ssa.esa.int/what-is-space-weather |access-date=2023-03-10 |website=swe.ssa.esa.int}}</ref> and infrastructure, thus it is crucial that such events are detected early. The [[Space Weather Prediction Center]] (SWPC) runs MHD models to predict the arrival and impacts of space weather events at Earth.

=== Astrophysics ===
MHD applies to [[astrophysics]], including stars, the [[interplanetary medium]] (space between the planets), and possibly within the [[interstellar medium]] (space between the stars) and [[Relativistic jet|jets]].<ref>{{cite book|last1=Kennel|first1=C.F. |last2=Arons|first2=J.|last3=Blandford|first3=R.|last4=Coroniti|first4=F.|last5=Israel |first5=M.|last6=Lanzerotti|first6=L.|last7=Lightman|first7=A.|title=Unstable Current Systems and Plasma Instabilities in Astrophysics |chapter=Perspectives on Space and Astrophysical Plasma Physics |chapter-url=https://authors.library.caltech.edu/96134/2/1985IAUS__107__537K.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://authors.library.caltech.edu/96134/2/1985IAUS__107__537K.pdf |archive-date=2022-10-09 |url-status=live|date=1985|volume=107 |doi=10.1007/978-94-009-6520-1_63|pages=537–552 |access-date=2019-07-22|isbn=978-90-277-1887-7 |bibcode=1985IAUS..107..537K |s2cid=117512943 }}</ref>  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]]).<ref>{{cite journal | url=https://link.springer.com/article/10.1007/s41114-021-00031-6 | doi=10.1007/s41114-021-00031-6 | title=Relativistic fluid dynamics: Physics for many different scales | year=2021 | last1=Andersson | first1=Nils | last2=Comer | first2=Gregory L. | journal=Living Reviews in Relativity | volume=24 | issue=1 | page=3 | arxiv=2008.12069 | bibcode=2021LRR....24....3A | s2cid=235631174 }}</ref><ref>{{cite web |url=https://www.astro.princeton.edu/~kunz/Site/AST521/AST521_lecture_notes_Kunz.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://www.astro.princeton.edu/~kunz/Site/AST521/AST521_lecture_notes_Kunz.pdf |archive-date=2022-10-09 |url-status=live |title=Lecture Notes on Introduction to Plasma Astrophysics (Draft) |first=Matthew W. |last=Kunz |date=9 November 2020 |website=astro.princeton.edu}}</ref>

[[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 [[Conservation law|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 [[Protostar|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]]s. The magnetic field in a solar [[active region]] over a sunspot can store energy that is released suddenly as a burst of motion, [[X-ray]]s, and [[radiation]] when the main current sheet collapses, reconnecting the field.<ref>{{cite web | url=https://link.springer.com/collections/djhjfaffha | title=Solar Activity }}</ref><ref>{{cite journal | doi=10.12942/lrsp-2011-6 | title=Solar Flares: Magnetohydrodynamic Processes | year=2011 | last1=Shibata | first1=Kazunari | last2=Magara | first2=Tetsuya | journal=Living Reviews in Solar Physics | volume=8 | issue=1 | page=6 | doi-access=free | bibcode=2011LRSP....8....6S | s2cid=122217405 | hdl=2433/153022 | hdl-access=free }}</ref>

=== Magnetic confinement fusion ===
MHD describes a wide range of physical phenomena occurring in fusion plasmas in devices such as [[tokamak]]s or [[stellarator]]s.

The [[Grad–Shafranov equation|Grad-Shafranov equation]] derived from ideal MHD describes the equilibrium of axisymmetric toroidal plasma in a tokamak. 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.

[[Plasma stability|MHD stability]] theory is known to govern the operational limits of tokamaks. For example, the ideal MHD kink modes provide hard limits on the achievable plasma beta ([[Troyon limit]]) and plasma current (set by the <math>q > 2</math> requirement of the [[Safety factor (plasma physics)|safety factor]]).

In a tokamak, instabilities also emerge from resistive MHD. For instance, [[Tearing mode|tearing modes]] are instabilities arising within the framework of non-ideal MHD.<ref>{{Cite book |last=Zohm |first=Hartmut |title=Magnetohydrodynamic Stability of Tokamaks |publisher=Wiley-VCH |year=2015 |isbn=978-3-527-41232-7}}</ref> This is an active field of research, since these instabilities are the starting point for disruptions.<ref>{{Cite thesis |last=Bauer |first=Magdalena |title=Analysis of magnetohydrodynamic instabilities in the ASDEX Upgrade tokamak by frequency dependent modelling of magnetic measurements |date=2025-03-28 |degree=Text.PhDThesis |publisher=Ludwig-Maximilians-Universität München |url=https://edoc.ub.uni-muenchen.de/35104/ |doi=10.5282/edoc.35104 |language=de}}</ref>

===Sensors===
<!-- Deleted image removed: [[Image:Principle of MHD Sensor.jpg|thumb|right|300 px|Principle of MHD sensor for angular velocity measurement]] -->
Magnetohydrodynamic sensors are used for precision measurements of [[Angular velocity|angular velocities]] in [[inertial navigation system]]s such as in [[aerospace engineering]]. Accuracy improves with the size of the sensor. The sensor is capable of surviving in harsh environments.<ref>{{cite web |url=http://read.pudn.com/downloads165/ebook/756655/Strapdown%20Inertial%20Navigation%20Technology/13587_04b.pdf |title=Archived copy |access-date=2014-08-19 |url-status=dead |archive-url=https://web.archive.org/web/20140820045250/http://read.pudn.com/downloads165/ebook/756655/Strapdown%20Inertial%20Navigation%20Technology/13587_04b.pdf |archive-date=2014-08-20 }} D.Titterton, J.Weston, Strapdown Inertial Navigation Technology, chapter 4.3.2</ref>

=== Engineering ===

MHD is related to engineering problems such as [[fusion power|plasma confinement]], liquid-metal cooling of [[nuclear reactor]]s, and [[Electromagnetism|electromagnetic]] casting (among others).

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 (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]].  Way, on leave from his job at [[Westinghouse Electric (1886)|Westinghouse Electric]], assigned his senior-year undergraduate students to develop a submarine with this new propulsion system.<ref>{{cite magazine |title=Run Silent, Run Electromagnetic |date=1966-09-23 |magazine=[[Time (magazine)|Time]] |url=http://www.time.com/time/magazine/article/0,9171,842848-1,00.html|archive-url=https://web.archive.org/web/20090114084102/http://www.time.com/time/magazine/article/0,9171,842848-1,00.html|url-status=dead|archive-date=January 14, 2009}}</ref>  In the early 1990s, a foundation in Japan (Ship & Ocean Foundation (Minato-ku, Tokyo)) built an experimental boat, the ''[[Yamato 1|Yamato-1]]'', which used a magnetohydrodynamic drive incorporating a [[superconductor]] cooled by [[helium|liquid helium]], and could travel at 15&nbsp;km/h.<ref name = "yamato">Setsuo Takezawa et al. (March 1995) ''Operation of the Thruster for Superconducting Electromagnetohydrodynamic Propu1sion Ship YAMATO 1''</ref>

[[MHD generator|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.<ref>''[http://navier.stanford.edu/PIG/PIGdefault.html Partially Ionized Gases] {{webarchive|url=https://web.archive.org/web/20080905113821/http://navier.stanford.edu/PIG/PIGdefault.html |date=2008-09-05 }}'', M. Mitchner and Charles H. Kruger, Jr., Mechanical Engineering Department, [[Stanford University]]. See Ch. 9 "Magnetohydrodynamic (MHD) Power Generation", pp. 214–230.</ref> One major engineering problem was the failure of the wall of the primary-coal combustion chamber due to abrasion.

In [[microfluidics]], MHD is studied as a fluid pump for producing a continuous, nonpulsating flow in a complex microchannel design.<ref name=Nguyen>{{cite book | author=Nguyen, N.T. |author2=Wereley, S. | title=Fundamentals and Applications of Microfluidics | date=2006 | publisher =[[Artech House]] }}</ref>

MHD can be implemented in the [[continuous casting]] process of metals to suppress instabilities and control the flow.<ref>{{cite conference |last=Fujisaki |first=Keisuke |title=Conference Record of the 2000 IEEE Industry Applications Conference. Thirty-Fifth IAS Annual Meeting and World Conference on Industrial Applications of Electrical Energy (Cat. No.00CH37129) |date=Oct 2000 |chapter=In-mold electromagnetic stirring in continuous casting |doi=10.1109/IAS.2000.883188 |conference=Industry Applications Conference |publisher=IEEE |volume=4 |pages= 2591–2598 |isbn=0-7803-6401-5 }}</ref><ref>{{cite journal |last1=Kenjeres |first1=S. |last2=Hanjalic |first2=K. |date=2000 |title=On the implementation of effects of Lorentz force in turbulence closure models |journal=International Journal of Heat and Fluid Flow |volume=21 |issue=3 |pages=329–337 |doi=10.1016/S0142-727X(00)00017-5 |bibcode=2000IJHFF..21..329K }}</ref>

Industrial MHD problems can be modeled using the open-source software EOF-Library.<ref>{{Cite journal|last1=Vencels|first1=Juris|last2=Råback|first2=Peter|last3=Geža|first3=Vadims|date=2019-01-01|title=EOF-Library: Open-source Elmer FEM and OpenFOAM coupler for electromagnetics and fluid dynamics|journal=SoftwareX|volume=9|pages=68–72|doi=10.1016/j.softx.2019.01.007|issn=2352-7110|bibcode=2019SoftX...9...68V|doi-access=free}}</ref> Two simulation examples are 3D MHD with a free surface for [[Magnetic levitation|electromagnetic levitation]] melting,<ref>{{Cite journal|last1=Vencels|first1=Juris|last2=Jakovics|first2=Andris|last3=Geza|first3=Vadims|date=2017|title=Simulation of 3D MHD with free surface using Open-Source EOF-Library: levitating liquid metal in an alternating electromagnetic field|journal=Magnetohydrodynamics|volume=53|issue=4|pages=643–652|doi=10.22364/mhd.53.4.5|issn=0024-998X}}</ref> and liquid metal stirring by rotating permanent magnets.<ref>{{Cite journal|last1=Dzelme|first1=V.|last2=Jakovics|first2=A.|last3=Vencels|first3=J.|last4=Köppen|first4=D.|last5=Baake|first5=E.|date=2018|title=Numerical and experimental study of liquid metal stirring by rotating permanent magnets|url=http://stacks.iop.org/1757-899X/424/i=1/a=012047|journal=IOP Conference Series: Materials Science and Engineering|language=en|volume=424|issue=1|pages=012047|doi=10.1088/1757-899X/424/1/012047|issn=1757-899X|bibcode=2018MS&E..424a2047D|doi-access=free}}</ref>

===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.<ref>{{Cite journal|last1=Nacev|first1=A.|last2=Beni|first2=C.|last3=Bruno|first3=O.|last4=Shapiro|first4=B.|date=2011-03-01|title=The Behaviors of Ferro-Magnetic Nano-Particles In and Around Blood Vessels under Applied Magnetic Fields|journal=Journal of Magnetism and Magnetic Materials|volume=323|issue=6|pages=651–668|doi=10.1016/j.jmmm.2010.09.008|issn=0304-8853|pmc=3029028|pmid=21278859|bibcode=2011JMMM..323..651N}}</ref>