Editing Magnetohydrodynamics (section)

== Extensions ==
; Resistive
: Resistive MHD describes magnetized fluids with finite electron diffusivity ({{math|''η'' ≠ 0}}).  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 and discontinuities (magnetohydrodynamics)|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]].  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.<ref>M. J. Lighthill, "Studies on MHD waves and other anisotropic wave motion," ''Phil. Trans. Roy. Soc.'', London, vol. 252A, pp. 397–430, 1960.</ref> It concerned the neglect of the "[[Hall current]] term" in Ohm's law, a frequent simplification made in magnetic fusion theory.  Hall-magnetohydrodynamics (HMHD) takes into account this electric field description of magnetohydrodynamics, and Ohm's law takes the form
::<math>\mathbf{E} + \mathbf{v}\times\mathbf{B}-\underbrace{\frac{1}{n_e e}(\mathbf{J}\times\mathbf{B})}_{\text{Hall current term}} = \eta\mathbf{J},</math>
:where <math>n_e</math> is the electron number density and <math>e</math> is the [[elementary charge]]. 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.<ref>{{cite journal | last1 = Witalis | first1 = E.A. | year = 1986 | title = Hall Magnetohydrodynamics and Its Applications to Laboratory and Cosmic Plasma | journal = IEEE Transactions on Plasma Science | volume = PS-14 | issue = 6| pages = 842–848 | bibcode=1986ITPS...14..842W|doi = 10.1109/TPS.1986.4316632 | s2cid = 31433317 }}</ref>
; 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]], [[magnetic reconnection]], [[ion thrusters]], [[neutron stars]], and plasma switches.  
; Collisionless
: MHD is also often used for collisionless plasmas. In that case the MHD equations are derived from the [[Vlasov equation]].<ref name="space">W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997</ref>
; Reduced
: By using a [[Multiple-scale analysis|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.<ref name=paper:hegna>{{cite web|last1=Kruger|first1=S.E.|last2=Hegna|first2=C.C.|last3=Callen|first3=J.D.|title=Reduced MHD equations for low aspect ratio plasmas|url=http://epsppd.epfl.ch/Praha/98icpp/g096pr.pdf|archive-url=https://web.archive.org/web/20150925113607/http://epsppd.epfl.ch/Praha/98icpp/g096pr.pdf|url-status=dead|archive-date=25 September 2015|publisher=University of Wisconsin|access-date=27 April 2015}}</ref>