Editing Magnetohydrodynamics (section)

=== Importance of resistivity ===

In an imperfectly conducting fluid the magnetic field can generally move through the fluid following a [[Diffusion equation|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<ref>{{cite journal | url=https://iopscience.iop.org/article/10.1088/0029-5515/18/1/010 | doi=10.1088/0029-5515/18/1/010 | title=Hydromagnetic stability of tokamaks | year=1978 | last1=Wesson | first1=J.A. | journal=Nuclear Fusion | volume=18 | pages=87–132 | s2cid=122227433 }}</ref>—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 [[Instability|instabilities]] exist that can increase the effective resistivity of the plasma by factors of more than 10<sup>9</sup>. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic [[Magnetohydrodynamic turbulence|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 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]].