The magnetic diffusivity controls the rate of magnetic field diffusion. Since its role in the evolution equation for the magnetic field is analogous to that of the

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

for the velocity field, some authors refer to it as the 'magnetic viscosity'. The magnetic diffusivity appears in the definition of the magnetic Reynolds number. A finite value of the magnetic Reynolds number (i.e. a nonzero magnetic diffusivity) is associated with violation of

Alfvén's theorem In ideal magnetohydrodynamics, Alfvén's theorem, or the frozen-in flux theorem, states that electrically conducting fluids and embedded magnetic fields are constrained to move together in the limit of large magnetic Reynolds numbers. It is name ...

. The magnetic diffusivity has SI units of m²/s and is defined as:W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997.

\eta = \frac,

while in

Gaussian units Gaussian units constitute a metric system of units of measurement. This system is the most common of the several electromagnetic unit systems based on the centimetre–gram–second system of units (CGS). It is also called the Gaussian unit syst ...

it can be defined as

\eta = \frac.

In the above,

\mu_0

is the

permeability of free space The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionall ...

c

is the speed of light, and

\sigma_0

is the

electrical conductivity Electrical resistivity (also called volume resistivity or specific electrical resistance) is a fundamental specific property of a material that measures its electrical resistance or how strongly it resists electric current. A low resistivity in ...

of the material in question. In case of a plasma, this is the conductivity due to

Coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). It is defined to be equal to the electric charge delivered by a 1 ampere current in 1 second, with the elementary charge ''e'' as a defining c ...

or neutral collisions:

\sigma_0 = \frac

, where *

n_e

is the

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

. *

e

is the

electron charge C, or c, is the third letter of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''cee'' (pronounced ), plural ''cees''. History "C ...

. *

m_e

is the electron

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

. *

\nu_c

is the collision frequency.

References

Plasma parameters {{plasma-stub

See also

References