magnetic diffusivity

{{Short description|A parameter in plasma physics}}

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 for the velocity field, some authors{{cite book |last1=Somov |first1=Boris V. |title=Plasma Astrophysics, Part I |date=2012 |publisher=Springer |location=New York, NY |isbn=978-1-4614-4283-7 |edition=2nd}} 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.

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.

$$\backslash eta\; =\; \backslash frac\{1\}\{\backslash mu\_0\; \backslash sigma\_0\},$$

while in Gaussian units it can be defined as

$$\backslash eta\; =\; \backslash frac\{c^2\}\{4\backslash pi\backslash sigma\_0\}.$$

In the above, $\backslash mu\_0$ is the permeability of free space, $c$ is the speed of light, and $\backslash sigma\_0$ is the electrical conductivity of the material in question. In case of a plasma, this is the conductivity due to Coulomb or neutral collisions: $\backslash sigma\_0\; =\; \backslash frac\{n\_e\; e^2\}\{m\_e\backslash nu\_c\}$, where

• $n\_e$ is the electron density.
• $e$ is the electron charge.
• $m\_e$ is the electron mass.
• $\backslash nu\_c$ is the collision frequency.