Magnetic diffusivity

Magnetic diffusivity, or magnetic viscosity, is a measure of the rate of magnetic flux transfer in an electrically conducting medium. It controls the rate of magnetic field diffusion and dissipation, and appears in the magnetohydrodynamic induction equation and in the definition of the magnetic Reynolds number.

It has SI units of m²/s and is defined as:

$\eta ={\frac {1}{\mu _{0}\sigma _{0}}}$,

while in Gaussian units it can be defined as

$\eta ={\frac {c^{2}}{4\pi \sigma _{0}}}$.

In the above, $\mu _{0}$ is the permeability of free space, $c$ is the speed of light, and $\sigma _{0}$ is the electrical conductivity of the material in question. In case of a plasma, this is the conductivity due to Coulomb or neutral collisions: $\sigma _{0}={\frac {n_{e}e^{2}}{m_{e}\nu _{c}}}$, where

• $n_{e}$ is the electron density.
• $e$ is the electron charge.
• $m_{e}$ is the electron mass.
• $\nu _{c}$ is the collision frequency.

See also

• Electrical resistivity and conductivity