Themagnetic diffusivity controls the rate ofmagnetic field diffusion.Since its role in theevolution equation for the magnetic field is analogous to that of theviscosity for the velocity field, some authors^[1] refer to it as the 'magnetic viscosity'.The magnetic diffusivity appears in the definition of themagnetic Reynolds number.A finite value of the magnetic Reynolds number (i.e. a nonzero magnetic diffusivity) is associated with violation ofAlfvén's theorem.

The magnetic diffusivity has SI units of m²/s and is defined as:^[2]$${\displaystyle \eta =\frac{1}{{\mu }_0{\sigma }_0},}$$while inGaussian units it can be defined as$${\displaystyle \eta =\frac{c^2}{4\pi {\sigma }_0}.}$$In the above,${\displaystyle {\mu }_0}$ is thepermeability of free space,${\displaystyle c}$ is the speed of light, and${\displaystyle {\sigma }_0}$ is theelectrical conductivity of the material in question. In case of a plasma, this is the conductivity due toCoulomb or neutral collisions:${\displaystyle {\sigma }_0=\frac{n_e{e}^2}{m_e{\nu }_c}}$, where

• ${\displaystyle n_e}$ is theelectrondensity.
• ${\displaystyle e}$ is theelectron charge.
• ${\displaystyle m_e}$ is the electronmass.
• ${\displaystyle {\nu }_c}$ is the collision frequency.

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