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The resistive timescale is the typical time for the diffusion of a magnetic field into a resistive plasma.
Based on Faraday's Law,
:<math>\frac{d\vec B}{dt} = \vec \nabla \times \vec E,</math>
Ohm's Law,
:<math>\vec E = \eta \vec j,</math>
where ''&eta;'' is the resistivity (assumed homogeneous), and Ampère's Law,
:<math> \vec \nabla \times \vec B = \mu_0 \vec j,</math>
one immediately derives a diffusion type equation for the magnetic field:
:<math>\frac{d\vec B}{dt} = \frac{\eta}{\mu_0} \vec \nabla \times \vec \nabla \times \vec B = - \frac{\eta}{\mu_0} \nabla^2 \vec B,</math>
since 
: <math>\vec \nabla \cdot \vec B = 0.</math>
From this, one can deduce the typical timescale
:<math> \tau_R \simeq \frac{\mu_0 L^2}{\eta}.</math>
Here, ''L'' is the typical length scale of the problem, often taken equal to ''a'', the [[Toroidal coordinates|minor radius]] of the toroidal plasma.

== See also ==

* [[:Wikipedia:Lundquist number|Lundquist number]]