The resistive timescale is the typical time for the diffusion of a magnetic field into a resistive plasma. Based on Faraday's Law,
where η is the resistivity (assumed homogeneous), and Ampère's Law,
one immediately derives a diffusion type equation for the magnetic field:
From this, one can deduce the typical timescale
Here, L is the typical length scale of the problem, often taken equal to a, the minor radius of the toroidal plasma.