# Resistive timescale

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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,

Ohm's Law,

where η is the resistivity (assumed homogeneous), and Ampère's Law,

one immediately derives a diffusion type equation for the magnetic field:

since

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.