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,

Bt=×E,

Ohm's Law,

E=ηj,

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

×B=μ0j,

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

Bt=ημ0××B=ημ02B,

since

B=0.

From this, one can deduce the typical timescale

τRμ0L2η.

Here, L is the typical length scale of the problem, often taken equal to a, the minor radius of the toroidal plasma.

See also