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# Lundquist number

In plasma physics, the Lundquist number (denoted by S) is the dimensionless ratio of an Alfvén wave crossing timescale to a diffusion timescale. In SI units, it is given by

$S\equiv\frac{\mu_0LV_A}{\eta}$,

where L is a typical length scale, μ0 is the permeability of free space, $V_A=\frac{B}{\sqrt{\mu_0\rho}}$ is the Alfvén speed, and η is the plasma resistivity. High Lundquist numbers indicate highly conducting plasmas, while low Lundquist numbers indicate more resistive plasmas. Laboratory plasma experiments typically have Lundquist numbers between 50 − 108, while in astrophysical situations the Lundquist number can be greather than 1020. Considerations of Lundquist number are especially important in magnetic reconnection.