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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

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

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where $L$ is a typical length scale, $μ 0$ 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 $50 - 10 8$ , while in astrophysical situations the Lundquist number can be greather than $1020$ . Considerations of Lundquist number are especially important in magnetic reconnection.