# Lundquist number

In plasma physics, the Lundquist number (denoted by $S$) is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale. In SI units, it is given by
$S = \frac{\mu_0LV_A}{\eta} ,$
where $L$ is a typical length scale, $\mu_0$ is the permeability of free space, $V_A=\frac{B}{\sqrt{\mu_0 n_0 m_i}}$ is the Alfvén speed for a plasma with magnetic field $B$, density $n_0$, ion mass $m_i$ and $\eta$ 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 $10^2-10^8$, while in astrophysical situations the Lundquist number can be greater than $10^{20}$. Considerations of Lundquist number are especially important in magnetic reconnection.