# Lundquist number

In plasma physics, the Lundquist number (denoted by ${\displaystyle S}$) is a dimensionless ratio which compares the timescale of an Alfvén wave crossing to the timescale of resistive diffusion. It is a special case of the Magnetic Reynolds number when the Alfvén velocity is the typical velocity scale of the system, and is given by
${\displaystyle S={\frac {Lv_{A}}{\eta }},}$
where ${\displaystyle L}$ is the typical length scale of the system, ${\displaystyle \eta }$ is the magnetic diffusivity and ${\displaystyle v_{A}}$ is the Alfvén velocity of the plasma.
High Lundquist numbers indicate highly conducting plasmas, while low Lundquist numbers indicate more resistive plasmas. Laboratory plasma experiments typically have Lundquist numbers between ${\displaystyle 10^{2}-10^{8}}$, while in astrophysical situations the Lundquist number can be greater than ${\displaystyle 10^{20}}$. Considerations of Lundquist number are especially important in magnetic reconnection.