Lundquist number

In plasma physics, the Lundquist number (denoted by $$S$$) 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


 * $$S = \frac{Lv_A}{\eta} ,$$

where $$L$$ is the typical length scale of the system, $$\eta$$ is the magnetic diffusivity and $$v_A$$ 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 $$10^2-10^8$$, while in astrophysical situations the Lundquist number can be greater than $$10^{20}$$. Considerations of Lundquist number are especially important in magnetic reconnection.