Lundquist number

In plasma physics, the Lundquist number (denoted by formula_1) 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
where formula_3 is the typical length scale of the system, formula_4 is the magnetic diffusivity and formula_5 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 formula_6, while in astrophysical situations the Lundquist number can be greater than formula_7. Considerations of Lundquist number are especially important in magnetic reconnection.