title: Lundquist number
text: # 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.
  
  