# Lundquist number

## Description

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.

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.

Related formulas## Variables

S | Lundquist number (dimensionless) (dimensionless) |

L | typical length scale of the system (m) |

v_{A} | Alfvén velocity of the plasma (m/s) |

η | magnetic diffusivity (m^{2}/s) |