Physics:Lundquist number

In plasma physics, the Lundquist number (denoted by [math]\displaystyle{ S }[/math]) 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

[math]\displaystyle{ S = \frac{Lv_A}{\eta} , }[/math]

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

See also

• Magnetic Prandtl number
• Péclet number
• Stuart number

References

• Priest, Eric; Forbes, Terry (2000), Magnetic Reconnection, Cambridge University Press, ISBN 978-0-521-48179-3, http://assets.cambridge.org/0521481791/sample/0521481791WSN01.pdf