Lundquist number

In plasma physics, the Lundquist number (denoted by $S$) is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale. In SI units, it is given by

$S\equiv {\frac {\mu _{0}LV_{A}}{\eta }}$,

where $L$ is a typical length scale, $\mu _{0}$ is the permeability of free space, $V_{A}={\frac {B}{\sqrt {\mu _{0}n_{0}m_{i}}}}$ is the Alfvén speed for a plasma with magnetic field $B$, density $n_{0}$, ion mass $m_{i}$ and $\eta$ is the plasma resistivity. 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.

See also

• Magnetic Reynolds number

References

• Priest, Eric; Forbes, Terry (2000), Magnetic Reconnection (PDF), Cambridge University Press, ISBN 0521481791