Lundquist number
Encyclopedia
In plasma physics, the Lundquist number (denoted by 
) is the dimensionless ratio of an Alfvén wave
crossing timescale to a resistive diffusion timescale. In SI units, it is given by
,
where
is a typical length scale, 
is the permeability of free space, 
is the Alfvén speed
for a plasma with magnetic field
, density
, ion
mass
and 
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
, while in astrophysical situations the Lundquist number can be greater than 
. Considerations of Lundquist number are especially important in magnetic reconnection
.
) is the dimensionless ratio of an Alfvén waveAlfvén wave
An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
crossing timescale to a resistive diffusion timescale. In SI units, it is given by
,where
is a typical length scale, is the permeability of free space, is the Alfvén speedAlfvén wave
An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
for a plasma with magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
, densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, ionIon
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
mass
Mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...
and is the plasma resistivityResistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
. High Lundquist numbers indicate highly conducting plasmas, while low Lundquist numbers indicate more resistive plasmas. Laboratory plasma experiments typically have Lundquist numbers between
, while in astrophysical situations the Lundquist number can be greater than . Considerations of Lundquist number are especially important in magnetic reconnectionMagnetic reconnection
Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration...
.