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Lundquist number

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Title: Lundquist number  
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Subject: Magnetohydrodynamics, Dimensionless quantity, Magnetic reconnection, Spheromak, Magnetic Reynolds number, Lundquist
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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 = \frac{\mu_0LV_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.

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