# Mag_Reynolds¶

plasmapy.formulary.dimensionless.Mag_Reynolds(U: Unit("m / s"), L: Unit("m"), sigma: Unit("S / m")) -> Unit(dimensionless)

The Magnetic Reynolds number is a dimensionless quantity that estimates the relative contributions of advection and induction to magnetic diffusion in a conducting medium.

$Rm = \frac{U L}{\eta}$

where $$\eta = \frac{1}{\mu_0 \sigma}$$ and $$\mu_0$$ is the permeability of free space.

Parameters: U (Quantity) – The velocity scale of the plasma. L (Quantity) – The length scale of the plasma. sigma (Quantity) – The conductivity of the plasma. ~astropy.units.UnitsWarning – If units are not provided, SI units are assumed. TypeError – The U is not a Quantity and cannot be converted into a ~astropy.units.Quantity. UnitConversionError – If the U is not in appropriate units.

Examples

>>> import astropy.units as u
>>> sigma = 5.96e7 * u.S / u.m
>>> U = 10 * u.m / u.s
>>> L = 1 * u.cm
>>> Mag_Reynolds(U, L, sigma)
<Quantity 7.48955689>
>>> rho = 1e-8 * u.S / u.m
>>> U = 0.1 * u.m / u.s
>>> L = 0.05 * u.m
>>> Mag_Reynolds(U, L, sigma)
<Quantity 0.37447784>

Returns: Rm – Dimensionless quantity. Quantity