Magnetic Reynolds Number

What is this formula?

The magnetic Reynolds number formula measures the relative importance of magnetic field advection compared with magnetic diffusion in a conducting plasma.

A large magnetic Reynolds number means the magnetic field is approximately frozen into the plasma flow. A small value means magnetic diffusion is dominant.

When to use it

Use this formula in magnetohydrodynamics when analyzing whether plasma motion carries magnetic field lines with it or whether resistive diffusion significantly changes the magnetic field structure.

Example

A plasma has:

μ0 = 4π×10^-7 H/m

σ = 2×10^5 S/m

v = 3×10^4 m/s

L = 0.5 m

Formula:

Rm = μ0*σ*v*L

Substitution:

Rm = (4π×10^-7)(2×10^5)(3×10^4)(0.5)

Result:

Rm ≈ 3.77×10^3

Applications

- Magnetohydrodynamic flow analysis

- Fusion plasma modeling

- Solar and astrophysical plasmas

- Magnetic field diffusion studies

- Plasma confinement systems

- Dynamo theory