Lundquist Number

What is this formula?

The Lundquist number formula measures the ratio between the Alfvén wave propagation timescale and the magnetic diffusion timescale in a conducting plasma.

It is a key dimensionless parameter in magnetohydrodynamics and plasma stability analysis.

Large Lundquist numbers indicate that magnetic field lines are approximately frozen into the plasma motion.

When to use it

Use this formula when studying plasma confinement, magnetic reconnection, fusion plasmas, solar flares, astrophysical plasmas, and magnetohydrodynamic instabilities.

Example

A plasma has:

μ0 = 4π×10^-7 H/m

L = 2 m

vA = 4×10^5 m/s

η = 2×10^-5 Ω·m

Formula:

S = (μ0*L*vA)/η

Substitution:

S = ((4π×10^-7)*2*(4×10^5))/(2×10^-5)

Result:

S ≈ 5.03×10^4

Applications

- Magnetic reconnection analysis

- Fusion plasma confinement

- Solar flare studies

- Tokamak stability analysis

- Magnetohydrodynamic simulations

- Plasma turbulence research

- Astrophysical plasma modeling