MHD Alfvén Wave Propagation

Transverse waves in magnetized plasma along field lines

Parameters

Alfvén speed vₐ = 2.00
Frequency ω = 4.00

Alfvén Waves

Alfvén waves are transverse electromagnetic waves that propagate along magnetic field lines in a conducting plasma. Discovered by Hannes Alfvén (Nobel Prize 1970), they are fundamental to space and astrophysical plasmas.

v_A = B₀ / √(μ₀ρ)    ω = k · v_A

The restoring force is magnetic tension (not pressure), analogous to a vibrating string where tension/linear-density sets the wave speed. The dispersion relation is linear — Alfvén waves are non-dispersive.

Visualization: Background field B₀ points along x (gold arrows). The perturbation b_y (blue) and velocity perturbation v_y (orange) are shown. They are in phase for forward-propagating waves.

Two counter-propagating Alfvén waves are shown: one driven at the left boundary, one at the right. The superposition creates a standing pattern when their wavelengths match the domain.

b_y = A · sin(kx − ωt)    v_y = ±(A/√(μ₀ρ)) · sin(kx ∓ ωt)