Alfvén Waves — MHD Dispersion

Magnetohydrodynamic wave modes: shear Alfvén, fast/slow magnetosonic

Alfvén speed vA2.0

Sound speed cs1.5

Wave angle θ45°

Mode

ω²(Alfvén) = k²vA²cos²θ | ω²(fast/slow) = k²/2·[(vA²+cs²) ± √((vA²+cs²)² − 4vA²cs²cos²θ)]

vA = 2.0 | cs = 1.5 | β = 0.56 | vphase = 0.00

In ideal MHD, a magnetized plasma supports three wave modes. The shear Alfvén wave (transverse) propagates along field lines at vA = B/√(μ₀ρ). Fast/slow magnetosonic waves are compressive, with phase speeds that vary with angle θ between k and B₀. Left: Friedrichs diagram (phase speed polar plot). Right: wave animation.