Transverse plasma oscillations propagating along magnetic field lines at v_A = B/√(μ₀ρ)
Alfvén waves (Hannes Alfvén, Nobel Prize 1970) are transverse MHD waves where the magnetic field acts as a restoring force, analogous to tension in a string. The plasma velocity and magnetic field perturbation oscillate perpendicular to both the field direction and the wave propagation direction.
v_A = B / √(μ₀ρ) — Alfvén speed
ω = k · v_A — linear dispersion (non-dispersive!)
Three MHD wave modes for propagation at angle θ to B₀:
Alfvén: ω² = k²v_A²cos²θ
Fast: ω² = k²(v_A² + c_s²)/2 + √(...) [+ branch]
Slow: ω² = v_A²c_s²k²cos²θ / (v_A² + c_s²) [approx]
Plasma β parameter: β = 2μ₀p/B² = thermal pressure / magnetic pressure.
β ≪ 1: magnetically dominated (corona, magnetosphere).
β ≫ 1: thermally dominated (stellar interiors, tokamak core).
Alfvén waves are crucial in solar corona heating, magnetospheric dynamics, and fusion plasma control.