Alfvén Wave Propagation — Frozen-In Magnetized Plasma

Magnetized Plasma

Magnetic field B 1.5 T

Plasma density n 5.0 ×10¹⁹ m⁻³

Resistive damping 0.05

Drive frequency f 0.40 Hz

Alfvén speed

Theoretical v_A

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Measured v_A

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Match (measured vs theory)

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Wavelength λ = v_A/f

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Sim time

0.0 s

How it works

A magnetic field threading a highly-conducting plasma is "frozen in": the field lines act like stretched elastic strings, and the ionized gas rides along them like beads glued to the string. Displace the strands sideways and the magnetic tension pulls them back, launching a transverse Alfvén wave that carries the attached plasma with it — exactly the way a plucked guitar string carries a wave, but here the "string tension" comes from the magnetic field itself.

v_A = B / sqrt(μ₀ ρ),  ρ = n · m_ion
∂²y/∂t² = v_A² ∂²y/∂x² − γ ∂y/∂t

Magnetic field B — stronger field means stiffer "string tension"; the pulse races down the flux rope faster.
Plasma density n — denser plasma means more inertia per unit length of field line; the same field pulls a heavier load more slowly.
Resistive damping — models finite conductivity: the wave loses amplitude as it travels instead of staying frozen-in forever.
Pluck & measure — sends one pulse from the left end and times how long its crest takes to cross the rope, then back-computes a measured speed to check against the B/√(μ₀ρ) prediction above.
Continuous drive — oscillates the left end at frequency f so you can read off the resulting wavelength λ = v_A / f directly off the rope.

Real-world relevance: Alfvén waves are how energy and momentum move through the solar wind, a tokamak's confined plasma and planetary magnetospheres — anywhere a magnetic field is strong enough to dominate over gas pressure.

Flux-rope field lines Frozen-in ions Wave crest marker

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Alfvén Wave Propagation in a Magnetized Plasma