The Alfvén speed sets how fast magnetic tension communicates transverse disturbances along a field line. Stronger B or lower density gives a higher v_A.

Why use fixed ends on the field line?

Anchoring at both boundaries (e.g. photosphere–photosphere loop, or tied flux tubes) traps wave energy and produces standing modes and reflections, as in a vibrating string.

What is the dispersion relation?

In this linear shear-Alfvén model, ω = k v_A — phase speed independent of wavelength along the field.

Landau damping, resistive diffusion, compressional coupling, field-line curvature, and finite β effects are not included.

Alfvén Wave on a Magnetic Field Line

Transverse MHD Alfvén wave: v_A = B/√(μ₀ρ), animated field-line displacement, standing modes and pulse reflections at fixed boundaries.

About this model

Alfvén waves are low-frequency, transverse magnetohydrodynamic disturbances that propagate along magnetic field lines in a conducting fluid or plasma. In the ideal MHD limit the phase speed is the Alfvén velocity v_A = B/√(μ₀ρ), where B is the field strength and ρ is the mass density. For a proton-electron plasma with mass density ρ ≈ m_p n, v_A increases with magnetic field and decreases with density. A field line of length L with fixed ends supports standing Alfvén modes ξ(z,t) ∝ sin(mπz/L) cos(mπv_A t/L), analogous to a vibrating string tied at both boundaries. A traveling pulse partially reflects at each end, producing the characteristic bouncing of wave energy along the line — important in coronal loops, the solar wind, and planetary magnetospheres. This simulator animates transverse displacement of a field line, shows a ξ(z) snapshot and the linear dispersion ω = k v_A, and plots v_A versus B and versus number density. It is a cold, single-fluid, linear MHD cartoon without dissipation, ion–electron separation, or curvature of the background field.

Who it's for: Undergraduate plasma physics, space physics, or MHD students after Langmuir waves and before magnetospheric storms or reconnection.

Key terms

Alfvén wave
Alfvén velocity
Magnetic field line
MHD
Standing wave
Wave reflection
Plasma density

How it works

Alfvén wave on a magnetic field line: transverse MHD wave at v_A = B/√(μ₀ρ), standing modes and pulse reflections at boundaries.

Frequently asked questions

What is v_A?: The Alfvén speed sets how fast magnetic tension communicates transverse disturbances along a field line. Stronger B or lower density gives a higher v_A.
Why use fixed ends on the field line?: Anchoring at both boundaries (e.g. photosphere–photosphere loop, or tied flux tubes) traps wave energy and produces standing modes and reflections, as in a vibrating string.
What is the dispersion relation?: In this linear shear-Alfvén model, ω = k v_A — phase speed independent of wavelength along the field.
What is left out?: Landau damping, resistive diffusion, compressional coupling, field-line curvature, and finite β effects are not included.

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Alfvén Wave on a Magnetic Field Line

About this model

How it works

Frequently asked questions

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How it works

Frequently asked questions