Alfvén Velocity Calculator

Background.

Alfvén velocity is the characteristic speed at which a transverse magnetic disturbance travels along a magnetic field in the ideal magnetohydrodynamic model. This calculator evaluates the SI form vA = B / √(μρ), where B is magnetic flux density, μ is magnetic permeability, and ρ is total mass density. It keeps those three quantities visible because replacing mass density with an unsourced particle-count shortcut would silently assume a plasma composition.

Enter magnetic field in tesla, mass density in kilograms per cubic metre, and permeability in henries per metre. The default permeability is the 2022 CODATA vacuum value published by NIST, 1.25663706127 × 10^-6 H/m. That value is measured under the post-2019 SI and carries uncertainty; it is not labelled exact. Replace it if the medium model calls for another permeability.

The result scales directly with field strength and inversely with the square root of density and permeability. Doubling B doubles the speed, while quadrupling ρ halves it. Those relationships make useful input checks. The output is an ideal-MHD characteristic speed, not a measured bulk-flow velocity. Composition, kinetic effects, anisotropy, relativistic corrections, and spatial variation are outside this three-input model.

What is alfvén velocity calculator?

Alfvén velocity is an ideal-MHD wave speed determined by magnetic field strength and the inertia represented by mass density.

How to use this calculator.

1. 01Enter magnetic flux density in tesla.
2. 02Enter total plasma mass density in kilograms per cubic metre.
3. 03Keep the CODATA vacuum permeability or replace it with a sourced medium value.
4. 04Read metres per second or kilometres per second with the model-scope note.

The formula.

The calculator multiplies permeability by mass density, takes the positive square root, and divides magnetic field strength by that result. Coherent SI units reduce to metres per second. Decimal arithmetic is retained through the calculation and rounded once at the return boundary to twelve significant digits.

A worked example.

Frequently asked questions.

References& sources.

1. [1]U.S. Naval Research Laboratory, 2019 NRL Plasma Formulary, p. 29, Velocities: Alfvén velocity equation.
2. [2]NASA Goddard OMNIWeb, Detailed Derivation of Parameters, Characteristic speeds: independent Alfvén-speed definition.
3. [3]NIST SP 961, 2022 CODATA recommended values, May 2024: vacuum magnetic permeability value and uncertainty.