What Is the Alfvén Velocity?
The Alfvén velocity is the characteristic propagation speed of Alfvén waves — transverse magnetohydrodynamic (MHD) waves that travel along magnetic field lines in an electrically conducting fluid such as a plasma. It is a fundamental quantity in space physics, solar physics, astrophysics, and fusion research, describing how quickly magnetic disturbances move through ionized matter.
How to Use This Calculator
Enter the magnetic field strength B in tesla and the plasma mass density ρ in kilograms per cubic metre. The calculator returns the Alfvén velocity in metres per second. Mass density is the number density of particles multiplied by the average particle mass (e.g. for a hydrogen plasma, \rho ≈ n × 1.6726 × 10^{-27}\ kg).
The Formula Explained
The Alfvén speed is given by:
Here \mu_0 = 4π × 10^{-7}\ H/m is the vacuum permeability (magnetic constant). A stronger magnetic field increases the wave speed, while a denser plasma (more inertia) slows it down. In SI units the result comes out directly in m/s.
Worked Example
Suppose B = 0.01\ T and \rho = 1 × 10^{-12}\ kg/m^3. Then
Constants Used in the Calculation
The Alfvén velocity formula requires the vacuum permeability \mu_0. The other constants below are useful for converting a measured particle number density into a mass density \rho (for a hydrogen plasma, \rho ≈ n m_p) and for checking whether the result is non-relativistic (v_A \ll c).
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Vacuum permeability | \mu_0 | 4π×10^{-7} ≈ 1.25664×10^{-6} | H/m (T·m/A) |
| Proton mass | m_p | 1.6726×10^{-27} | kg |
| Electron mass | m_e | 9.109×10^{-31} | kg |
| Speed of light | c | 2.998×10^{8} | m/s |
Note that the electron mass is about 1836 times smaller than the proton mass, so in a quasi-neutral hydrogen plasma the mass density is dominated almost entirely by the ions. The factor \mu_0 is exact in the older SI definition (4π×10^{-7}); since the 2019 SI redefinition it is an experimentally determined quantity that remains equal to this value to within measurement uncertainty.
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