Alfven Velocity Calculator

What Is Alfvén Velocity?

Alfvén velocity is the characteristic speed of magnetohydrodynamic (MHD) waves in a magnetized plasma. Named after Hannes Alfvén, it describes how magnetic field lines and ionized gas move together in space plasmas, fusion devices, and the solar wind.

Alfvén Velocity Formula

$$v_A = \frac{B}{\sqrt{\mu_0\,\rho}}$$

where $B$ is magnetic field strength (tesla), $\rho$ is plasma mass density (kg/m³), and $\mu_0 = 4\pi \times 10^{-7}$ H/m is the permeability of free space. Stronger fields and lower densities produce faster Alfvén waves.

Example: Earth's magnetosphere with $B \approx 50$ nT and $\rho \approx 10^{-12}$ kg/m³ gives $v_A$ on the order of hundreds of km/s.

Frequently Asked Questions

What are Alfvén waves used for?

They transport energy in the solar corona, auroras, and fusion plasmas. Alfvén velocity sets the timescale for magnetic energy release and plasma dynamics.

What units should I enter?

Magnetic field in tesla (T) and density in kg/m³. Use scientific notation for small values — e.g. 5e-5 T for 50 microtesla.

How does density affect Alfvén speed?

Velocity is inversely proportional to the square root of density. Doubling density slows Alfvén waves by about 29%.

Is this the same as the speed of light?

No. Alfvén velocity depends on B and ρ and is usually much slower than light in space plasmas, though it can approach relativistic speeds in extreme conditions.

Where is μ₀ defined?

μ₀ is the vacuum magnetic permeability, exactly 4π × 10⁻⁷ H/m in SI units. It links magnetic field to plasma inertia in the MHD approximation.

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Alfven Velocity Calculator

What Is Alfvén Velocity?

Alfvén Velocity Formula

Frequently Asked Questions

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