Alfvén Speed Calculator

What Is the Alfvén Speed?

The Swedish physicist Hannes Alfvén discovered that in a magnetized plasma, disturbances can propagate along magnetic field lines much like waves on a stretched string. These waves, now called Alfvén waves, play a central role in space and astrophysical plasmas. The speed at which they travel is known as the Alfvén speed, given in ideal magnetohydrodynamics by the relation below.

Here $B$ is the magnetic field strength, $\rho$ is the mass density, and ${\mu }_0$ is the magnetic constant. Stronger fields or lighter plasmas both increase the resulting wave speed.

How the Calculation Works

Once you provide a magnetic field and density, the calculator divides the field by the square root of the product ${\mu }_0\rho$ using SI units. The output is displayed in meters per second and converted to kilometers per second for quick interpretation. Values entered with scientific notation such as 1e-9 are handled automatically.

Example Environments

The table below illustrates typical inputs for several plasmas. It shows how tenuous space environments and dense laboratory plasmas lead to distinct propagation speeds.

Environment	Magnetic field (T)	Mass density (kg/m³)	Alfvén speed (km/s)
Solar corona loop	5 × 10−4	1 × 10−12	440
Earth magnetosphere plasma sheet	1 × 10−8	1 × 10−20	90
Tokamak edge plasma	0.3	1 × 10−7	850

Why the Speed Matters

Alfvén waves influence solar flares, auroral displays, and fusion plasma stability. Engineers and researchers rely on the speed to forecast how energy travels along magnetic field lines, how quickly instabilities can grow, and how efficiently turbulence distributes heat.

Continue exploring plasma physics with related tools such as the plasma frequency calculator, the magnetic Reynolds number calculator, and the magnetopause standoff distance estimator to map how magnetic fields shape space environments.