How this calculator works
An Alfvén wave bends magnetic field lines in a conducting plasma. Magnetic tension supplies the restoring force and the plasma mass supplies inertia. Number-density mode uses a single ion species and neglects electron mass. The vacuum permeability is approximated as 4 pi times 10^-7 H/m; this is adequate for this ideal nonrelativistic model. Very low densities can require relativistic MHD.
Formula
vA = B/sqrt(mu0 rho); rho = ni mi; B = vA sqrt(mu0 rho); rho = B²/(mu0 vA²).
Worked example
If rho = 795774.715459 kg/m3, mu0 rho = 1 approximately. A field of 2 T then gives a speed of 2 m/s. Doubling the field doubles the speed.
Advertisement
Frequently asked questions
Is this ordinary sound speed?
No. It is the speed of a magnetic-tension disturbance in an ideal conducting fluid.
Which ion mass should I enter?
Use the mass of the dominant ion in proton masses, or use total mass density for a mixture.
Can the result exceed light speed?
The classical expression can, but such inputs are rejected because relativistic corrections are essential.