In a magnetised plasma, magnetic field lines behave like plucked strings and carry waves along them. These Alfvén waves heat the solar corona and shape the solar wind and Earth’s magnetosphere. Their speed depends only on the field and the plasma density.
How to use the Alfvén Velocity Calculator
- Magnetic field B
- Ion density n
- Ion species
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the magnetic field, the ion number density and the ion species.
Inputs explained
| Field | What to enter |
|---|---|
| Magnetic field B | Units: nT, µT, mT, G, T |
| Ion density n | Units: cm⁻³, m⁻³ |
| Ion species | Choose one: Protons (H⁺), Helium (He⁺), Oxygen (O⁺), Electron–positron pairs |
What each result means
- Mass density = [Ion density n]×[Ion species]×1.66053906660e-27
- Alfvén velocity v_A = [Magnetic field B]÷sqrt(1.25663706212e-6×[Mass density])
- As a fraction of c = [Alfvén velocity v_A]÷299792458
Example values
How the main result changes when Magnetic field B changes and everything else stays at the example values above:
| Magnetic field B (nT) | Alfvén velocity v_A (km/s) |
|---|---|
| 2.5 | 24.3866 |
| 3.75 | 36.5799 |
| 5 | 48.7732 |
| 6.25 | 60.9665 |
| 7.5 | 73.1598 |
| 10 | 97.5464 |
Formula
v_A = B / √(μ₀·ρ), ρ = n·m_i
Worked example
Inputs — Magnetic field B: 5 nT; Ion density n: 5 cm⁻³; Ion species: Protons (H⁺).
Results — Mass density = 8.3631e-21 kg/m³; Alfvén velocity v_A = 48.7732 km/s; As a fraction of c = 0.000163.
Key terms
- Plasma
- An ionised gas of free ions and electrons.
Frequently asked questions
Who was Alfvén?
Hannes Alfvén, who predicted these waves in 1942 and won the 1970 Nobel Prize.
Where are Alfvén waves found?
In the solar wind, corona, magnetospheres and fusion plasmas.
What is a typical solar-wind value?
About 50 km/s (B ≈ 5 nT, n ≈ 5 cm⁻³).
Can v_A exceed light speed?
The formula can, but relativistic corrections cap the real wave speed below c.