Alfvén Speed Calculator
Calculate the speed of Alfvén waves in various plasma environments. Select a preset or enter custom values.
What Is the Alfvén Speed?
The Alfvén speed is the characteristic velocity at which low-frequency oscillations of the magnetic field and plasma ions propagate along magnetic field lines. Named after Nobel laureate Hannes Alfvén, who predicted their existence in 1942, these waves are fundamental to the field of magnetohydrodynamics (MHD).
In a magnetized plasma, the magnetic field lines behave somewhat like stretched elastic strings. When these "strings" are plucked, the disturbance travels along them. The speed of this wave depends on the tension of the string (related to the magnetic field strength, ) and the inertia of the medium (related to the mass density, ).
The Formula
The formula for Alfvén speed () in SI units is:
- : Magnetic field strength in Tesla (T).
- : Plasma mass density in kg/m³.
- : The permeability of free space ( H/m).
Applications in Astrophysics and Fusion
Alfvén waves are ubiquitous in the universe and play a crucial role in several high-energy phenomena:
- Solar Coronal Heating: One of the biggest mysteries in solar physics is why the sun's corona is millions of degrees hotter than its surface. Alfvén waves transporting energy from the surface to the corona are a leading candidate for the heating mechanism.
- Space Weather: In Earth's magnetosphere, Alfvén waves can accelerate electrons to relativistic speeds, contributing to the aurora borealis and potentially damaging satellites.
- Fusion Energy: In magnetic confinement fusion devices like Tokamaks, Alfvén waves can be excited by high-energy particles (such as alpha particles from fusion reactions). If these waves grow unstable, they can eject the fast particles, cooling the plasma and damaging the reactor walls.
Typical Values
The calculator includes presets for common environments. Here is a comparison of typical values:
| Environment | Magnetic Field (T) | Density (kg/m³) | Alfvén Speed (km/s) |
|---|---|---|---|
| Solar Corona | 5 × 10−4 | 1 × 10−12 | ~440 |
| Earth Magnetosphere | 1 × 10−8 | 1 × 10−20 | ~90 |
| Tokamak Edge | 0.3 | 1 × 10−7 | ~850 |
| Interstellar Medium | 1 × 10−10 | 1 × 10−21 | ~30 |
How to Use This Calculator
- Select a Preset: Choose a predefined environment like "Solar Corona" to auto-fill typical values.
- Enter Custom Values: If you have specific data, enter the magnetic field in Tesla and the
mass density in kg/m³. Scientific notation (e.g.,
1e-9) is supported. - Calculate: Click the button to compute the speed. The result is shown in both meters per second (m/s) and kilometers per second (km/s).
Explore more about plasma physics with our plasma frequency calculator or the magnetic Reynolds number calculator.