Alfvén Velocity Calculator
Calculate the velocity of magnetohydrodynamic waves in plasma using magnetic field strength and ion density
Calculate Alfvén Velocity
Strength of the external magnetic field
Mass density of ions in the plasma
Alfvén Velocity Results
Formula used: v = B / √(μ₀ × ρ)
Input values: B = 0.00e+0 T, ρ = 0.00e+0 kg/m³
Magnetic permeability: μ₀ = 1.26e-6 T⋅m/A
Wave Properties (f = 1 Hz)
Wavelength: 0.00e+0 km
Period: 1 s
Angular frequency: 6.28 rad/s
Energy Transport
Group velocity: 0.0 km/s
Phase velocity: 0.0 km/s
Dispersion: Dispersionless
Velocity Analysis
Example Calculation
Earth's Ionosphere Example
Environment: Earth's ionosphere plasma
Magnetic field (B): 10 μT
Ion density (ρ): 1×10⁻¹⁵ kg/m³
Magnetic permeability (μ₀): 4π×10⁻⁷ T⋅m/A
Calculation
v = B / √(μ₀ × ρ)
v = 10×10⁻⁶ / √(4π×10⁻⁷ × 1×10⁻¹⁵)
v = 10⁻⁵ / √(1.257×10⁻²¹)
v = 10⁻⁵ / 3.546×10⁻¹¹
v = 282,100 m/s = 282.1 km/s
Typical Alfvén Velocities
Earth's Ionosphere
~280 km/s
B ≈ 10 μT, ρ ≈ 10⁻¹⁵ kg/m³
Solar Corona
~4,460 km/s
B ≈ 500 μT, ρ ≈ 10⁻¹² kg/m³
Interstellar Medium
~10-100 km/s
B ≈ 5 μT, ρ ≈ 10⁻²¹ kg/m³
Laboratory Plasma
~1,000-10,000 km/s
B ≈ 0.1 T, ρ ≈ 10⁻⁸ kg/m³
Alfvén Wave Facts
Alfvén waves are magnetohydrodynamic plasma waves
They propagate along magnetic field lines
Group and phase velocities are equal (dispersionless)
Important for energy transport in space plasmas
May contribute to aurora formation
Understanding Alfvén Waves and Velocity
What are Alfvén Waves?
Alfvén waves are a type of magnetohydrodynamic wave that propagates in plasma. They result from the balance between the inertia of plasma particles and the restoring force due to magnetic field tension. These waves are named after Hannes Alfvén, who predicted their existence in 1942.
Key Properties
- •Propagate along magnetic field lines
- •Dispersionless (group velocity = phase velocity)
- •Transverse wave motion perpendicular to B-field
- •Excellent for energy transport in space plasmas
Formula Explanation
v = B / √(μ₀ × ρ)
- v: Alfvén velocity (m/s)
- B: Magnetic field strength (T)
- μ₀: Magnetic permeability of free space (4π×10⁻⁷ T⋅m/A)
- ρ: Ion mass density (kg/m³)
Physical Insight: Higher magnetic fields and lower densities result in faster Alfvén waves. This is why solar corona has much higher Alfvén velocities than Earth's ionosphere.
Applications in Astrophysics
Solar Physics
Alfvén waves transport energy from the Sun's surface to its corona, potentially explaining coronal heating and solar wind acceleration.
Magnetosphere
Earth's magnetosphere supports Alfvén waves that may contribute to aurora formation and plasma heating in the ionosphere.
Plasma Confinement
In fusion reactors, Alfvén waves can affect plasma stability and confinement, making their study crucial for controlled fusion.