Variables
Description
What is this formula?
The electron plasma frequency formula calculates the natural oscillation frequency of electrons in a plasma when displaced from their equilibrium position relative to ions.
It is one of the most fundamental characteristic frequencies in plasma physics and determines how rapidly electrons respond to electric field disturbances.
When to use it
Use this formula when analyzing:
- plasma oscillations,
- electromagnetic wave propagation in plasma,
- fusion plasmas,
- ionospheric physics,
- laboratory plasma diagnostics,
- and space plasmas.
It is especially important for determining whether electromagnetic waves can propagate through a plasma medium.
Example
A plasma has an electron density of:
n_e = 5×10^18 m⁻³
Using:
e = 1.602×10^-19 C
ε0 = 8.854×10^-12 F/m
m_e = 9.109×10^-31 kg
Formula:
ωpe = √((ne*e²)/(ε0*me))
Substitution:
ωpe = √((5×10^18 × (1.602×10^-19)²)/(8.854×10^-12 × 9.109×10^-31))
Result:
ωpe ≈ 1.26×10^11 rad/s
Applications
- Controlled nuclear fusion
- Tokamak plasma analysis
- Space plasma studies
- Plasma antennas
- Microwave-plasma interaction
- Plasma diagnostics
- Astrophysical plasmas