Plasma Frequency Calculator
Enter electron number density and mass to compute the plasma (Langmuir) frequency ω_p = √(n·e²/(ε₀·m_e)).
Input Data
Results
At a glance:The plasma frequency (Langmuir frequency) is the natural oscillation frequency of the free electrons in a plasma relative to the heavy positive ions: ω_p = √(n·e²/(ε₀·m)), with n the electron number density, e = 1.602×10⁻¹⁹ C, ε₀ = 8.854×10⁻¹² F/m and m the electron mass (9.109×10⁻³¹ kg). Frequencies below ω_p cannot propagate through the plasma (the medium reflects them) — this is why radio waves bounce off the ionosphere below its plasma frequency (~a few MHz). f_p = ω_p/(2π). This tool returns ω_p and f_p (Hz/MHz/GHz) from n and m.
Formula
ω_p = √(n·e²/(ε₀·m))
f_p = ω_p/(2π)
$$\omega_p = \sqrt{\frac{n e^2}{\varepsilon_0 m}}, \quad f_p = \frac{\omega_p}{2\pi}$$How to Use
- Enter the electron number density n (1/m³).
- Enter the carrier mass m (default electron mass).
- The calculator returns ω_p and f_p in Hz, MHz, GHz.
Case Studies
Ionosphere
n ≈ 10¹² m⁻³.
f_p ≈ (8.98e3)√n ≈ 8.98e3×1e6 = 9 MHz.
Signals below ~9 MHz reflect; above pass through.
FAQ
Why can't low frequencies pass through plasma?
Electrons oscillate at ω_p and screen the field; waves with ω < ω_p are reflected (evanescent). Above ω_p they propagate — enabling satellite communications through the ionosphere.
What sets the ionosphere cutoff?
Its electron density gives ω_p of a few MHz; AM radio (≲1.6 MHz) reflects and travels beyond the horizon, while FM/TV (≫MHz) pass through to satellites.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.