Enter Plasma Parameters
Use scientific notation such as 1.0e20 when values become very large or very small.
Plotly Graph
This graph tracks how plasma frequency changes as density varies around the selected calculation point on logarithmic axes.
Formula Used
ωp = √(n Z e² / (ε0 εr m))
fp = ωp / (2π)
λ = c / fp
E = h fp / e
n is carrier number density, Z is charge state, e is elementary charge, ε0 is vacuum permittivity, εr is relative permittivity, and m is the particle mass.
When electron mode is selected, the code uses m = (m*/me) × me. This lets you model free electrons and effective masses used in condensed matter physics.
How to Use This Calculator
- Enter the electron density using either m^-3 or cm^-3.
- Choose the charge state for the oscillating carriers.
- Set the relative permittivity for the medium.
- Select electron effective mass or a custom particle mass.
- Press calculate to see angular frequency, hertz, wavelength, and energy.
- Use the export buttons to save the current result as CSV or PDF.
- Review the graph to see how density shifts the plasma frequency.
Example Data Table
| Example | Density (m^-3) | Frequency (Hz) | Wavelength (m) | Energy (eV) |
|---|---|---|---|---|
| Low-density laboratory plasma | 1.000000e+15 | 2.839302e+8 | 1.055867e+0 | 0.000001 |
| Glow discharge plasma | 1.000000e+18 | 8.978663e+9 | 3.338943e-2 | 0.000037 |
| Doped semiconductor carriers | 1.000000e+23 | 2.839302e+12 | 1.055867e-4 | 0.011742 |
| Metal-like electron gas | 1.000000e+28 | 8.978663e+14 | 3.338943e-7 | 3.713277 |
Frequently Asked Questions
1. What is plasma frequency?
Plasma frequency is the natural oscillation rate of free charge carriers after they are displaced from equilibrium. It helps describe how plasmas, metals, and carrier-rich materials respond to electromagnetic fields.
2. Why does the frequency increase with density?
A higher carrier density means stronger restoring forces after displacement. Because the formula contains the square root of density, frequency rises as density increases, but not linearly.
3. What does relative permittivity change?
Relative permittivity reduces the effective restoring field in the medium. Larger εr values lower the plasma frequency because the denominator of the equation becomes larger.
4. Why is effective mass important?
In solids, carriers can behave as if their inertia differs from free electrons. Effective mass captures that behavior. Larger effective mass lowers the plasma frequency.
5. Can this calculator model ions too?
Yes. Choose the custom mass option and enter the ion mass in kilograms. Since ions are much heavier, their plasma frequencies are usually far lower than electron plasma frequencies.
6. Why are metal plasma frequencies so high?
Metals contain extremely high free-electron densities. That makes the restoring force strong, producing plasma frequencies commonly in ultraviolet or visible-adjacent ranges.
7. What does the wavelength output represent?
It is the free-space wavelength associated with the calculated plasma frequency. This is useful when comparing the oscillation scale with electromagnetic wave behavior.
8. Which density unit should I use?
Use whatever unit your source provides. The calculator converts cm^-3 to m^-3 internally, so both common laboratory and SI density formats are supported.