Plasma Frequency Calculator
Plasma Frequency Calculator computes plasma frequency, visualizing effect of electron density.
Formulas Used in Plasma Frequency Calculator
The calculator uses the following formula for the plasma frequency:
Plasma Frequency:
\\[ \omega_p = \sqrt{\frac{n_e e^2}{m_e \epsilon_0}} \\]Where:
- \\( \omega_p \\): Plasma frequency (rad/s)
- \\( n_e \\): Electron density (m⁻³)
- \\( e = 1.60217662 \times 10^{-19} \, \text{C} \\): Electron charge
- \\( m_e = 9.1093837 \times 10^{-31} \, \text{kg} \\): Electron mass
- \\( \epsilon_0 = 8.854187817 \times 10^{-12} \, \text{F/m} \\): Permittivity of free space
Example Calculations
Example 1: Typical Plasma
Input: nₑ = 1e16 m⁻³
\\[
\omega_p = \sqrt{\frac{1 \times 10^{16} \cdot (1.60217662 \times 10^{-19})^2}{9.1093837 \times 10^{-31} \cdot 8.854187817 \times 10^{-12}}} \approx 5.641 \times 10^8 \, \text{rad/s}
\\]
Result: ω_p ≈ 5.641e8 rad/s
Example 2: Higher Density
Input: nₑ = 1e18 m⁻³
\\[
\omega_p = \sqrt{\frac{1 \times 10^{18} \cdot (1.60217662 \times 10^{-19})^2}{9.1093837 \times 10^{-31} \cdot 8.854187817 \times 10^{-12}}} \approx 5.641 \times 10^9 \, \text{rad/s}
\\]
Result: ω_p ≈ 5.641e9 rad/s
Example 3: Lower Density
Input: nₑ = 1e14 m⁻³
\\[
\omega_p = \sqrt{\frac{1 \times 10^{14} \cdot (1.60217662 \times 10^{-19})^2}{9.1093837 \times 10^{-31} \cdot 8.854187817 \times 10^{-12}}} \approx 5.641 \times 10^7 \, \text{rad/s}
\\]
Result: ω_p ≈ 5.641e7 rad/s