Editing Critical frequency (section)

== Relationship with plasma frequency ==
The dependence of critical frequency with respect with electron density can be related through [[plasma oscillation]] concept particularly the [[Plasma oscillation#'Cold' electrons|'Cold' Electrons]] mechanism.

<math>\omega_{\mathrm{pe}} = \sqrt{\frac{n_\mathrm{e} e^{2}}{m^*\varepsilon_0}}, \left[\mathrm{rad/s}\right]</math>

Using the [[electron charge]] <math>e=1.602\cdot 10^{-19} Coulombs</math>, [[electron mass]] <math>m^*=9.10938356\cdot 10^{-31} kilograms</math> and [[Permittivity of Free Space|permittivity of free space]] <math>\epsilon_o=8.854187817\cdot 10^{-12}A^2s^4m^{-3}kg^{-1}</math>gives,

<math>\omega_{\mathrm{pe}} = 2\pi f=56.415 \sqrt{n_e}</math>

and solving for the frequency,

<math>f_\text{c} = 8.979\sqrt{N_\text{max}} \approx 9\sqrt{N_\text{max}}</math>