Plasma frequency

![[plasma_lecture2.mp4]]

1D study case

Let's assume:

A slab of electrons with number density $n_{0}$
A fixed ion background with $n_{i} = n_{0}$
And let's displace the electrons by $Δ x$ . What will be the frequency of the resulting oscillation?
Gauss Law:

\frac{\partial E}{\partial x} = \frac{ρ}{ϵ_{0}}

Equation of motion for electrons:

m_{e} \frac{d^{2} Δ x}{d t^{2}} = - e E = - \frac{n_{0} e^{2}}{ϵ_{0} m_{e}} Δ x

\frac{d^{2} Δ x}{d t^{2}} + \frac{n_{0} e^{2}}{ϵ_{0} m_{e}} Δ x = 0

where

\frac{n_{0} e^{2}}{ϵ_{0} m_{e}} Δ = ω_{p e}^{2}

is the **electron plasma frequency.

timestamp: 5:50