%info@http:://golem.fjfi.cvut.cz/wiki/root/GW4reports

\def\GWslide{\slide{Plasma Oscillations}{
\begin{center}
\GWig{width=0.5\tw}{Theory/PlasmaDiagnostics/ActiveRadiationMeasurements/Interferometry/SimpleModelUnmagnetized/PlasmaOscillation/fig/fig.png}
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\begin{itemize}
\item Outside agency {\bf (e.g. EM wave)} cause all of the electrons to be displaced by the very small amount of $\Delta x$.
\item Equation of motion: $m_{tot}\frac{d^2}{dt^2} \Delta x = q_{tot}E$, where $m_{tot}=m_e n_0 V$.
\item Integral form of the Gauss law: $EA = \frac{e n_0 A \Delta x}{\epsilon_0}$ gives: $E= \frac{e n_0 }{\epsilon_0 } \Delta x$.
\item Then: $m_e n_0 V \frac{d^2}{dt^2} \Delta x = -e n_0 V \frac{e n_0} {\epsilon_0} \Delta x$, typical LHO form with oscillation at {\bf electron plasma frequency} $\omega_{pe} = \sqrt{ \frac{e^2 n_0}{m_e \epsilon_0} }$.
\end{itemize}
\credit{underthehood.blogwyrm:PlasmaOscillation}{}
}}