this is for holding javascript data
Chris Spencer edited Theory.tex
about 10 years ago
Commit id: 130e576e73e80dabc06c440861b4aa8c8aa01388
deletions | additions
diff --git a/Theory.tex b/Theory.tex
index 3fe1689..89fb115 100644
--- a/Theory.tex
+++ b/Theory.tex
...
For a cold plasma in an electric field, there will be no contribution to the to the dielectric tensor due to the ions having low thermal velocity in comparison to the electrons. Then the dielectric tensor has components \[\kappa_{xx}=\kappa_{yy}=1-\frac{\omega_{pe}^2}{\omega^2-\omega_{ce}^2}\]
\[\kappa_{xy}=\kappa_{yx}=\frac{i\omega_{ce}\omega_{ce}^2}{\omega^2-\omega_{ce}^2}\]
\[\kappa_{\parallel}=1-\frac{\omega_{pe}^2}{\omega^2}\]
Need to define an oscillating point charge in this system. Define $\rho$ from Gaus's law as
\[\rho=qe^{i\omega \[\rho=qe^-{i\omega t}\sigma(\vec{r})\]
where $\sigma(\vec{r})$ is the delta function at $\vec{r}$ at zero.