= Magnetized cold-plasma dielectric tensor
{title2=$\boldsymbol\epsilon$}
For $e^{-i\omega t}$, <Gaussian units> give $\boldsymbol\epsilon=\mathbf I+4\pi i\boldsymbol\sigma/\omega$, where $\boldsymbol\sigma$ is the summed <conductivity tensor>. With the equilibrium <magnetic field> along $z$, write $\epsilon_{xx}=\epsilon_{yy}=S$, $\epsilon_{zz}=P$, and $\epsilon_{xy}=-\epsilon_{yx}=ig$. For signed <cyclotron frequencies> $\Omega_s=q_sB/(m_sc)$,
$$
S=1-\sum_s\frac{\omega_{ps}^2}{\omega^2-\Omega_s^2},\quad P=1-\sum_s\frac{\omega_{ps}^2}{\omega^2},\quad g=-\sum_s\frac{\omega_{ps}^2\Omega_s}{\omega(\omega^2-\Omega_s^2)}.
$$
Here $\omega_{ps}$ is the species <plasma frequency>. The two circular eigenvalues are $S\mp g$; defining the sign convention before naming their <polarizations> prevents ambiguity.
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