Cold magnetized plasma

A plasma whose linear wave response retains the equilibrium magnetic field and particle inertia but neglects pressure forces, thermal dispersion and collisions. Its applicability requires $k{v}_{\mathrm{th},s}\ll |\omega |$ and separate care near cyclotron resonances.

A limiting point of a plasma wave branch with divergent refractive index. At finite coefficients of the magnetized cold-plasma dielectric tensor, the generic condition is $S{\sin }^2\theta +P{\cos }^2\theta =0$. Poles of that magnetized cold-plasma dielectric tensor require a separate limiting analysis. Collisions, thermal dispersion or mode conversion can regularize a singular cold prediction.

A point on a plasma wave branch where the local wavenumber tends to zero at finite frequency. The mode may change between propagation and evanescence. For a finite magnetized cold-plasma dielectric tensor, candidate cutoffs satisfy $PRL=0$; special propagation angles require checking which factor belongs to the chosen branch.

For propagation perpendicular to the equilibrium magnetic field, this plasma wave has its electric field perpendicular to that magnetic field and generally both parallel and perpendicular to its wavevector. Its dispersion relation is $n^2=RL/S$, using the magnetized cold-plasma dielectric tensor conventions $R=S-g$, $L=S+g$.

For propagation perpendicular to an equilibrium magnetic field, an ordinary plasma wave has its electric field parallel to that magnetic field, so the particle response involves no magnetic deflection. With immobile ions, the dispersion relation is ${\omega }^2={\omega }_{pe}^2+c^2{k}^2$. It is a transverse electromagnetic wave, despite its parallel particle motion.

With the same conventions as the cold-plasma right-handed wave, this transverse electromagnetic wave has $E_y=-i{E}_x$ and refractive index $n^2=S+g$. With immobile ions, $L=1-{\omega }_{pe}^2/[\omega (\omega +{\Omega }_e)]$.

For propagation along $+{\mathbf{B}}_0$, use $e^{ikz-i\omega t}$ and ${ϵ}_{xy}=ig$. This transverse electromagnetic wave has $E_y=i{E}_x$ and refractive index $n^2=S-g$. Its real electric field rotates in the sense of electron gyration. With immobile ions and positive electron cyclotron frequency magnitude ${\Omega }_e$, $R=1-{\omega }_{pe}^2/[\omega (\omega -{\Omega }_e)]$.

For $e^{-i\omega t}$, Gaussian units give $\mathbf{ϵ}=\mathbf{I}+4\pi i\mathbf{\sigma }/\omega$, where $\mathbf{\sigma }$ is the summed conductivity tensor. With the equilibrium magnetic field along $z$, write ${ϵ}_{xx}={ϵ}_{yy}=S$, ${ϵ}_{zz}=P$, and ${ϵ}_{xy}=-{ϵ}_{yx}=ig$. For signed cyclotron frequencies ${\Omega }_s=q_{s}B/(m_{s}c)$,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.