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\section{appendix}  The electron cyclotron frequency is given by \[\omega_{ce}=\frac{eB}{m_e}\] where $e$ is the elementary charge, $B$ is the magnetic field and $m_e$ is the electron mass.  The plasma frequency is given by \[\omega_{pe}=\sqrt{\frac{ne^2}{m\epsilon_0}}\] where $n$ is the plasma density,and $\epsilon_0$ is the permittivity of free space.