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\section{Appendix}  For Appletons's equation, The 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 masst  The plasma frequency is given by \[\omega_{pe}=\sqrt{\frac{ne^2}{m_{e}\epsilon_0}}\] where $n$ is the plasma density,and $\epsilon_0$ is the permittivity of free space and $\nu$ is the collision frequency.