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\section{Theory}  \center{Appleton's equation is given by}\[\eta^2=1-\frac{\omega_{pe}^2}{\omega^2\left((1+\frac{i\nu}{\omega})-\frac{\omega_{ce}^2\sin^2\theta}{2\omega^2\left(1-\frac{\omega_{pe}^2}{\omega^2}\right)}\pm\sqrt{\frac{(\omega_{ce}^2\sin^2\theta)^2}{4(1-\frac{\omega_{pe}^2}{\omega^2})}+\frac{\omega_{ce}^2cos^2\theta}{\omega^2}}\right)}\]for an infinite plasma[2]. This describes the index of refraction for a whistler wave where $\eta^2=\left(\frac{kc}{\omega}\right)^2$. $\omega_{pe}$ is the plasma frequency,$\omega_{ce}$ is the electron cyclotron frequency, and \nu\ $\nu$  is the rate of collisions in the plasma.