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\subsection{Ray Tracing}  Additional understanding of magneto-gravity waves can be gained using a ray tracing technique. This process allows us to explicitly follow the time evolution of a wave as it propagates into a region of increasing magnetic field. We follow the basic technique outlined in Lignieres \& Georgeot (2009). In the case of magneto-gravity waves in the WKB limit, the Hamiltonian describing their equations of motion is  \begin{equation}  \label{hamiltonian}  H = \omega = \sqrt{ \frac{{\bf k_\perp}^2 N^2}{{\bf k}^2} + ({\bf k} \cdot {\bf v_A})^2 } \, .  \end{equation}  Here, ${\bf k}$ is the wave vector, ${\bf k_\perp}$ is its component normal to the gravitational field, and ${\bf v_A} = {\bf B}/\sqrt{4 \pi \rho}$. In reality the Hamiltonian contains additional terms that allow for the existence of pure Alfven waves, although we ignore this subtlety here.  The equations of motion corresponding to the Hamiltonian of equation \ref{hamiltonian} are  \begin{equation}  \label{dxdt}  \frac{ d{\bf x}}{dt} = \frac{ \partial H}{\partial {\bf k}} = \frac{N^2}{\omega k} \bigg[ \bigg( 1 - \frac{k_\perp^2}{k^2} \bigg) \frac{{\bf k_\perp}}{k} - \frac{k_\perp^2}{k^2} \frac{k_r {\bf \hat{r}}}{k} \bigg] + \frac{\omega_A}{\omega} {\bf v_A} \, ,  \end{equation}  where $\omega_A = ({\bf k} \cdot {\bf v_A})$, and   \begin{equation}  \label{dkdt}  \frac{ d{\bf k}}{dt} = - \frac{ \partial H}{\partial {\bf x}} = - \frac{N}{\omega} \frac{k_\perp^2}{k^2} \bnab N - \frac{\omega_A}{\omega} \bigg[ ({\bf k} \cdot \bnab){\bf v_A} + {\bf k} \times (\bnab \times {\bf v_A} ) \bigg] \, .  \end{equation}  Equation \ref{dxdt} describes the group velocity of the wave, while equation \ref{dkdt} describes the evolution of its wave vector, which is related to the momentum of the wave. Note that in the absence of a magnetic field in a spherical star, only the radial component of the wave vector changes, and the horizontal component is conserved. This is not surprising, as in this case the Hamiltonian is spherically symmetric and thus angular momentum (and hence angular wave vector) is conserved.   However, in the presence of a magnetic field, the last two terms of equation \ref{dkdt} break the spherical symmetry. Except in the unphysical case of a purely radial field or a constant field, these terms are non-zero, and therefore the angular component of the wave vector must change. Therefore, dipolar waves will obtain higher multipole moments as they propagate through magnetized regions of the star.  \subsection{Magnetized Waves in Stars}  Although there exists a great deal of literature on the interaction between magnetism and waves in stars, very few of these works have explored magnetic wave reflection in stellar interiors as described by equation \ref{eqn:magnetogravity}. Here we review some relevant literature and its relation to magneto-gravity waves in red giants.