each frequency (3 mHz and 5 mHz). The fast wave is evanescent, and so contributes no flux. Similarly, Time-Distance travel time perturbations relative to quiet Sun (same atmospheric model but no magnetic field) are also plotted against $\theta$ and $\phi$.[^4] These are displayed and analysed in Section \[results\].

Results
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In this section, wave energy fluxes at the top of the computational box will be compared with ‘travel time’ perturbations relative to the quiet Sun for a range of magnetic field inclinations $\theta$ and orientations $\phi$, field strengths (500 G and 1 kG), horizontal wavenumbers ($k_h=1$, 0.75, and 0.5 $\rm Mm^{-1}$), and wave frequencies (3 mHz and 5 mHz).

Wave Energy Fluxes {#fluxes}
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![image](\figdir/500G_5mHz_grid){width=".497\hsize"} ![image](\figdir/1kG_5mHz_grid){width=".497\hsize"}\
![image](\figdir/500G_3mHz_grid){width=".497\hsize"} ![image](\figdir/1kG_3mHz_grid){width=".497\hsize"}

With magnetic field strengths of 500 G and 1 kG, Figure \[fig:Fz\] depicts the top vertical acoustic and magnetic wave energy fluxes at 3 mHz and 5 mHz as functions of field inclination from the vertical $\theta$ and wave orientation as selected by the wavevector space ball filter $\phi$. The (vector) fluxes are calculated according to $${{{\bmath{F}}}}_{\rm ac}=\langle p\,{{\bmath{v}}}\rangle\,, \quad {{{\bmath{F}}}}_{\rm mag}=\langle {{{\bmath{b}}}}{{\bmath{\times}}}({{\bmath{v}}}{{\bmath{\times}}}{{\bmath{B}}}_0)\rangle/\mu_0\,,  \label{flux}$$ where ${{\bmath{v}}}$, $p$, and ${{{\bmath{b}}}}$ are the Eulerian velocity, pressure, and magnetic field perturbations, $\mu_0$ is the magnetic 