where $p_{\rm mag}={{\bmath{B}}}_0{{\bmath{\cdot}}}{{{\bmath{b}}}}/\mu_0$. This comprises the magnetic flux contributions to both the magnetoacoustic and Alfvén waves. To select the ‘pure’ Alfvén contribution, we project both ${{{\bmath{b}}}}$ and ${{\bmath{v}}}$ in the asymptotic Alfvén wave polarization direction $
\hat{{{\bmath{E}}}}_{\rm Alf}=(\cos^2\theta\sin\phi,\cos\phi,\sin\theta\cos\theta\sin\phi)/\sqrt{1-\sin^2\theta\sin^2\phi}
$ (this is the ${{\hat{\bmath{e}}}}_{\rm perp}$ of @KhoCal11aa rotated into our present frame and normalized) to obtain the components $b_{\rm Alf}$ and $v_{\rm Alf}$, and identify $F_{\rm Alf}=-\langle b_{\rm Alf} v_{\rm Alf} B_0\rangle/\mu_0$. Similarly, $F_{\parallel\rm ac}=\langle p\,{{\bmath{v}}}{{\bmath{\cdot}}}\hat{{\bmath{B}}}_0\rangle$ is the pure field-aligned acoustic flux. Figure \[fig:Fpar\] plots these pure parallel acoustic and Alfvén fluxes against $\phi$ and $\theta$.

For horizontal field $\theta=90^\circ$ there is skew-symmetry in Alfvén flux about $\phi=90^\circ$, as there must be, with the Alfvén flux propagating in the positive direction for $\phi<90^\circ$ and the negative direction for $\phi>90^\circ$. As $\theta$ decreases though, the positive flux on $\phi<90^\circ$ is favoured since it follows the field lines sloping upward from the interaction region. On $\phi>90^\circ$ the census height $z_f$ is above the bulk of this interaction region, and so $F_{\rm Alf}$ does not yet exhibit substantial negative values – it will do so as we move lower in the atmosphere. Indeed, if we could reliably measure $F_{\rm Alf}$ on $\phi>90^\circ$ at lower 