grid of spacings $\Delta x=\Delta y=1.09$ Mm covering heights $-25\,{\rm Mm} \le z \le 1.53\,{\rm Mm}$ with nonuniform $\Delta z$. Periodic lateral boundaries and absorbing PML layers at top (starting at $z_t=1.26$ Mm) and bottom complete the definition of the computational region.

Without loss of generality, the field lines are assumed to lie parallel to the $x$-$z$ plane. As with most such codes, SPARC normally employs an Alfvén speed ‘limiter’ or ‘controller’ (or similar) in the atmosphere to avoid infeasibly small time steps required to satisfy the CFL numerical stability condition [*e.g.*. @Han08aa; @RemSchKno09aa; @CamGizSch11aa]. These commonly cap the Alfvén speed at 20–60 $\rm km\,s^{-1}$. We do not impose such a limiter though, as it corrupts the very processes of fast wave reflection and conversion that we seek to explore [@MorCal13aa]. This is why we adopt lower box heights than usual, so as to keep the peak Alfvén speed manageable. Numerical experiment has allowed us to select box heights sufficient to encompass fast-to-Alfvén conversion without mandating impossibly small time steps. For the 500 G case we use $\Delta t=0.1$ s, and half that for 1 kG.

Data cubes are produced from the simulations consisting of vertical velocity values at each 