Table 1: Simulations of circularly polarised Alfvén waves in a stratified medium with density $\rho_0 (0)= 5 \times 10^{-13}~$ kg m^-3 at the bottom of the grid. $\Delta t, N$ and L denote the time step measured in seconds, the number of grid points, and the length of the computational domain in scale heights, H, respectively. The vertical magnetic field, B₀, is given in T. $v_{\rm A0}$ , $\beta _0$ and $\eta _0= B_\perp /B_0$ are computed at z = 0.
Run $\Delta t$ (s) N L (H) B₀ (T) $v_{\rm A0}$ (m s^-1) $\eta_0$ $\beta _0$

1a 0.0625 21 600 50 $3 \times 10^{-5}$ $3.8 \times 10^4$ 0.007 23

1b 0.0625 21 600 50 $3 \times 10^{-5}$ $3.8 \times 10^4$ 0.07 23

1c 0.0625 21 600 50 $3 \times 10^{-5}$ $3.8 \times 10^4$ 0.7 23

2a 0.125 21 600 50 $1.5 \times 10^{-5}$ $1.8 \times 10^4$ 0.007 82

2b 0.125 21 600 50 $1.5 \times 10^{-5}$ $1.8 \times 10^4$ 0.07 82

2c 0.125 21 600 50 $1.5 \times 10^{-5}$ $1.8 \times 10^4$ 0.7 82

**Table 1:** Simulations of circularly polarised Alfvén waves in a stratified medium with density $\rho_0 (0)= 5 \times 10^{-13}~$ kg m^-3 at the bottom of the grid. $\Delta t, N$ and L denote the time step measured in seconds, the number of grid points, and the length of the computational domain in scale heights, H, respectively. The vertical magnetic field, B₀, is given in T. $v_{\rm A0}$ , $\beta _0$ and $\eta _0= B_\perp /B_0$ are computed at z = 0.
Run	$\Delta t$ (s)	N	L (H)	B₀ (T)	$v_{\rm A0}$ (m s^-1)	$\eta_0$	$\beta _0$
1a	0.0625	21 600	50	$3 \times 10^{-5}$	$3.8 \times 10^4$	0.007	23
1b	0.0625	21 600	50	$3 \times 10^{-5}$	$3.8 \times 10^4$	0.07	23
1c	0.0625	21 600	50	$3 \times 10^{-5}$	$3.8 \times 10^4$	0.7	23
2a	0.125	21 600	50	$1.5 \times 10^{-5}$	$1.8 \times 10^4$	0.007	82
2b	0.125	21 600	50	$1.5 \times 10^{-5}$	$1.8 \times 10^4$	0.07	82
2c	0.125	21 600	50	$1.5 \times 10^{-5}$	$1.8 \times 10^4$	0.7	82

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