Table 1: Simulations of Alfvén waves in a homogeneous medium. The wave is characterised by the two quantities $\eta $, the amplitude of the imposed Alfvén wave in terms of the vertical magnetic field, and $\beta _{\rm }={2 \mu _0 p}/{B_z^2}$ the plasma beta. For the different Runs we further specify the length of the time step $\Delta t$ in terms of the period of the wave, P, the length of the computational domain, L in terms of the wave length, $\lambda $, and the number of grid points, N.
Run $\Delta t/P$ N $L/\lambda$ $\eta $ $\beta $
1a 0.003 3 3 600 78 0.007 0.042
1b 0.003 3 3 600 78 0.07 0.042
1c 0.003 3 3 600 78 0.7 0.042
2a 0.003 3 13 500 193 0.007 0.96
2b 0.003 3 13 500 193 0.07 0.96
2c 0.003 3 13 500 193 0.7 0.96
3a 0.003 3 13 500 278 0.007 2
3b 0.003 3 13 500 278 0.07 2
3c 0.003 3 13 500 278 0.7 2
4a 0.001 7 36 000 77.2 0.007 17
4b 0.001 7 36 000 77.2 0.07 17
4c 0.001 7 36 000 77.2 0.7 17


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