Time evolution of the total magnetic energy for the 2 × 2 case with several different upper boundary conditions located at one of two heights. The “normal, closed, vertical” case refers to our standard 2 × 2 run. The “normal, closed, potential” refers to a case where the magnetic field was matched to a potential field at the top boundary. For the “tall” cases the top boundary was moved upwards by 280 km, and “open” refers to cases where flow, temperature and pressure were smoothly extrapolated through the upper boundary.