  At low temperatures the critical state in superconducting films can be
unstable with respect to thermomagnetic dendritic avalanches. By numerical
simulations of disk-shaped superconductors, we consider how the dynamics and
morphology of the avalanches depend on the disk thickness. We find that as the
disks get thicker, the jumps in magnetic moment caused by the avalanches get
larger and the threshold magnetic field for the appearance of the first
avalanche increases. At the same time, the branches are straighter and the
number of branches decreases. Comparison with theory suggests that strong
spatial disorder to some extent cancels the stabilizing effects of the
substrate kept at constant temperature.
