Linear stability of scroll waves

A full linear stability of a straight scroll wave in an excitable medium is presented. The five eigen-mode branches which correspond to deformation in the third dimension of the five main modes of two-dimensional (2D) spiral dynamics are found to play a dominant role. For untwisted scroll waves, modulations in the third dimension have stabilizing or destabilizing effects on the different modes depending on the parameter regimes, in partial agreement with previous predictions. The influence of twist on the different branches is investigated, in particular, the sproing instability is seen to arise from the twist-induced deformation of the translation branches above a threshold twist.