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Planetary rings sustain a continual bombardment of hypervelocity meteoroids that erode the surfaces of ring particles on time‐scales of 10 5 –10 7  years. The debris ejected from such impacts re‐accretes on to the ring, though often at a slightly different orbital radius from the point of emission. This ‘ballistic transport’ leads to a rearrangement of the disc's mass and angular momentum, and gives rise to a linear instability that generates structure on relatively large scales. It is likely that the 100‐km wavetrains in Saturn's inner B‐ring and the plateaus and 1000‐km undulations in Saturn's C‐ring are connected to the non‐linear saturation of the instability. In this paper the physical problem is reformulated so as to apply to a local patch of disc (the shearing sheet). This new streamlined model helps facilitate our physical understanding of the instability, and also makes more tractable the analysis of its non‐linear dynamics. We concentrate on the linear theory in this paper, showing that the instability is restricted to a preferred range of intermediate wavenumbers and optical depths. We subsequently apply these general results to the inner B‐ring and the C‐ring and find that in both regions the ballistic transport instability should be near marginality, a fact that may have important consequences for its prevalence and non‐linear development. Owing to damping via self‐gravity wakes, the instability should not be present in the A‐ring. A following paper will explore the instability's non‐linear saturation and how it connects to the observed large‐scale structure.

The ballistic transport instability in Saturn's rings – I. Formalism and linear theory