Abstract
Rayleigh–Taylor, Kelvin–Helmholtz and drift-wave instabilities are studied in the context of the heads of unsteady-beam models of extended radio sources, and the physical consequences of this preliminary analysis are discussed. It is shown that the Rayleigh–Taylor instability sets in on small scales, although complete mixing of the head and ambient materials might not occur. Thus tails may be knotty or have a shell structure (depending upon the nature of the unsteadiness of the beam) whilst hotspots are unlikely to contain any entrained intergalactic material. It is argued that Kelvin–Helmholtz and drift-wave instabilities tend to be suppressed by field shear and density gradients in the interface between the shocked beam and shocked intergalactic flows.

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