The Kelvin-Helmholtz instability for relativistic particle beams - I. Stability analyses in the time and space domains for vortex-sheet flows

A differential equation governing the evolution of first-order pressure perturbations of a cylindrical, relativistic, hydrodynamical beam with density and velocity structure is derived. Solutions for the simple vortex-sheet case are used to investigate the stability problem within the framework of the convective nature of Kelvin–Helmholtz instabilities. It is shown that the spatial domain and the temporal domain lead to significantly different results for the growth lengths of instabilities. The results do not support the hypothesis that these instabilities are responsible for the structures observed in jet-like radio sources: as an illustration, the structure of 3C 449 is compared with the structures expected for beams with Mach numbers 4 and 10.