Cartoon illustrating the configurations used in the linear analysis, adapted from Komissarov et al. (2019). Top panel: Relativistic jet with a purely azimuthal magnetic field undergoes recollimation due to the confining action of an external pressure. The white inner region represents the freely expanding, unshocked flow, while the shaded area corresponds to the shocked outer layer. The interface between the two is the conical reconfinement shock driven into the jet. Bottom panel: < agnetised, rotating cylindrical shell with a purely axial magnetic field, representing the idealised configuration analysed in this work.