Stability of a relativistic rotating electron-positron jet: nonaxisymmetric perturbations

We investigate the linear stability of a hydrodynamic relativistic flow of magnetized plasma in the force--free approximation. We considered the case of light cylindrical jet in cold and dense environment, so the jet boundary remains at rest. Continuous and discrete spectra of frequencies are investigated analytically. An infinite sequence of eigenfrequencies is found near the edge of Alfv\'en continuum. Numerical calculations showed that modes are stable and have attenuation increment $\gamma$ small. The dispersion curves $\omega =\omega (k_\parallel )$ have a minimum for $k_{{\parallel}_0}\simeq 1/R$ ($R$ is the jet radius ). This results in accumulation of perturbations inside the jet with wavelength of the order of the jet radius. The wave crests of the perturbation pattern formed in such a way move along the jet with the velocity exceeding light speed. If one has relativistic electrons emitting synchrotron radiation inside the jet, than this pattern will be visible. This provide us with the new type of superluminal source. If the jet is oriented close to the line of sight, than the observer will see knots moving backward to the core.