Stability of a relativistic rotating electron-positron jet: non-axisymmetric perturbations

Abstract

We investigate the linear stability of a hydrodynamic relativistic flow of magnetized plasma in the simplest case where the energy density of the electromagnetic fields is much greater than the energy density of the matter (including the rest mass energy). This is 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 Alfvén continuum. Numerical calculations showed that modes having reasonable values of azimuthal wavenumber m and radial number n are stable and have attenuation increment γ small. The dispersion curves ω = ω(k ) have a minimum for k 0 ≃ 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.

Relativistic jets and current driven instabilities

“…See, for instance, the left panel in Fig 3. For larger magnetic field strengths (case B5), we observe a stable behavior even in long term integration, as shown in the right panel of Fig 3. In the regime of strong magnetizations, in fact, the system can be well described by the force-free approximation. In this limit, our simulation results are in agreement with the findings of Istomin & Pariev (1994), (1996 who have shown that a jet with a longitudinal electric current remains stable with respect to helical as well as axially symmetric (pinch) modes. We believe that the induced stability owes to the stabilizing action of the electric field and, therefore, it has to be considered as a purely relativistic effect.…”

“…Current driven instabilities have been studied in the non-relativistic linear limit by Appl & Camenzind (1993), while Relativistic Jets 411 relativistic linear studies have been presented by Istomin & Pariev (1994), (1996. Linear studies are strongly affected by the assumed boundary conditions and cannot follow the complex nonlinear effects that may damp unstable modes.…”

The Role of Macroscopic and Microscopic Jet Instabilities

“…Cylindrical force-free jets are kink stable if the poloidal field is independent of the radius [65,66], but are kink unstable if the poloidal field decreases with the radius [50,53]. In a static reference frame or jet confined by rigid walls [67], the Kruskal-Shafranov criterion for instability, |B φ /B p | > 2πR/z, indicates that the instability develops if the length of a static plasma column is long enough for the field lines to go around the column at least once [68].…”

The stability of astrophysical jets

“…This instability excites large scale helical motions that may disrupt the system. Cylindrical force-free jets are kink stable if the poloidal field is independent of the radius (Istomin & Pariev 1994, Istomin & Pariev 1996, but cylindrical force-free jets are kink unstable if the poloidal field decreases with the radius (Begelman 1998;Lyubarskii 1999). In the case of non-relativistic rotation, force-free jets are kink unstable if |B φ /B p | > |Ω|R/c (Tomimatsu et al 2001).…”