Current-driven instabilities in astrophysical jets: Linear analysis

Current-driven instabilities of force-free screw pinches are studied for a large variety of magnetic configurations by means of a global linear analysis in an ideal MHD framework. The magnetic pitch, P = rB_z/B_φ, in particular its value on the axis, P₀, essentially determines the growth rate of the fastest growing kink instability and allows to identify two regimes. In the large pitch regime, representative for the majority of controlled fusion devices, the stability properties are highly sensitive to the radial pitch profile. Astrophysical jets of magnetic origin are likely to have dominantly azimuthal fields. For such configurations the properties of the fastest growing kink instability become nearly independent of the details of the pitch profile. The most unstable mode grows with an e-folding time t_g = 7.52 P₀/ν_A and an axial wavelength λ = 8.43 P₀ in the rest frame of the jet. The magnetic structure of jets with dominantly azimuthal fields will be modified by the fast growing kink instability. An analysis of the eigenfunction shows however that the kink is an internal mode which does not cause a significant sidewise displacement of the jet surface.