2007ApJ...664...26H

We derive linearized relativistic magnetohydrodynamic (RMHD) equations describing a uniform axially magnetized cylindrical relativistic jet spine embedded in a uniform axially magnetized relativistically moving sheath. The displacement current is retained in the equations, so that effects associated with Alfvén wave propagation near light speed can be studied. A dispersion relation for the normal modes is obtained. Analytical solutions for the normal modes in the low- and high-frequency limits are found, and a general stability condition is determined. A trans-Alfvénic and even a super-Alfvénic relativistic jet spine can be stable to velocity shear-driven Kelvin-Helmholtz modes. The resonance condition for maximum growth of the normal modes is obtained in the kinetically and magnetically dominated regimes. Numerical solution of the dispersion relation verifies the analytical solutions and is used to study the regime of high sound and Alfvén speeds.