Local simulations of instabilities in relativistic jets - I. Morphology and energetics of the current-driven instability

We present the results of a numerical investigation of current-driven instability (CDI) in magnetized jets. Utilizing the well-tested, relativistic magnetohydrodynamic code ATHENA, we construct an ensemble of local, comoving plasma columns in which initial radial force balance is achieved through various combinations of magnetic, pressure and rotational forces. We then examine the resulting flow morphologies and energetics to determine the degree to which these systems become disrupted, the amount of kinetic energy amplification attained and the non-linear saturation behaviours. Our most significant finding is that the details of initial force balance have a pronounced effect on the resulting flow morphology. Models in which the initial magnetic field is force-free deform, but do not become disrupted. Systems that achieve initial equilibrium by balancing pressure gradients and/or rotation against magnetic forces, however, tend to shred, mix and develop turbulence. In all cases, the linear growth of CDI is well represented by analytic models. CDI-driven kinetic energy amplification is slower and saturates at a lower value in force-free models than in those that feature pressure gradients and/or rotation. In rotating columns, we find that magnetized regions undergoing rotational shear are driven towards equipartition between kinetic and magnetic energies. We show that these results are applicable for a large variety of physical parameters, but we caution that algorithmic decisions (such as choice of Riemann solver) can affect the evolution of these systems more than physically motivated parameters.