Relaxation of current-carrying flux tubes and flux rope formation

Flux ropes are ubiquitous structures in space and laboratory plasma environments. Although their equilibrium states have been extensively studied, how they relax from non-equilibrium states is an important process that has been relatively less explored. By analogy to previous studies on current sheets, particle orbits are analyzed and their phase-space trajectories are studied. Analytical calculations show that orbital transitions must occur in a non-equilibrium current sheet and leave distinct footprints in the phase-space distributions. These footprints are verified by kinetic simulations of disequilibrated current sheets, confirming the relaxation process. It is shown that any small parallel current will relax to a flux rope configuration.