Non-equilibrium formation and relaxation of magnetic flux ropes at kinetic scales

Magnetic flux ropes are pivotal structures and building blocks in astrophysical and laboratory plasmas, and various equilibrium models have thus been studied in the past. However, flux ropes in general form at non-equilibrium, and their pathway from formation to relaxation is a crucial process that determines their eventual properties. Here we show that any localized current parallel to a background magnetic field will evolve into a flux rope via non-equilibrium processes. The detailed kinetic dynamics are exhaustively explained through single-particle and Vlasov analyses and verified through particle-in-cell simulations. This process is consistent with many proposed mechanisms of flux rope generation such as magnetic reconnection. A spacecraft observation of an example flux rope is also presented; by invoking the non-equilibrium process, its structure and properties can be explicated down to all six components of the temperature tensor. Flux ropes are fundamental structures that govern much of the dynamics in astrophysical and space plasmas. The authors show how out-of-equilibrium processes can form small-scale flux ropes and compare them to simulations and spacecraft observations.