A New Kind of Dynamic Instability in Electrodynamic Tethers

Abstract. Simulation of the dynamics of an electrodynamic tether on a circular inclined orbit shows a very complex motion driven by the electrodynamic forces acting on the conductive tether. These forces depend on the current owing in the wire, the Earth magnetic eld, the orbital velocity and the tether position. In this paper we use a simple model to describe the dynamic eects of these forces. The tether is modelled as a rigid rod with point masses at the ends. We also adopt a non-tilted dipole model for the Earth magnetic eld, and we assume that the tether current is constant. When the current is null, the sytem has a stable equilibrium position with the tether aligned along the local vertical. When the current is dierent from zero, a periodic motion appears. A non-linear analysis of the motion shows that the periodic solutions are always unstable (within the limitation of the model considered in the paper). The physical reason for the instability is that the electrodynamic forces pump energy continually into the system. The net energy increase per orbit for the periodic solution (or state space trajectory) is zero. However, any non-periodic trajectory in its neighborhood has a positive net energy ux per orbit so that after several orbits the in plane libration becomes a rotation. The mechanism responsible for this instability depends on the orbital inclination. Unlike other destabilizing mechanisms found in electrodynamic tethers, this one is present in any kind of tether system with either a exible or a rigid tether, operating in the generator or thruster mode and utilizing a bare tether or a large spherical termination to collect the ionospheric electrons. The instability described in this paper is independent of the presence of resonant force components that may be generated by the magnetic and plasma elds.