Stability and control of electrodynamic tethers for de-orbiting applications

Electrodynamic tethers provide a very promising propulsion system for de-or biting of spent upper stages or LEO satellites. In this application, the Lo rentz force generated by the interaction between the current in the wire an d the geomagnetic field produces an electrodynamic drag leading to a fast o rbital decay. The attractiveness of tether system lies especially in their capability to operate with uncontrollable satellites and in the modest mass requirement. The need for significant along-track forces leads however to the onset of a n undesirable torque which, if not controlled, may drive the system into a dangerous instability. The electrodynamic torque determines inplane and out -of-plane librations whose amplitude depends upon the current in the wire, mass distribution and system dimensions. Even more important, this torque i s modulated along the orbit due to the changing magnetic field and ionosphe ric plasma density, giving rise to forced oscillations. The counteracting l and stabilizing) gravity-gradient torque is generally to small to ensure st ability in typical, strongly non-symmetrical mass distributions, where a ma ssive satellite or upper stage is attached at the lower end and a light ele ctron collecting device (or passive ballast mass) is deployed a few kilomet ers above. Reducing the electron current or increasing the mass at the uppe r end are both unattractive solutions. In this paper we show how the electrodynamic torque pumps energy into the s ystem (finally leading to large librations angles) and indicate that many p roposed configurations are intrinsically unstable. Our results point out th e need for a control strategy. Fortunately, the librations amplitudes can b e limited by acting on the current flowing in the wire. Our model of a rigi d, conductive tether shows that a control based upon timely current switch- off, using energy criteria, is indeed effective and simple to implement. Th e resultant duty-cycles are satisfactory and affect only marginally the deo rbiting times. (C) 2001 International Astronautical Federation. Published b y Elsevier Science Ltd.