Eddy currents applied to de-tumbling of space debris: Analysis and validation of approximate proposed methods

Abstract

The space debris population has greatly increased over the last few decades. Active debris removal (ADR) methods may become necessary to remove those objects in orbit that pose the biggest collision risk. Those ADR methods that require contact with the target, show complications if the target is rotating at high speeds. Observed rotations can be higher than 60 deg/s combined with precession and nutation motions. "Natural" rotational damping in upper stages has been observed for some space debris objects. This phenomenon occurs due to the eddy currents induced by the Earth's magnetic field in the predominantly conductive materials of these man made rotating objects. Existing solutions for the analysis of eddy currents require time-consuming finite element models to solve a Poisson equation throughout the volume. The first part of this paper presents a new method to compute the eddy current torque based on the computation of a new tensor called the 'Magnetic Tensor'. The general theory to compute this tensor by Finite Element Method is given as well as a particular Frame Model. This last model enables an explicit formula to be determined to evaluate the magnetic tensor. Analytical solutions for the spherical shell, the open cylinder and flat plates are given for the magnetic tensor and the eddy current torque model is validated with existing published work. The second part of the paper presents an active de-tumbling method for space debris objects based on eddy currents. The braking method that is proposed has the advantage of avoiding any kind of mechanical contact with the target. The space debris object is subjected to an enhanced magnetic field created from a chaser spacecraft which has one or more deployable structures with an electromagnetic coil at its end. The braking time and the possible induced precession is analysed for a metallic spherical shell considering different ratios of conductive vs. non-conductive material. The paper finalises with a case study based on the de-tumbling of an Ariane-4 Upper Stage H10 under the effect of the gravity gradient and a preliminary analysis of the non-uniformity of the magnetic field is presented.

Guidance, Navigation, and Control for the Eddy Brake Method

“…• Robustness with respect to any illumination conditions: The magnetic field generated by the chaser should be perpendicular to the angular velocity of the target in order to maximize the induced eddy currents [22]. In addition, the chaser spacecraft may need to acquire different relative configurations in order to damp all the components of the angular velocity of the target object.…”

“…Figure 1 indicates the characteristic time of decay of the de-tumbling process for a spherical shell filled in with different percentages of non-conductive material and for different relative distances, using the baseline coil described in Section II. The characteristic time is the time needed to decrease the angular velocity to approximately a third of its initial value [22].…”

“…High temperature superconducting (HTS) wires are used for this purpose. The sizing of the coil is driven by the maximum fairing diameter of the launcher employed [22]. The baseline design of the coil considered throughout this article consists of a coil with a 1.65 meter radius, 500 turns of wire, an electrical intensity of 115 Amperes and a working temperature of 65 K. This is the selected design for the Agora phase 0 study [19].…”

“…The magnetic interaction between the chaser and the target is analyzed using the Magnetic Tensor Theory (MTT) [22]. A metallic object, hereinafter referred to as the target, when subjected to an external time-varying magnetic field will generate eddy current loops (also called Foucault currents) in its metallic components due to Faraday's law of induction [41].…”

“…A de-tumbling method based on the generation of eddy currents was first proposed by Kadaba [20] and some additional research has been carried out since then [21,22]. The controllability of the magnetic interactions of a two-body system in the context of a de-tumbling process in space is a research area that has not yet been studied and it is of paramount importance in order to prove the feasibility of the 'Eddy Brake' method.…”