Energy Analysis of Bare Electrodynamic Tethers

The design of an electrodynamic tether is a complex task that involves the control of dynamic instabilities, optimization of the generated power (or the descent time in deorbiting missions), and minimization of the tether mass. The electrodynamic forces on an electrodynamic tether are responsible for variations in the mechanical energy of the tethered system and can also drive the system to dynamic instability. Energy sources and sinks in this system include the following: 1) ionospheric impedance, 2) the potential drop at the cathodic contactor, 3) ohmic losses in the tether, 4) the corotational plasma electric field, and 5) generated power and/or 6) input power. The analysis of each of these energy components, or bricks, establishes parameters that are useful tools for tether design. In this study, the nondimensional parameters that govern the orbital energy variation, dynamic instability, and power generation were characterized, and their mutual interdependence was established. A space-debris mitigation mission was taken as an example of this approach for the assessment of tether performance. Numerical simulations using a dumbbell model for tether dynamics, the International Geomagnetic Reference Field for the geomagnetic field, and the International Reference Ionosphere for the ionosphere were performed to test the analytical approach. The results obtained herein stress the close relationships that exist among the velocity of descent, dynamic stability, and generated power. An optimal tether design requires a detailed tradeoff among these performances in a real-world scenario

Three-Body Dynamics and Self-Powering of an Electrodynamic Tether in a Plasmasphere

The dynamics of an electrodynamic tether in a three-body gravitational environment are investigated. In the classical two-body scenario the extraction of power is at the expense of orbital kinetic energy. As a result of power extraction, an electrodynamic tether satellite system loses altitude and deorbits. This concept has been proposed and well investigated in the past, for example for orbital debris mitigation and spent stages reentry. On the other hand, in the three-body scenario an electrodynamic tether can be placed in an equilibrium position fixed with respect to the two primary bodies without deorbiting, and at the same time generate power for onboard use. The appearance of new equilibrium positions in the perturbed three-body problem allow this to happen as the electrical power is extracted at the expenses of the plasma corotating with the primary body. Fundamental differences between the classical twobody dynamics and the new phenomena appearing in the circular restricted three-body problem perturbed by the electrodynamic force of the electrodynamic tether are shown in the paper. An interesting application of an electrodynamic tether placed in the Jupiter plasma torus is then considered, in which the electrodynamic tether generates useful electrical power of about 1 kW with a 20-km-long electrodynamic tether from the environmental plasma without losing orbital energy

Asymptotic Solution for the Current Profile of Passive Bare Electrodynamic Tethers

A relatively high-accuracy analytical solution for the current and potential profile along a passive bare electrodynamic tether is provided using perturbation theory. An ad hoc nondimensional formulation of the governing local bias and orbital motion limited current collection equations allows one to approach the problem with a perturbation technique in which a parameter, epsilon, quantifies the influence of ohmic effects on the final solution. For the case of small ohmic effects an approximate solution is obtained with a third-order expansion. Conversely, the case of dominant ohmic effects is treated based on an extension of the exact analytical solution available for the particular case of zero load and negligible potential drop at the cathodic end of the tether. After computing the analytical current and potential profile the maximum and average current, the Lorentz force and torque, as well as the optimum load impedance for maximum power generation are obtained. When compared with the exact, numerically-computed solution an accuracy of better than5%is achieved for the computation of the average current across the full parameter space. The error with respect to the generated power becomes negligible when the load impedance is set to the optimum value, while it can grow to a maximum of about 30% for the less relevant case in which the load impedance of the power generation system is badly mismatched. The results, which are valid for a general rectilinear passive electrodynamic tether with constant cross section satisfying orbital motion limited theory and irrespective of the particular orbit configuration, will be of aid in the design and analysis of space missions involving bare electrodynamic tethers

Power density of a bare electrodynamic tether generator

The maximum performance of bare electrodynamic tethers as power generating systems under OML-theory is analyzed. Results show that best performance in terms of power density is achieved by designing the tether in such a way to increase ohmic impedance with respect to plasma contact impedance, hence favoring longer and thinner tethers. In such condition the corresponding optimal value of the load impedance is seen to approach the ohmic impedance of the conducting tether. At the other extreme, when plasma contact impedance dominates (which is not optimal but can be relevant for some applications) optimum power generation is found by matching the load impedance with an effective tether-plasma contact impedance whose expression is derived

Performance Analysis of Bare Electrodynamic Tethers as Microsats Deorbiting Systems

It has recently been proposed to use bare electrodynamic tethers (EDTs) in connection with micro- and nano-satellites, either to provide a cheap test of OML current collection theory or to devise a lightweight deorbiting system for cubesats experiments. In the present article we investigate the orbital evolution of small satellites (2 kg) equipped with electrodynamic tethers of different lengths (100 m to 300 m) different ionospheric conditions and focusing on a nominal VEGA polar orbit of 700 km altitude. Issues of tether integration in the microsatellite system and tether deployment are also addressed. Results show that, given sufficient power availability and once a safe and effective deployment strategy is devised, a small dedicated experiment involving two cubesats is feasible in favorable conditions with tether length of 100-300

Versatile Electro-Dynamic Tethers Dynamics Simulator for Debris Mitigation Tools Design

As far as the space debris mitigation is concerned, the electro-dynamic tethers (EDTs) represent a valuable alternative for de-orbiting. The paper presents a high accuracy numerical simulator developed to support the design and verify the effectiveness of such systems: accurate models are exploited for the mechanical, electrodynamical and environmental representation. Results confirmed the known instabilities of EDTs; to cope with them a control strategy is here proposed, traded off among different laws. The selected control relies on varying either the load resistance or the cathodic emitter voltage drop, at the system cathode, being the current profile the controlled variable. The sensitivity analysis, run on several design parameters, is presented and the interdependencies with stability and performance are discussed

Jovian Capture of a Spacecraft with a Self-Balanced Electrodynamic Bare Tether

This paper proposes and analyzes the use of a nonrotating tethered system for a direct capture in Jovian orbit using the electrodynamic force generated along the cable. A detailed dynamical model is developed showing a strong gravitational and electrodynamic coupling between the center of mass and the attitude motions. This paper shows the feasibility of a direct capture in Jovian orbit of a rigid tethered system preventing the tether from rotating. Additional mechanical–thermal requirements are explored, and preliminary operational limits are defined to complete the maneuver. In particular, to ensure that the system remains nonrotating, a nominal attitude profile for a self-balanced electrodynamic tether is proposed, as well as a simple feedback control

Optimizing Electrodynamic Tether System Performance

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76123/1/AIAA-2009-6734-525.pd

Saturn power generation with electrodynamic tethers in polar orbit

A power generation scheme based on bare electrodynamic tethers (EDT), working in passive mode is investigated for the purpose of supplying power to scientific missions at Saturn. The system employs a spinning EDT on a lowaltitude polar orbit which permits to efficiently convert plasmasphere energy into useful power. After optimizing the tether design for power generation we compute the supplied power along the orbit and the impact of the Lorentz force on the orbital elements as function of the tether and orbit characteristics. Although uncertainties in the current ionosphere density modeling strongly affect the performance of the system the peak power density of the EDT appears be greater than conventional power systems