Spherical Collectors versus Bare Tethers for Drag, Thrust and Power Generation

Abstract - We have compared performances in LEO of a bare tether and a tether using a spherical anodic collector, for common values of length L and cross-section area A. The standard space-charge limited model of current to a full sphere, with neither magnetic nor plasma-motion effects considered (i.e., the Alpert-Gurevich-Pitaevskii model), is used. The bare tether would have a thin tape cross-section shape. Currents are normalized with the short-circuit current in the absence of applied power, allowing a comparison of performances for all three applications in terms of characteristic dimensionless numbers. For a light deorbit mission (L = 4 km, A = 1 mm2) the sphere would need a radius of about 8 m for its tether to achieve the drag exerted by the bare tape. For a heavy deorbit mission (L = 20 km, A = 5 mm2), the sphere would need a radius about 20 m; on the other hand, a sphere of radius 2 m would exert a drag 10 times smaller than the bare tape. For both power generation and thrusting, differences in performances are not that extreme for tether systems involving, for thrusting, a power-supply, and, for power generation, a chemical rocket (to balance the Lorentz drag).