Trade-off study on deorbiting S/C in near polar orbit

Usual long, flexible, ED tethers kept vertical by the gravity gradient might be less efficient for deorbiting S/C in near-polar orbits than conventional (Hall, Ion) electrical thrusters. A trade-off study on this application is here presented for tethers kept horizontal and perpendicular to the orbital plane. A tether thus oriented must be rigid and short for structural reasons, requiring a non-convex cross section and a power supply as in the case of electrical thrusters. Very recent developments on bare-tether collection theory allow predicting the current collected by an arbitrary cross section. For the horizontal tether, structural considerations on length play the role of ohmic effects in vertical tethers, in determining the optimal contribution of tether mass to the overall deorbiting system. For a given deorbiting-mission impulse, tether-system mass is minimal at some optimal length that increases weakly with the impulse. The horizontal-tether system may beat both the vertical tether and the electrical thruster as regards mass requirements for a narrow length range centered at about 100 m, allowing, however, for a broad mission-impulse range.

A theory of electron collection by a grid sphere

Use of a spherical grid as electron collector at the anodic end of a tether, as recently proposed, is considered. The standard analysis of space-charge limited current to a solid sphere (with neither magnetic nor plasma-motion effects), which has been shown to best fit TSS1R in-orbit results at very high bias, is used to determine effects from grid transparency on current collected; the analysis is first reformulated in the formalism recently introduced in the two-dimensional analysis of bare-tethers. A discussion of the electric potential created by a spherical grid in vacuum is then carried out; it is shown that each grid-wire collects current well below its maximum OML current, the effective grid transparency being close to its optical value. Formulae for the current to a spherical grid, showing the effects of grid transparency, is determined. A fully consistent analysis of electric potential and electron density, outside and inside the grid, is completed.

Relativistic current collection by a cylindrical Langmuir probe

The current I to a cylindrical Langmuir probe with a bias Φp satisfying β≡eΦp/mec2∼O(1) is discussed. The probe is considered at rest in an unmagnetized plasma composed of electrons and ions with temperatureskTe∼kTi≪mec2. For small enough radius, the probe collects the relativistic orbital-motion-limited (OML) current I OML , which is shown to be larger than the non-relativistic result; the OML current is proportional to β1/2 and β3/2 in the limits β≪1 and β≫1, respectively. Unlike the non-relativistic case, the electron density can exceed the unperturbed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/I OML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed density value. An asymptotic theory allowed to compute the maximum radius of the probe to collect OML current, the sheath radius for probe radius well below maximum and how the ratio I/IOML drops below unity when the maximum radius is exceeded. A numerical algorithm that solves the Vlasov-Poisson system was implemented and density and potential profiles presented. The results and their implications in a possible mission to Jupiter with electrodynamic bare tethers are discussed.

Current collection by an active spherical electrode in an unmagnetized plasma

A theoretical model for the steady-state response of anodic contactors that emit a plasma current Ii and collect electrons from a collisionless, unmagnetized plasma is presented. The use of a (kinetic) monoenergetic population for the attracted species, well known in passive probe theory, gives both accuracy and tractability to the theory. The monoenergetic population is proved to behave like an isentropic fluid with radial plus centripetal motion, allowing direct comparisons with ad hoc fluid models. Also, a modification of the original monoenergetic equations permits analysis of contactors operating in orbit-limited conditions. Besides that, the theory predicts that, only for plasma emissions above certain threshold current a presheath/double layer/core structure for the potential is formed (the core mode), while for emissions below that threshold, a plasma contactor behaves exactly as a positive-ion emitter with a presheath/sheath structure (the no-core mode). Ion emitters are studied as a particular case. Emphasis is placed on obtaining dimensionless charts and approximate asymptotic laws of the current-voltage characteristic.

Bare-tether sheath and current: comparison of asymptotic theory and kinetic simulations in stationary plasma

Analytical expressions for current to a cylindrical Langmuir probe at rest in unmagnetized plasma are compared with results from both steady-state Vlasov and particle-in-cell simulations. Probe bias potentials that are much greater than plasma temperature (assumed equal for ions and electrons), as of interest for bare conductive tethers, are considered. At a very high bias, both the electric potential and the attracted-species density exhibit complex radial profiles; in particular, the density exhibits a minimum well within the plasma sheath and a maximum closer to the probe. Excellent agreement is found between analytical and numerical results for values of the probe radiusR close to the maximum radius Rmax for orbital-motion-limited (OML) collection at a particular bias in the following number of profile features: the values and positions of density minimum and maximum, position of sheath boundary, and value of a radius characterizing the no-space-charge behavior of a potential near the high-bias probe. Good agreement between the theory and simulations is also found for parametric laws jointly covering the following three characteristic R ranges: sheath radius versus probe radius and bias for Rmax; density minimum versus probe bias for Rmax; and (weakly bias-dependent) current drop below the OML value versus the probe radius for R > Rmax.

The theory of electrostatic probes in strong magnetic fields : Thesis submitted to the Faculty of The Graduate School of the University of Colorado for the Degree Doctor of Philosophy Department of Aerospace Engineering Science

A theory is developed of an electrostatic probe in a fully-ionized plasma in the presence of a strong magnetic field. The ratio of electron Larmor radius to probe transverse dimension is assumed to be small. Poisson's equation, together with kinetic equations for ions and electrons are considered. An asymptotic perturbation method of multiple scales is used by considering the characteristic lengths appearing in the problem. The leading behavior of the solution is found. The results obtained appear to apply to weaker fields also, agreeing with the solutions known in the limit of no magnetic field. The range of potentials for wich results are presented is limited. The basic effects produced by the field are a depletion of the plasma near the probe and a non-monotonic potential surrounding the probe. The ion saturation current is not changed but changes appear in both the floating potential Vf and the slope of the current-voltage diagram at Vf. The transition region extends beyond the space potential Vs,at wich point the current is largely reduced. The diagram does not have an exponential form in this region as commonly assumed. There exists saturation in electron collection. The extent to which the plasma is disturbed is determined. A cylindrical probe has no solution because of a logarithmic singularity at infinity. Extensions of the theory are considered.

PIC computation of electron current collection to a moving bare tether in the mesothermal condition

In tethered satellite technology, it is important to estimate how many electrons a spacecraft can collect from its ambient plasma by a bare electrodynamic tether. The analysis is however very difficult because of the small but significant Geo-magnetic field and the spacecraft’s relative motion to both ions and electrons. The object of our work is the development of a numerical method, for this purpose. Particle-In-Cell (PIC) method, for the calculation of electron current to a positive bare tether moving at orbital velocity in the ionosphere, i.e. in a flowing magnetized plasma under Maxwellian collisionless conditions. In a PIC code, a number of particles are distributed in phase space and the computational domain has a grid on which Poisson equation is solved for field quantities. The code uses the quasi-neutrality condition to solve for the local potential at points in the plasma which coincide with the computational outside boundary. The quasi-neutrality condition imposes ne - ni on the boundary. The Poisson equation is solved in such a way that the presheath region can be captured in the computation. Results show that the collected current is higher than the Orbital Motion Limit (OML) theory. The OML current is the upper limit of current collection under steady collisionless unmagnetized conditions. In this work, we focus on the flowing effects of plasma as a possible cause of the current enhancement. A deficit electron density due to the flowing effects has been worked and removed by introducing adiabatic electron trapping into our model.