Juan R. Sanmartin

Electrodynamic Tether Applications and Constraints

Propulsion and power generation by bare electrodynamic tethers are revisited in a unified way and issues and constraints are addressed. In comparing electrodynamic tethers, which do not use propellant, with other propellantconsuming systems, mission duration is a discriminator that defines crossover points for systems with equal initial masses. Bare tethers operating in low Earth orbit can be more competitive than optimum ion thrusters in missions exceeding two-three days for orbital deboost and three weeks for boosting operations. If the tether produces useful onboard power during deboost, the crossover point reaches to about 10 days. Power generation by means of a bare electrodynamic tether in combination with chemical propulsion to maintain orbital altitude of the system is more efficient than use of the same chemicals (liquid hydrogen and liquid oxygen) in a fuel cell to produce power for missions longer than one week. Issues associated with tether temperature, bowing, deployment, and arcing are also discussed. Heating/cooling rates reach about 4 K/s for a 0.05-mm-thick tape and a fraction of Kelvin/second for the ProSEDS (0.6-mm-radius) wire; under dominant ohmic effects, temperatures areover200K (night) and 380 K (day) for the tape and 320 and 415 K for that wire. Tether applications other than propulsion and power are briefly discussed.

Electrodynamic Tether at Jupiter—I: Capture Operation and Constraints

Tethered spacecraft missions to the Jovian system suit the use of electrodynamic tethers because: 1) magnetic stresses are 100 times greater than at the Earth; 2) the stationary orbit is one-third the relative distance for Earth; and 3) moon <i>Io</i> is a nearby giant plasma source. The (bare) tether is a reinforced aluminum foil with tens of kilometer length <i>L</i> and a fraction of millimeter thickness <i>h</i>, which collects electrons as an efficient Langmuir probe and can tap Jupiters rotational energy for both propulsion and power. In this paper, the critical capture operation is explicitly formulated in terms of orbit geometry and established magnetic and thermal plasma models. The design parameters <i>L</i> and <i>h</i> and capture perijove radius <i>r</i> _p face opposite criteria independent of tape width. Efficient capture requires a low <i>r</i> _p and a high <i>L</i> ^3/2/<i>h</i> ratio. However, combined bounds on tether bowing and tether tensile stress, arising from a spin made necessary by the low Jovian gravity gradient, require a high <i>r</i> _p and a low <i>L</i> ^5/2/<i>h</i> ratio. Bounds on tether temperature again require a high <i>r</i> _p and a low <i>L</i> ^3/8/(tether emissivity)^1/4 ratio. Optimal design values are discussed.

Exploration of outer planets using tethers for power and propulsion

a = radius of circular orbit a(max) = radius at mechanical-energy maximum ast = radius of stationary orbit B = planetary magnetic field Em = motional electric field ht = thickness of tape tether I = current on tether Iav = length-averaged tether current Lt = tether length Msc = overall spacecraft mass mt = tether mass Npl = ionospheric electron density RJ = radius of Jupiter r = radial distance rper = radius at perijove T = tether temperature Te = ionospheric electron temperature vorb = orbital velocity vpl = ionospheric plasma velocity vrel = relative velocity vorb − vpl v∞ = hyperbolic excess velocity wt = width of tape tether e = tether emissivity emech = mechanical energy ρAl = aluminum density σAl = aluminum conductivity σB = Stefan–Boltzmann constant

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrodinger equation, has been analyzed; wave 1 is linearly unstable with growth rate Γ, and waves 2 and 3 are stable with damping γ2 and γ3, respectively. The dependence of gross dynamical features on the damping model (as characterized by the relation between damping and wave-vector ratios, γ2∕γ3, k2∕k3), and the polarization of the waves, is discussed; two damping models, Landau (γ∝k) and resistive (γ∝k2), are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist for Γ<2(γ2+γ3)∕3, as against flow contraction ju...

Survival Probability of Round and Tape Tethers Against Debris Impact

The current space environment, consisting of manmade debris and micrometeoroids, poses a risk to safe operations in space, and the situation is continuously deteriorating due to in-orbit debris col...

A review of electrodynamic tethers for science applications

A bare electrodynamic tether (EDT) is a conductive thin wire or tape tens of kilometres long, which is kept taut in space by gravity gradient or spinning, and is left bare of insulation to collect (and carry) current as a cylindrical Langmuir probe in an ambient magnetized plasma. An EDT is a probe in mesothermal flow at highly positive (or negative) bias, with a large or extremely large 2D sheath, which may show effects from the magnetic self-field of its current and have electrons adiabatically trapped in its ram front. Beyond technical applications ranging from propellantless propulsion to power generation in orbit, EDTs allow broad scientific uses such as generating electron beams and artificial auroras, exciting Alfven waves and whistlers, modifying the radiation belts and exploring interplanetary space and the Jovian magnetosphere. Asymptotic analysis, numerical simulations, ground and space tests and past and planned missions on EDTs are briefly reviewed.

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 radius R 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 R Lt Rmax; density minimum versus probe bias for R cong Rmax; and (weakly bias-dependent) current drop below the OML value versus the probe radius for R > R.

Electrodynamic Tether at Jupiter—II: Fast Moon Tour After Capture

An electrodynamic bare-tether mission to Jupiter, following the capture of a spacecraft (SC) into an equatorial highly elliptical orbit with perijove at about 1.3 times the Jovian radius, is discussed. Repeated applications of the propellantless Lorentz drag on a spinning tether, at the perijove vicinity, can progressively lower the apojove at constant perijove, for a tour of Galilean moons. Electrical energy is generated and stored as the SC moves from an orbit at 1 : 1 resonance with a moon, down to resonance with the next moon; switching tether current off, stored power is then used as the SC makes a number of flybys of each moon. Radiation dose is calculated throughout the mission, during capture, flybys and moves between moons. The tour mission is limited by both power needs and accumulated dose. The three-stage apojove lowering down to Ganymede, Io , and Europa resonances would total less than 14 weeks, while 4 Ganymede, 20 Europa, and 16 Io flybys would add up to 18 weeks, with the entire mission taking just over seven months and the accumulated radiation dose keeping under 3 Mrad (Si) at 10-mm Al shield thickness.

Hard transition to chaotic dynamics in Alfvén wave fronts

The derivative nonlinear Schrodinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Jupiter Power Generation with Electrodynamic Tethers at Constant Orbital Energy

An electrodynamic tether system for power generation at Jupiter is presented that allows extracting energy from Jupiters corotating plasmasphere while leaving the system orbital energy unaltered to first order. The spacecraft is placed in a polar orbit with the tether spinning in the orbital plane so that the resulting Lorentz force, neglecting Jupiters magnetic dipole tilt, is orthogonal to the instantaneous velocity vector and orbital radius, hence affecting orbital inclination rather than orbital energy. In addition, the electrodynamic tether subsystem, which consists of two radial tether arms deployed from the main central spacecraft, is designed in such a way as to extract maximum power while keeping the resulting Lorentz torque constantly null. The power-generation performance of the system and the effect on the orbit inclination is evaluated analytically for different orbital conditions and verified numerically. Finally, a thruster-based inclination-compensation maneuver at apoapsis is added, resulting in an efficient scheme to extract energy from the plasmasphere of the planet with minimum propellant consumption and no inclination change. A tradeoff analysis is conducted showing that, depending on tether size and orbit characteristics, the system performance can be considerably higher than conventional power-generation methods.