Charge Drag Research Articles

Collision avoidance of satellites using ionospheric drag

50,000+ satellites are scheduled for launch by 2030, bringing both massive opportunities and equally massive challenges. Key among these challenges is the ability to sustainably operate Low Earth Orbit (LEO) spacecraft in an increasingly congested environment where collision avoidance manoeuvres are routine and fuel is limited. This paper explores the application of ionospheric drag as an alternative, propellantless collision avoidance mechanism for satellites with altitudes ranging between 350 and 500 km. This is achieved through the use of an in-house propagation suite developed to support UNSW Canberra Space’s in-orbit Ionospheric Aerodynamic Experiment (IEX) on the M2 spacecraft (NORAD ID: 47967 & 45727). The relative impact of neutral (thermospheric) to charged (ionospheric) drag on along-track separation for a range of spherical bodies with surface potentials ranging between 0 V to -100 V with respect to a quasi-neutral freestream plasma was investigated. This provides a first-order indication of the potential effectiveness of ionospheric drag for collision avoidance based on prior numerical and ground-based investigations into ionospheric drag. The Debris Risk Assessment and Mitigation Analysis software from the European Space Agency was also harnessed to discern the relative performance of both the charged and flared attitude satellites against a common control satellite. The ESA stipulates that a Collision Probability Level value greater than the accepted value of 1E−04 between two satellites requires a risk avoidance manoeuvre, with a conservative approach requiring manoeuvres for values greater than 1E−05. For all test regimes at 350km altitude, at least a 60% reduction in time to achieve the NASA approved risk reduction factor of 31.6 at the time of closest approach for a pre-manoeuvre Collision Probability Level of 2.8E−05 was achieved when using the flared neutral method in comparison to the feathered charged method. Based on these results, this paper finds that ionospheric drag may represent a useful alternative propellantless collision avoidance mechanism for satellites within the altitude range of 350 to 500 km. Future work is needed to refine ionospheric drag models and consider the absolute effectiveness of using ionospheric drag at higher altitudes and in tandem applications to the flared arrangement.

Ionospheric drag for accelerated deorbit from upper low earth orbit

Orbit debris mitigation restrictions placed on the growing number of miniaturised spacecraft often constrain their operational altitudes to less than approximately 600km where drag accelerations are sufficient to deorbit the spacecraft within 25 year guidelines. Operation at higher, Low Earth Orbit (LEO) altitudes often necessitates active measures to deorbit miniaturised spacecraft such as propulsion systems. However, the inclusion of propulsion systems is not always desirable because of the added cost and complexity. This work investigates the feasibility of ionospheric drag, the component of drag caused by an electrically charged body’s exchange of momentum with the ionosphere, to accelerate the deorbit of miniaturised spacecraft in high LEO (600–1000 km altitude). This work studies how actively charging the surface of a miniaturised satellite in high LEO may enhance the overall magnitude of the drag acceleration, due to the ionospheric drag, acting to deorbit the spacecraft. This is achieved using surrogate models of the charged drag coefficient, as a function of plasma scaling parameters, generated by Particle-in-Cell simulations. The charged drag coefficient surrogate model is incorporated into an orbit propagator where deorbit times are predicted over various orbital and vehicular initial conditions. Results suggest that the magnitude of ionospheric drag can be an order of magnitude larger than the neutral drag at 850 km altitude compared to approximately half the magnitude of neutral drag at 500 km altitude. Therefore, ionospheric drag is relatively more efficient at deorbiting spacecraft at high LEO compared to neutral drag. Additionally, the magnitude of ionospheric drag is tailorable based on changes in the electrical surface potential of the satellite relative to a quasi-neutral free-stream plasma. The primary payload of many miniaturised spacecraft often require high-voltage electrical systems. These same electrical systems could conceivably be utilised to generate ionospheric drag via surface charging, at the end of the mission-life, at little additional cost or system complexity. Thus, the implications of this work include the possible uncovering of a simple mechanism for deorbiting miniaturised spacecraft from high LEO altitudes for compliance with orbit debris mitigation guidelines.

Characterising satellite aerodynamics in Very Low Earth Orbit inclusive of ion thruster plume-thermosphere/ionosphere interactions

This work presents particle-based kinetic simulations of ion thruster plasma plumes, in an analysis of the modified spacecraft charged drag profile, resultant of plume interactions with the ambient thermosphere/ionosphere in Very Low Earth Orbit (VLEO). VLEO is a highly appealing region for spacecraft operations, as it offers high-performing economical spacecraft platforms, but the mission lifetime is very limited owing to high drag from the residual atmosphere. Detailed characterisation of plume dynamics is vital in exploring the feasibility of Electric Propulsion (EP) as a means of continuous drag compensation at such altitudes. Quasi-neutral Direct Simulation Monte-Carlo – Particle-in-Cell simulations, involving interactions of ion thruster plumes with rarefied ambient thermosphere/ionosphere, are presented for steady drag-compensating thruster firings in orbits of 150 and 400 km. It is shown that the flow profile is affected by a combination of collisional and indirect electrostatic field mechanisms. In the immediate aft region of the spacecraft, the interaction is driven by pick-up of freestream ions within the charge-exchange cloud. The main effect of the plume is to simply deflect the freestream, as ionosphere particles collide with primary beam propellant, and the freestream number density increases at the spacecraft trailing edge as particles are captured at the charge-exchange cloud. The consequences of the observed mechanisms on the spacecraft drag are theorised, and it is shown that effects of EP plume plasma in VLEO should be included in future analyses, to ensure drag models are complete.

Energy Drag in Particle-Hole Symmetric Systems as a Quantum Quench.

Two conducting quantum systems coupled only via interactions can exhibit the phenomenon of Coulomb drag, in which a current passed through one layer can pull a current along in the other. However, in systems with particle-hole symmetry-for instance, the half filled Hubbard model or graphene near the Dirac point-the Coulomb drag effect vanishes to leading order in the interaction. Its thermal analog, whereby a thermal current in one layer pulls a thermal current in the other, does not vanish and is indeed the dominant form of drag in particle-hole symmetric systems. By studying a quantum quench, we show that thermal drag, unlike charge drag, displays a non-Fermi's golden rule growth at short times due to a logarithmic scattering singularity generic to one dimension. Exploiting the integrability of the Hubbard model, we obtain the long-time limit of the quench for weak interactions. Finally, we comment on thermal drag effects in higher dimensional systems.

Effect of ionospheric drag on atmospheric density estimation and orbit prediction

Accurate prediction of aerodynamic forces in Low Earth Orbit (LEO) remains a key challenge for space situational awareness (SSA) and space traffic management (STM) activities. A neglected aspect of the LEO aerodynamics problem is the force resulting from the charged aerodynamic interaction of LEO objects with the ionosphere, i.e. ionospheric aerodynamics. This work studies the effect accounting for ionospheric drag may have on the motion of LEO objects. This work aims to assess the influence of ionospheric aerodynamics on atmospheric density estimation and orbit prediction capabilities essential to SSA and STM services. The approach taken in this work was to apply Particle-in-Cell (PIC) simulations to develop a surrogate model that describes the variation of a charged drag coefficient (CD,C) as a function of plasma scaling parameters. This surrogate model was then incorporated into an orbit propagator, and the influence of ionospheric drag on body motion is studied for a range of conditions. Results indicate that, when inferring atmospheric neutral density from orbit data, neglecting the contribution of ions without accounting for electrodynamic phenomena, may cause an over-prediction of neutral density ranging between 1% and 45% for the space weather condition considered (F10.7=150,ap=5). Including electrodynamic phenomena was seen to increase this over-prediction for all cases. Objects with thick plasma sheaths were shown to be particularly sensitive to ionospheric drag forces; thick plasma sheaths caused by either a reduction in object scale (rB) or increase in surface potential (ϕ). This result has important implications for modelling space debris populations as thick plasma sheaths may arise at natural floating potentials (-0.75V) when debris fragmentation occurs. For example, accounting ionospheric drag on a spherical debris object with a radius of 0.005 m, area-to-mass ratio of 0.0157 m2/kg and floating potential of -0.75 V in a circular equatorial orbit at 350 km altitude was predicted to cause a change in along-track position of 299 m (and a reduction in semi-major axis of 4 m) over a 24-h period. Results also have important implications for modern satellites, where the trend is toward nano/micro-satellite platforms (e.g. CubeSats) with high-voltage powers systems that may inadvertently cause large artificial surface potentials and therefore enhanced ionospheric aerodynamic forces.

Direct and indirect charged aerodynamic mechanisms in the ionosphere

Objects in a flowing plasma may exchange momentum both directly, through gas-surface interactions, and indirectly, through field effects. Applying a control surface approach developed in the study of dusty (complex) plasmas, this work outlines a framework for investigating the relative contribution of direct and indirect charged aerodynamic forces that may arise from the aerodynamic interaction of LEO objects with the ionosphere i.e. ionospheric aerodynamics. In particular, this work focuses on plasma interaction phenomena described by the scaling parameters αk and χ, which describe the ratio of body potential energy to ion kinetic energy and the ratio of body size to sheath thickness respectively. Ion kinetic dominated flows (αk≪1) were found to be well approximated by neutral aerodynamic treatments, the charged drag coefficient (CD,C) of a long (2D) cylinder with a diffusely reflecting surface with complete thermal accommodation to a 500 K wall calculated as 2.232. Body potential dominated systems (αk≫1), however, were dominated by indirect charged aerodynamic mechanisms, an example being the indirect thrust required to balance the sheath driven acceleration of ions through the fore-body sheath, which caused an 82% reduction in net charged drag for the αk=16.9 case. This drag reduction was partially offset by indirect drag forces caused by the deflection of non-colliding ions, the net CD,C being 7.741 for the αk=16.9. A similar study of the relative sheath thickness, described by χ, saw asymptotic behaviours given a constant αk of 1.072; direct charged drag forces becoming either Orbital Motion Limit (OML) for thick-sheath systems (χ→0) or sheath-limited (χ≫1). These results demonstrate the importance of accounting for both direct and indirect charged aerodynamic forces when studying ionospheric aerodynamics, while also providing new physical insights into physical mechanisms momentum exchange processes between a flowing plasma and immersed object.

Effect of Relaxation on Drag Forces and Diffusivities of Particles Confined in Rectangular Channels

When a particle is moving inside a channel, its hydrodynamic interaction with channel walls increases its drag coefficient, causing a diffusivity reduction. For charged particles moving in an electrolytic solution, there is an additional drag due to the distortion of an electrical double layer caused by particle motion known as the relaxation effect. Effects of relaxation on drag forces on spheres confined in rectangular channels are computed employing perturbations involving particle Peclet number and surface charge densities. Results indicate that confinement amplifies electrokinetic retardation; increasing the relative particle size or decreasing the channel cross section area enhances the relaxation effect. With the relative particle size kept constant, the relaxation effect on the drag exerted on charged spheres in cylindrical pores with its smaller cross section area is stronger than that on charged spheres in rectangular channels and slit pores. However, for certain values of Debye length and particle size, the ratio between excess drag due to relaxation on confined charged spheres and hydrodynamic drag on uncharged spheres confined at the same location is higher for particles in rectangular channels, resulting in higher percentages of diffusivity reduction. Diffusivity reduction due to relaxation of charged particles in square ducts displays a maximum as a function of relative particle size, whereas that of charged particles in rectangular channels with higher cross section aspect ratio increases monotonically as particle size increases.

A closer look at charge drag

The observation that charges flowing through one quantum wire can drag charges in a second, unconnected wire either forwards or backwards requires a re-interpretation of Coulomb drag.

Dynamical correlations in electronic transport through a system of coupled quantum dots

Current auto and cross correlations are studied in a system of two capacitively coupled quantum dots. We are interested in a role of Coulomb interaction in dynamical correlations, which occur outside the Coulomb blockade region (for high bias). After decomposition of the current correlation functions into contributions between individual tunneling events, we can show which of them are relevant and lead to sub-/super-Poissonian shot noise and negative/positive cross correlations. The results are differentiated for weak and strong interdot couplings. Interesting results are for the strong-coupling case when electron transfer in one of the channel is strongly correlated with charge drag in the second channel. We show that cross correlations are nonmonotonic functions of bias voltage and they are in general negative (except some cases with asymmetric tunnel resistances). This is effect of local potential fluctuations correlated by Coulomb interaction, which mimics the Pauli exclusion principle.

Can charge drag explain the Pioneer anomaly?

Abstract According to precise measurements of Doppler shift for the signals from Pioneers 10 and 11, these two spacecraft have been experiencing a drag-like force of about 2 × 10 −7 Newtons since they passed into the outer solar system. Recently, Nieto et al. [M.M. Nieto, et al., Phys. Lett. B 613 (2005) 11] have estimated the drag on these craft that would be caused by impacting dust grains in the region beyond 20 AU. They conclude that the amount of dust required to explain the anomaly is excessive, about 3 × 10 −19 g / cc . However, if the two spacecraft carry a large electric charge, then charge drag against the dusty plasma in this region could be significant. In the present Letter, estimates of this force are made, and conditions are found under which the observed level of drag is obtained. A density of charged dust of around 5 × 10 −22 g / cc at a kinetic temperature of 105 K suffices, provided that the dust grains are very small (mass ∼ 100 amu ) and the spacecraft charge is near its reported maximum ( Z ∼ 10 12 ).

Reassessment of the charge and neutral drag of LAGEOS and its geophysical implications

The influence of an external drag to account for the secular decrease of the semi‐major axis of LAGEOS is reexamined. We develop a theory for the neutral and electric drag more refined than those previously available. The charge drag appears to be the most likely cause of the secular decrease of LAGEOS of about 1.1 mm day−1. Likewise we show the existence of annual and semiannual variations connected with the orientation of the satellite's orbital plane with respect to the sun. Finally we express the electric drag as n5/6 T2/3 in terms of ion number density and absolute temperature. The rate of fall of LAGEOS constrains the range of possible physical states of the plasmasphere at altitudes as high as 6000 km.

On the secular decrease in the semimajor axis of Lageos's orbit

The semimajor axis of the Lageos satellite's orbit is decreasing secularly at the rate of 1.1 mm day−1. Ten possible mechanisms are investigated to discover which one (s), if any, might be causing the orbit to decay. Six of the mechanisms, resonance with the Earth's gravitational field, gravitational radiation, the Poynting-Robertson effect, transfer of spin angular momentum to the orbital angular momentum, drag from near-earth dust, and atmospheric drag by neutral hydrogen are ruled out because they are too small or require unacceptable assumptions to account for the observed rate of decay. Three other mechanisms, the Yarkovsky effect, the Schach effect, and terrestrial radiation pressure give perturbations whose characteristic signatures do not agree with the observed secular decrease (terrestrial radiation pressure appears to be too small in any case); hence they are also ruled out. Charged particle drag with the ions at Lageos's altitude is probably the principal cause of the orbital decay. An estimate of charged particle drag based upon laboratory experiments and satellite measurements of ion number densities accounts for 60 percent of the observed rate of decrease in the semimajor axis, assuming a satellite potential of −1V. This figure is in good agreement with other estimates based on charge drag theory. A satellite potential of −1.5V will explain the entire decay rate. Atmospheric drag from neutral hydrogen appears to be the next largest effect, explaining about 10 percent of the observed orbital decay rate.

Experimental bound on the orbital effects of charge drag

In May 1963 a package containing 4.8×10s copper dipoles, each 1.78 cm in length and 0.00178 cm in diameter, was ejected from a parent satellite into a nearly circular, nearly polar orbit at a mean altitude of about 3650 km. These Project West Ford dipoles were subsequently dispensed individually such that each tumbled rapidly about its center of mass [Waldron et al., 1964; Shapiro et al., 1964]. Because of their extreme thinness, the dipoles are more susceptible to charge (i.e., Coulomb) drag perturbations than are any other satellites; they thus enable a stringent upper bound to be placed on the orbital effects of the drag [Shapiro, 1963a]. As is well known, the main effect of a drag force is to decrease the period and the mean altitude of a satellite. Since orbital period can be measured more accurately, its variations are commonly used to study drag phenomena. But West Ford dipoles can neither be distinguished nor detected individually; it is therefore impossible to monitor the orbital period variations of any given dipole. Fortunately, the dipoles were dispensed in a manner such that their density along the orbit exhibited a logarithmic singularity [Shapiro et al., 1964]. For the first 80 days (i.e., for the first 700 orbital revolutions) the motion of this peak in the density represented essentially the group velocity of the dipole ensemble, and the changes in its orbital period contained the average effects of charge drag. After 80 days, the peak became asymmetrically ‘contaminated’ by dipoles that had lapped and been lapped by it; in addition the peak became far less pronounced and was therefore no longer useful for studying charge drag.

Orbital properties of the West Ford dipole belt

Early in May, 1963 a package containing 4.8×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sup> copper dipoles, each 0.00178 cm in diameter and 1.78 cm in length, was placed into a nearly circular, nearly polar orbit at a mean altitude of 3650 km. A detailed theoretical model including all known perturbing forces was constructed to predict the motion of the individual dipoles from dispensing to final re-entry through the atmosphere. Photoelectric observations, analyzed on the basis of this model, indicate that only about half of the dipoles are orbiting individually. Radar determinations of the spreading of these dipoles along the orbit agree well with the theoretical calculations. Radar observations also confirmed the prediction that the dipole ensemble would exhibit a symmetric, double-jawed structure in the early stages of its development. The ensemble formed a complete belt in about 40 days, as expected. Theory indicated that the in-plane diameter of the physical cross section of the belt would increase most rapidly near perigee and apogee and least rapidly near the semi-latus rectum points, whereas the out-of-plane diameter would increase fastest over the equator and slowest near the poles. In general, the greater the dipole reflectivity and the more isotropic the distribution of dipole tumbling axes, the more rapidly will the cross section grow. Despite the imprecisely known values of these and other initial conditions, predictions were in general accord with measurements: The "half-power width" of the in-plane diameter grew from about 10 km initially to about 140 km near perigee and to about 25 km near the semilatus rectum point 220 days after dispensing; the corresponding out-of-plane growth was from about the same initial value to about 25 km in middle north latitudes, where all measurements were made. The very small in-plane growth at the semilatus rectum point seems to indicate that the effects of dipole-micrometeoroid collisions were substantially less than expected; however, quantitative conclusions cannot yet be reached. The observed double-peak in the dipole density as a function of geocentric range appears to be a consequence of the particular method used for dipole dispensing. Radar determinations of the changes in the orbit that passes through the regions of highest dipole density are in excellent agreement with predictions based on a simple "equivalent-sphere" model, the rms residuals being less than 10 km. The most recent orbit determination, performed 250 days after dispensing, showed that the total decrease in perigee height was more than 800 km, which fortuitously happened to differ from the predicted change by only 1 km. The effects of charge drag were too small to be determined accurately, but could not have caused a decrease in mean altitude at a rate even as low as 10 km/yr, implying that the average magnitude of the electrostatic potential on a typical dipole could not have exceeded 0.15 volt. These results lend credence to the previous prediction that most individual dipoles will have an orbital lifetime of less than three years, and that none will have a lifetime exceeding five years. The dipoles are expected to survive re-entry into the lower atmosphere and to float back to earth unharmed. However, the probability of finding one is minuscule.

Experimental study of charge drag on orbiting dipoles

Six tin dipoles (length ≈34 cm, diameter ≈0043 cm) have been placed in a near-polar, near-circular orbit at a mean altitude of about 3100 km. Radar observations made at the RCA facility at Moorestown, N. J., over a period of about two months, while the dipoles were continuously in sunlight, indicate that charge drag has not produced a decrease in mean altitude at an average rate greater than 0.3 km/year. (The actual charge drag may be far less since, in fact, no systematic change in mean altitude is clearly discernible from the experimental results.) If an approximate scaling law is invoked, it is found that the corresponding upper bound on the decrease in mean altitude of 1-mil-diameter microwave dipoles is about 90 km/year. Making additional assumptions about the plasma leads to establishing an upper limit of 0.6 volt for the average magnitude of the electrostatic potential of the dipoles during this experiment.

Charge drag on Project West Ford Needles

The electrical potential surrounding pieces of wire in the ionosphere is computed assuming photoemission is negligible and is shown to depend essentially logarithmically on distance at small distances from the needle and exponentially on distance at distances of the order of the Debye length for the medium. The resulting drag due to the Coulombic deflection of hydrogen ions is probably an order of magnitude greater than neutral drag at the proposed altitude of 3700 km. At 300 km altitude the greater mass of the ambient O+ ions, the higher electron density, and the lower degree of ionization cause charge drag to be a completely negligible effect.

Comment on Wyatt's analysis of charge drag

Comment on Wyatt's analysis of charge drag

Decay of spin in sputnik I

A secular change took place in the spin-fading rate during the three weeks of observation of the radio transmissions from Sputnik I, between 4 October 1957 and 24 October 1957. This effect allows a determination of atmospheric density near the perigee point. For an assumed atmospheric scale height of 30 km, we derive a value 3.8 × 10 −13 g cm −3 for the density at 220 km. Some fluctuations in the spin decay appear to be real, and may result from small changes in the orientation of the spin axis within the satellite. An alternative interpretation in terms of charged drag resulting from motion of the satellite through the ionospheric plasma, requires a charge of at least 10 4 volts on the satellite. This charge might be acquired in the auroral zone.