Plasma Astrodynamics processes electromagnetic waves generated by charged space objects as they pass through the ionosphere
The number of known objects in orbit is over 45,000, ranging from mission-related, payload, debris, and unknown. The number of untracked pieces of space debris is about 130 million, and current technology, with telescopes and radars, finds it impossible to detect space debris with sizes of 10 cm or smaller. A new satellite-based approach is being developed to observe small objects with in situ observations of electromagnetic plasma waves emitted by space objects moving through the ionosphere in low Earth orbit (LEO). This would allow both detection and tracking of harmful, usually invisible, space shrapnel that could damage active orbital satellites by a process called Plasma Astrodynamics (PAD).
The reception of orbit-driven whistler and compressional Alfvén waves with satellite sensors has been recorded at ranges over 100 km.¹ All orbiting materials excite strong lower hybrid (LH) waves. These LH waves are electrostatic, but can interact with high-latitude irregularities to produce electromagnetic whistler and magnetohydrodynamic (MHD) waves.² Scaled observations and measurements have demonstrated that the Space Object Identification with Measurements of Orbit Driven Waves (SOIMOW) approach can detect 1 cm objects out to ranges of 10 km. This technique is being tested at low latitudes using small-scale irregularities found in equatorial plasma bubbles. Objects crossing horizontal magnetic field lines can launch waves to VLF receivers on the ground or to low-latitude satellite receivers. Simulations demonstrate that this space object detection technique can enhance the ephemeris database for space debris with a wide range of inclinations and altitudes.
Introduction
The SOIMOW/PAD Technique advances the capability for detection and tracking of space debris and other man-made objects in orbit around the Earth. This process requires identification of the object, discrimination from natural events, and extraction of orbit parameters. The steps in space object detection are illustrated in Fig. 1, starting with ground radar and optical observations and adding a Space Debris Hunter (SDH) for analysis of the plasma waves emitted by the targets of interest. A space object moving through the ionosphere will become charged and produce a trail of electrostatic LH waves that may enhance its radar cross section. When the target satellite passes through naturally occurring plasma structures, the LH waves are converted into electromagnetic waves that can propagate over a large distance to a SDH satellite, which processes the signals into an orbit estimation. The SDH satellite-based system developed for the PAD proposal will (1) specify satellite plasma wave instruments for space object detection, (2) provide algorithms to acquire position data on the target and discriminate from natural noise and artificial transmitters, and (3) provide prediction capability for the position of the target in terms of an orbit ephemeris. This will be accomplished with a single satellite or multiple satellites flown in a constellation.
PAD is a new technique that complements and provides more sensitivity than traditional optical and radar tracking of orbiting objects that are part of space domain awareness. The computational models of PAD have used RRI crossed-dipole observation data during actual satellite encounters with additional Line-of-Sight (LOS) estimations. These models show that new pieces of shrapnel can be detected in known regions of space debris and that transient space thruster events are measurable for ranges out to 400 km. Observations and numerical simulations have found that all charged objects in LEO produce electrostatic or electromagnetic plasma waves. The three primary emissions are LH waves in the wake of hypersonic materials, whistler waves excited in a 19.5-degree cone around the magnetic field direction, and compressional Alfvén waves launched across magnetic field lines with frequencies below the ion cyclotron (or lower hybrid) frequency. Applications of these findings include detection of space debris by remote measurements of the whistler and compressional Alfvén at ranges over 100 km, tracking of small, normally invisible space objects that are not detectable with conventional methods, and launching of plasma waves by space objects, particle clouds, and molecules.
This electromagnetic radiation occurs because of space material charging. The amount of charge on artificial material in orbit around the Earth depends on the object’s size. Debris can be products of satellite collisions with sizes ranging from submillimetre to metres. They become charged by both electron and ion collection and photoelectron emission on the surface of the small objects. Similarly, conventional satellites with sizes ranging from Femto- to Large Satellite Mass classifications acquire a spacecraft potential.
The primary advantage of SOIMOW is that the motion of all space objects (Astrodynamics) through a plasma launches waves because the objects become electrically charged and are moving at hypersonic velocities. These waves are either electrostatic (ES or quasi-stationary) or electromagnetic (EM or traveling at a fraction of the speed of light). The EM waves propagate for long distances for the orbiting target to be received as a vector field with temporal oscillatory or transient features that provide information on the source location. The most useful waves are those with speeds much higher than the orbital speed so that the transit time between the target and the host sensors can be neglected. The primary disadvantage of SOIMOW is that the space debris must (a) pass through a region of field-aligned density irregularities or (b) experience a transient charging event to launch electromagnetic waves for remote sensing.² Even though a charged object produces electrostatic waves, these slow or non-propagating waves are not detectable by host sensors in orbit. Ion acoustic solitons formed by “Nonlinear wave excitations by orbiting charged space debris objects” have never been detected in space, because theory predicts that ion-acoustic waves are strongly Landau damped and laboratory experiments with ion acoustic solitons production have shown a limited range for these disturbances. In fact, when electric field probes on the Radio Receiver Instrument (RRI) on the Canadian CASSIOPE satellite were tasked to find these artificial disturbances, ion acoustic signals were not detected but, instead, magnetised plasma signals mode-converted from LH waves to launch whistlers and Alfvén waves were discovered and labeled ‘FLASH’ signals.
Space debris emissions at high latitudes
The auroral region electric fields generate density irregularities along nearly vertical magnetic field lines at irregular time periods depending on solar activity. Forming these irregularities needs solar and geomagnetic storms, leading to enhanced energetic particle precipitation and a large electric field for enhanced plasma convection to drive a gradient drift instability.
Fluctuating energetic electron fluxes from aurora can excite detectable plasma waves from any object passing through the high-latitude space environment. The strength of the radiated signal depends on overall size, surface material, geometric shape, and charge accumulation for each debris object. All of these factors need to be considered when determining the physical size of the target object. The PAD instrument may be designed as a space debris observation system with better sensitivity, easier implementation on host spacecraft, and more reliable algorithms for target tracking than conventional techniques.
An example of SOIMOW/PAD data is finding pieces of shrapnel in known regions of space debris, such as the Chinese CZ-6A fragment detected as a FLASH signature with the Swarm-E RRI located at 75° Latitude, 115° Longitude, and 900 km Altitude (Fig. 2). Algorithms have been developed to distinguish and remove lightning generated whistler (LGW) noise from measurements of space debris signals based on the wave polarization.
The specific components for this PAD system are (1) Host satellite measurement device to record full electric and magnetic field components of plasma waves from space objects to determine direction of arrival, (2) Tested Wave Polarisation, and Wave Filtering to separate natural EM wave noise from PAD FLASH signals that come from man-made objects in LEO, (3) Signal Processing to extract the wave polarisation vector from the wave field vectors with the objective of determining the plasma wave mode and propagation properties, (4) Astrodynamics Algorithms to provide target trajectories of orbiting objects using both Direction Finding (DF) from multiple Host Sensors or a Single Host Platform. The goal of this effort will be to provide Initial Orbit Determination (IOD) data with propagation forward errors less than 1 km after one hour of observations.
A number of FLASH signatures were reported by Bernhardt et al.¹ for both active satellites and space debris. The PAD design has assumed artificial, space-object sources of whistler and compressional Alfvén wave modes. Examples of these electromagnetic FLASH signals detected by the RRI are small space debris (Fig. 2) or an unknown satellite (Fig. 3). The frequency range of these FLASH events is from below the ion cyclotron frequency at about 50 Hz to just above the local value of the lower hybrid frequency on the order of 8 kHz. Along with the space object wave signal, the in situ electric field instrument observes lighting-generated whistlers (LGW), Navy VLF transmitters above 16 kHz, and power line harmonics (PLH) below 500 Hz. The SDH system needs to suppress natural and manmade noise (Fig. 3.).
Space debris emissions at low latitudes
Within 20 degrees of the Earth’s equator, ionospheric irregularities are formed after sunset, with steepening at the bottom of the ionosphere and gravitational forcing to produce equatorial bubbles. These bubbles rise vertically with plasma irregularities that extend along magnetic lines. The equatorial irregularity formation a daily event that is more predictable than at high latitudes. The generation of electromagnetic plasma waves occurs when charged space debris passes through this region of field-aligned irregularities. This process is illustrated in Fig. 4 (left) with a charged target moving across magnetic field lines with field-aligned density irregularities. The electric field in the wake of the target is broken up by the presence of the plasma structures and is converted into both whistler and compressional Alfvén waves (Fig. 4, centre). Fig. 4 (right) shows this process near the equator with an orbit across plasma irregularities generated by a gravitational Rayleigh Taylor instability from the model of Yokoyama et al.⁴
Sensors and algorithms for space object detection sensors can be integrated into satellite constellations to estimate small objects in low Earth orbit. The PAD system will be based on an enhanced Vector Sensor Instrument (VSI) with electric and magnetic dipole antennas capable of simultaneous acquisition of 3-Axis Electric (E) and 3-Axis Magnetic (H) fields (Fig. 5) The plasma wave modes (e.g. whistler, lower hybrid, ion acoustic, shear and torsional Alfvén, etc.) are identified from the polarisation of the electric and magnetic fields and establish the group velocity of the signals traveling between source (target) and sensor (host) satellites. On-board processing will convert the electromagnetic measurements into an E x B Poynting Vector that provides the LOS direction from the source object.
Both Vector Sensor Instrument (VSI) and Null-Signal Direction finding (NSDF) use polarisation-sensitive, pattern-diverse antenna arrays that can be configured from a constellation of SDH sensors. Intelligent sensors will recognise signatures of space objects, reject natural sources, and determine space object flight trajectory. The vector sensor instrument (VSI) yields direction (α, δ)and Polarisation (γ, η) with both E and H fields through Estimation of Signal parameters via Rotational Invariance Techniques (ESPRIT). To get the target locations from these measurements, two astrodynamics methods that were developed for SOIMOW are used, which are called (a) the Single-Satellite Laplace (SS-L) and (b) the Dual-Sat Direction Finding (DS-DF) algorithm.³ For a single host, Laplace’s method employs a time sequence of measurements to determine the target orbit. The nonlinear time-dependent solution uses the two-body satellite motion and LOS range differential equations (2) with μE,the Earth’s gravitational constant. Validation of this procedure uses electric field data acquired from the CASSIOPE RRI as it passed within less than 500 m of the Starlink 2521 satellite on 4 March 2022 as reported by Bernhardt et al.¹ Both the target trajectory and the spacecraft orbit elements are extracted with the Laplace Single Host Algorithm to yield a 28 km position and a 34 m/s error 3000 seconds after observations. For these simulations, the angular accuracy of the vector sensor with harmonic waves impinging upon a single electromagnetic vector sensor is a function of the wave signal-to-noise ratio. For the RRI data on 4 March 2022, measured electric fields have 8 dB signal-to-noise near TCA and minimum RMS error in both azimuth and elevation of 0.3 degrees . The useful target range is less than 100 km.
The Dual-Sat Direction Finding (DS-DF) technique is tested next with simulations of two host satellites separated by 50 km. The space-object target location employs direction finding to determine the crossing of the two defined Lines-of-Sight vectors. The most accurate target locations are found when the target was nearly equidistant and equiangular to each host. The results of this simulated analysis can be seen in Fig. 6. A Gaussian distribution of angular measurement error produces the spread in red points called the target location ambiguity function. Using actual target and host trajectories, an accurate target location is determined for a period of five seconds of the target orbit.
These Initial Orbit Determinations (IODs) are used to derive the target orbit elements with the following expressions from Vallado,³ with μE, the gravitational constant for the Earth. The Orbit elements obtained with the Single-Host Laplace are more accurate than those obtained with the Dual-Sat Direction Finding (DS-DF) Algorithms, because the Single-Host Laplace has the added benefit of Newton’s Second Law of Motion. Future studies will explore improved algorithms for orbital dynamics estimation. These algorithms will be developed for a constellation of three or more satellites using least squares estimators with Singular Value Decomposition (SVD) to provide the target location.
Conclusion
In summary, the orbit determination accuracy of the SOIMOW/PAD technique is illustrated with estimated geocentric distances for the Starlink 2512 target. The three sets of orbit elements were used by the Simplified General Perturbations 4 (SGP4) orbit propagator³ to predict the positions and velocities of the Starlink-sized target (Fig. 7). The three orbit predictions almost overlap.
The difference between the actual and estimated target positions grow with time after observation. The DL-DF target distance error is 258 km, while the Laplace algorithm gives an improved target range error of 28 km after 3000 seconds. The Laplace algorithm gives a minimum target speed error of 34 m/s when compared to the DS-DF error of 300 m/s after 3000 seconds.
Future research will determine if an approach that uses multiple satellites with the addition of Newtonian orbits can yield more accurate measurements.
Acknowledgements
This research is based upon work supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), via 2023-23060200004. The views and conclusions contained herein are solely those of the authors. The U.S. Government is authorised to reproduce and distribute reprints for governmental purposes, notwithstanding copyright annotation therein.
References
- P.A. Bernhardt, et al. (2023) Observations of Plasma Waves
Generated by Charged Space Objects, Phys. Plasmas 30.
- B. Eliasson and P. A. Bernhardt (2025) The generation of whistler, lower hybrid and magnetosonic waves by satellites passing through ionospheric magnetic field aligned irregularities, Phys. of Plasmas, 32.
- Vallado, D.A., (2022), Fundamentals of Astrodynamics and Applications, Space Technology Library, Microcosm Press, Pages 20-33, 97-102, 439-445.
- Yokoyama et al., (2014), Nonlinear growth, bifurcation and pinching of equatorial plasma bubbles simulated by three-dimensional high resolution bubble model, JGR Space Physics, 119.
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