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At least 91 records · Page 5

Robust Controller Synthesis for Vision-based Spacecraft Guidance and Control

This work develops a method for Robust Controller for Vision-based Spacecraft (RCVS) guidance and control, integral to the robust autonomy framework for multi-spacecraft for- mation control and reconfiguration applications. The method is built around the use of a photo-realistic simulator, where a camera is deployed on a tracking spacecraft (ego) in order to observe an uncontrolled spacecraft (target) in a Low Earth Orbit (LEO). In this direction, the proposed approach performs the relative state (attitude and position) estimation of the target spacecraft using Convolutional Neural Network (CNN). The state estimation error is then modeled and the corresponding error-bounds are obtained around a nominal trajectory of the ego and target spacecraft. Next, this work proposes a linear matrix inequalities (LMIs) based approach to controller synthesis, guaranteed to be robust against both model uncertainties and measurement errors, resulting from vision-based estimation. This controller is comprised of two distinct components, one synthesized based on the nominal trajectory, while the “robust” component corrects for deviations from the nominal trajectory. Finally, a tracking scenario that directly utilize the image data for spacecraft guidance and control, is presented to showcase the performance of the proposed robust autonomy framework.

Rahmani, Amir↗

Interactive orbital proximity operations planning system instruction and training guide

This guide instructs users in the operation of a Proximity Operations Planning System. This system uses an interactive graphical method for planning fuel-efficient rendezvous trajectories in the multi-spacecraft environment of the space station and allows the operator to compose a multi-burn transfer trajectory between orbit initial chaser and target trajectories. The available task time (window) of the mission is predetermined and the maneuver is subject to various operational constraints, such as departure, arrival, spatial, plume impingement, and en route passage constraints. The maneuvers are described in terms of the relative motion experienced in a space station centered coordinate system. Both in-orbital plane as well as out-of-orbital plane maneuvering is considered. A number of visual optimization aids are used for assisting the operator in reaching fuel-efficient solutions. These optimization aids are based on the Primer Vector theory. The visual feedback of trajectory shapes, operational constraints, and optimization functions, provided by user-transparent and continuously active background computations, allows the operator to make fast, iterative design changes that rapidly converge to fuel-efficient solutions. The planning tool is an example of operator-assisted optimization of nonlinear cost functions.

Grunwald, Arthur J.↗

A Prognostics Framework Development for Swarm Satellite Formations

Prognostics is the science of predicting the failure(s) of a component or a system and understanding how the performance will change in the event of a failure or degradation mechanism. With accurate predictions of possible failures, autonomous mitigative actions can be taken to correct/repair any issues or alert human operators of a failure threshold exceedance requiring condition-based maintenance. Although there is extensive research on failure predictions for a component or a system, there are significantly more opportunities to foray into failure predictions and prognostics for a system of systems such as an airspace consisting of multiple aircraft, a fleet of unmanned aerial vehicles, and a swarm of intelligent satellite systems. Failure prediction and mitigation are particularly important in autonomous systems such as satellite swarm systems that need effective resource management and minimal human interactions. Based on NASA's decadal survey, there is a clear need to prioritize the development of satellite swarm technology for studies of space physics and Earth science. The science community will propose future missions that return in-situ measurements from a 3-D (three-dimensional) volume of space, with relative spacecraft motion and inter-satellite baselines controlled according to the mission objectives. For such multi-spacecraft missions, it is required that ground operations resources do not scale with the number of satellites, thus compromising the swarm or leading to inefficiencies in resource allocation. Swarms of tens or hundreds of small satellites will require autonomy in attitude control, navigation and failure. Although significant research has been conducted in the areas of autonomous formation flying algorithms, less attention has been given to the development of resilient systems robust to failures.The focus of this research paper is the integration of model-based prognostics into the swarm dynamics control and decision-making algorithms. We simulate swarm management strategies for a subsystem failure to demonstrate the importance of failure predictions by comparing two cases: (i) no health information is provided to the system and utilized in the decision-making process and (2) system health information is obtained using prognostics and employed by the control system. One example scenario presented is for the GPS (Global Positioning System) system of an individual satellite to perform off-nominally due to increasing estimated error. In this scenario, the keep-out zone for that satellite would become more conservative, thereby decreasing the risk of collision. This is achieved via tuning the individual artificial repulsive functions assigned to each satellite.This paper is structured as follows. First we provide an overview of current swarm technology development, where we specifically use the term swarm to define multiple satellites flying in formation in similar orbits, with cross-link communication and station-keeping capabilities. Second, we give an introduction to the Swarm Orbital Dynamics Advisor (SODA), a tool that accepts high-level configuration commands and provides the orbital maneuvers required to achieve the prescribed formation configuration. Third, we provide the details of the model-based prognostics algorithm implementation in SODA. Finally, we present different case studies for potential component/subsystem failures and the swarm responses based with and without failure prediction information.

prognostics↗

Interactive method for planning constrained, fuel-optimal orbital proximity operations

An interactive graphical method for planning fuel-efficient rendezvous trajectories in the multi-spacecraft environment of the space station is presented. The method allows the operator to compose a multi-burn transfer trajectory between arbitrary initial chaser and target trajectories. The available task time of the mission is limited and the maneuver is subject to various operational constraints, such as departure, arrival, plume impingement and spatial constraints. The maneuvers are described in terms of the relataive motion experienced in a Space-Station centered coordinate system. The optimization method is based on the primer vector and its extension to non-optimal trajectories. The visual feedback of trajectory shapes, operational constraints, and optimization functions, provided by user-transparaent and continuously active background computations, allows the operator to make fast, iterative design changes which rapidly converge to fuel-efficient solutions. The optimization functions are presented. A variety of simple design examples has been presented to demonstrate the usefulness of the method. In many cases the addition of a properly positioned intermediate waypoint resulted in fuel savings of up to 30%. Furthermore, due to the counter-intuitive character of the optimization functions, most fuel-optimal solutions could not have been found without the aid of the optimization tools. Operating the system was found to be very easy, and did not require any previous in-depth knowledge of orbital dynamics or trajectory. The planning tool is an example of operator assisted optimization of nonlinear cost-functions.

Abramovitz, Adrian↗

Spacecraft Software Maintenance: An Effective Approach to Reducing Costs and Increasing Science Return

Flight software is a mission critical element of spacecraft functionality and performance. When ground operations personnel interface to a spacecraft, they are typically dealing almost entirely with the capabilities of onboard software. This software, even more than critical ground/flight communications systems, is expected to perform perfectly during all phases of spacecraft life. Due to the fact that it can be reprogrammed on-orbit to accommodate degradations or failures in flight hardware, new insights into spacecraft characteristics, new control options which permit enhanced science options, etc., the on- orbit flight software maintenance team is usually significantly responsible for the long term success of a science mission. Failure of flight software to perform as needed can result in very expensive operations work-around costs and lost science opportunities. There are three basic approaches to maintaining spacecraft software--namely using the original developers, using the mission operations personnel, or assembling a center of excellence for multi-spacecraft software maintenance. Not planning properly for flight software maintenance can lead to unnecessarily high on-orbit costs and/or unacceptably long delays, or errors, in patch installations. A common approach for flight software maintenance is to access the original development staff. The argument for utilizing the development staff is that the people who developed the software will be the best people to modify the software on-orbit. However, it can quickly becomes a challenge to obtain the services of these key people. They may no longer be available to the organization. They may have a more urgent job to perform, quite likely on another project under different project management. If they havn't worked on the software for a long time, they may need precious time for refamiliarization to the software, testbeds and tools. Further, a lack of insight into issues related to flight software in its on-orbit environment, may find the developer unprepared for the challenges. The second approach is to train a member of the flight operations team to maintain the spacecraft software. This can prove to be a costly and inflexible solution. The person assigned to this duty may not have enough work to do during a problem free period and may have too much to do when a problem arises. If the person is a talented software engineer, he/she may not enjoy the limited software opportunities available in this position; and may eventually leave for newer technology computer science opportunities. Training replacement flight software personnel can be a difficult and lengthy process. The third approach is to assemble a center of excellence for on-orbit spacecraft software maintenance. Personnel in this specialty center can be managed to support flight software of multiple missions at once. The variety of challenges among a set of on-orbit missions, can result in a dedicated, talented staff which is fully trained and available to support each mission's needs. Such staff are not software developers but are rather spacecraft software systems engineers. The cost to any one mission is extremely low because the software staff works and charges, minimally on missions with no current operations issues; and their professional insight into on-orbit software troubleshooting and maintenance methods ensures low risk, effective and minimal-cost solutions to on-orbit issues.

Shell, Elaine M.↗

Internet Technologies for Space-based Communications: State of the Art and Challenges

The Internet is rapidly changing the ways we communicate information around the globe today. The desire to provide Internet-based services to anyone, anywhere, anytime has brought satellite communications to the forefront to become an integral part of the Internet. In spite of the distances involved, satellite links are proving to be capable of providing Internet services based on Internet protocol (TCP/IP) stack. This development has led to the question particularly at NASA; can satellites and other space platforms become an Internet-node in space? This will allow the direct transfer of information directly from space to the users on Earth and even be able to control the spacecraft and its instruments. NASA even wants to extend the near earth space Internet to deep space applications where scientists and the public here on Earth may view space exploration in real time via the Internet. NASA's future solar system exploration will involve intensive in situ investigations of planets, moons, asteroids, and comets. While past missions typically involved a single fly-by or orbiting science spacecraft, future missions will begin to use fleets of small, highly intelligent robotic vehicles to carry out collaborative investigations. The resulting multi-spacecraft topologies will effectively create a wide area network spanning the solar system. However, this will require significant development in Internet technologies for space use. This paper provides the status'of the Internet for near earth applications and the potential extension of the Internet for use in deep space planetary exploration. The paper will discuss the overall challenges of implementing the space Internet and how the space Internet will integrate into the complex terrestrial systems those forms the Internet of today in a hybrid set of networks. Internet. We envision extending to the deep space environment such Internet concepts as a well-designed layered architecture. This effort will require an ability to develop and infuse new physical layer technology to increase network bandwidth at very low-bit error rates. In addition, we identify network technologies such as routers and switches needed to maintain standard application layer interfaces, while providing low-cost, efficient, modular networking solutions. We will describe the overall architectural approach to extending the concept of the Internet to space and highlight the important technological challenges and initiatives that will make it a reality.

Bhasin, K.↗

Optimizing Spacecraft Placement for Liaison Constellations

A navigation and communications network is proposed to support an anticipated need for infrastructure in the Earth-Moon system. Periodic orbits will host the constellations while a novel, autonomous navigation strategy will guide the spacecraft along their path strictly based on satellite-to-satellite telemetry. In particular, this paper investigates the second stage of a larger constellation optimization scheme for multi-spacecraft systems. That is, following an initial orbit down-selection process, this analysis provides insights into the ancillary problem of spacecraft placement. Two case studies are presented that consider configurations of up to four spacecraft for a halo orbit and a cycler trajectory.

lunar cycler orbits↗

An X-ray Interferometry Concept for the ESA Voyage 2050 Programme

We have proposed the development of X-ray interferometry as part of ESA’s Voyage 2050 programme, to reveal the universe at high energies with ultra-high spatial resolution. With only a 1 m baseline, which could be accommodated on a single spacecraft, X-ray interferometry can reach 100μas resolution at 10 ̊A (1.24 keV) and exceed that of the Event Horizon Telescope at 2 ̊A (6.2 keV). A multi-spacecraft ‘constellation’ interferometer would resolve well below 1μas. Here we focus on the single-spacecraft interferometer design and discuss the process of fringe detection and image reconstruction from multiple baselines, showing simulated images of testcases from our Voyage 2050 White Paper. We also discuss the challenges and feasibility of reaching the technical requirements needed for a single-spacecraft interferometer. Most key requirements are already feasible or within easy reach. Besides a ground-based testbed, covered elsewhere in these proceedings, the most important areas for development include large format, small-pixel X-ray detectors and pointing which is stable or can be reconstructed to tens of μas precision.

Phil Uttley↗

Searching for Turbulent Spectra in Mutliple Spacecraft Observations

The subject of magnetohydrodynamic simulations in the 1980's, magnetic turbulence has reemerged as a favored explanation for the production of fast magnetic reconnection. Recent three-dimensional simulations reveal the formation of secondary islands that serve to shorten the current sheet and increase the accelerating electric field, while both simulations and observations witness electron holes whose collapse energizes electrons. However, little work has been done to investigate the presence of turbulent magnetic and electric field spectra in association with in situ reconnection observations in space. In this study we address this deficiency by analyzing the wavelength spectra of two reconnection events established by multiple spacecraft observations in previous publications. We apply a k-filtering analysis to determine the wave vectors. To optimize the quality of the k-filtering analysis and minimize aliasing, we select multi-spacecraft observations having optimal spacecraft tetrahedral geometry and dimensions that resolve wavelengths within the ion diffusion region. We have chosen one dayside and one nightside reconnection event each observed by the Cluster spacecraft. Spatial correlation between the reconnecting current sheet and a turbulent magnetic spectrum supports an association between turbulence and reconnection in space. The k-filtering method, a wavelet time-frequency spectrum, and a polarization analysis serve to identify wave modes associated with the turbulence. A calculation of the reconnection electric field based on the normal component of the reconnecting magnetic field provides an estimate of the reconnection rate.

Wendel, Deirdre E.↗

Communication-Aware Orbit Design for Small Spacecraft Swarms around Small Bodies

Exploration of small Solar System bodies has traditionally been performed by single monolithic spacecraft carrying a number of science instruments. However, science instruments typically cannot be operated simultaneously due to the instrument requirements including optimal viewing angle, surface illumination, altitude and ground resolution, power, and data constraints. This observation has motivated interest in multi-spacecraft architectures where a swarm of small spacecraft, each carrying a single science instrument, studies a small body after being deployed by a carrier spacecraft, which then collects data from the vehicles and relays it to Earth. Such architectures hold promise to yield significant improvements in mission efficiency, increases in data quality, and shorter mission duration. A key difficulty in the design of such missions is the selection of orbits for the small spacecraft, which must satisfy not only instrument requirements, but also strict inter-spacecraft communication and on-board storage constraints. To address this, in this paper, we present a novel computationally-efficient optimization algorithm for \emph{communication-aware design} of the orbits of a small spacecraft swarm orbiting a small body. The proposed approach captures constraints including instrument requirements, inter-spacecraft communication bandwidths, and on-board memory usage, and it can accommodate highly irregular gravity field models and surface geometries. We propose an efficient algorithm for optimization of instrument observations and inter-spacecraft communications; we then leverage the differentiable nature of the proposed algorithm to accelerate a gradient-based global search algorithm. Numerical simulations of a six-spacecraft swarm studying 433 Eros show that the proposed approach successfully identifies high-quality orbits, and significantly outperform communication-agnostic optimization techniques, resulting in a 10% increase in scientific returns and a 30% increase in the quality of the collected data.

Rahmani, Amir↗

Magnetic Reconnection: Theoretical and Observational Perspectives: Preface

Magnetic reconnection is a fundamental plasma-physical process by which energy stored in a magnetic field is converted, often explosively, into heat and the kinetic energy of the charged particles that constitute the plasma. It occurs in a variety of astrophysical settings, ranging from the solar corona to pulsar magnetospheres and winds, as well as in laboratory fusion experiments, where it is responsible for sawtooth crashes. First proposed by R.G. Giovanelli in the late I 940s as the mechanism responsible for solar flares, magnetic reconnection was invoked at the beginning of the space age to explain not just solar flares but also the transfer of energy, mass, and momentum from the solar wind to Earth's magnetosphere and the subsequent storage and release of the transferred energy in the magnetotai\. During the half century or so that has followed the seminal theoretical works by J.W. Dungey, P.A. Sweet, E.N. Parker, and H.E. Petschek, in-situ measurements by Earth-orbiting satellites and remote-sensing observations of the solar corona have provided a growing body of evidence for the occurrence of reconnection at the Sun, in the solar wind, and in the near-Earth space environment. The last thirty years have also seen the development of laboratory reconnection experiments at a number of institutions. In parallel with the efforts of experimentalists in both space and laboratory plasma physics, theorists have investigated, analytically and with the help of increasingly powerful MHD, hybrid, and kinetic numerical simulations, the structure of the diffusion region, the factors controlling the rate, onset, and cessation of reconnection, and the detailed physics that enables the demagnetization of the ions and electrons and the topological reconfiguration of the magnetic field. Moreover, the scope of theoretical reconnection studies has been extended well beyond solar system and laboratory plasmas to include more exotic astrophysical plasma systems whose strong (10(exp 14)-10(exp 15) G) magnetic fields require that models of reconnection in these systems incorporate quantum electrodynamical, special relativistic, and radiative effects. The papers collected in this topical issue of Space Science Reviews cover different aspects of recent theoretical and observational work on magnetic reconnection in solar and space physics, astrophysics, and laboratory plasma physics. They derive from presentations given at a workshop on magnetic reconnection held in the Yosemite National Park, February 8-12,2010. The intent of the workshop was to stimulate, through a combination of tutorial talks, shorter focused talks, and extensive informal discussions, an interdisciplinary dialogue among members of the different research communities working on the problem of magnetic reconnection. One of the motivating considerations for holding the workshop was its relevance to NASA's Magnetospheric Multiscale (MMS) mission, scheduled for launch in 2014. The four identically instrumented MMS spacecraft are designed to study reconnect ion in Earth's magnetosphere and, specifically, to probe the electron diffusion region in order to determine the microphysical processes that enable the change in the topology of the magnetic field. Building on the achievements of the multi spacecraft Cluster and THEMIS missions, MMS will use the magnetosphere as an astrophysical plasma laboratory in which to test, through in-situ measurement of the plasma, energetic particles, and electric and magnetic fields, various models and theories that have emerged during the past twenty years, a period of extraordinarily productive theoretical and observational work.

Lewis, W. S.↗

Collaborative Pose Estimation of An Unknown Target Using Multiple Spacecraft

A reliable method for pose estimation of an unknown and uncooperative space target using monocular vision remains an open problem. Vision-based pose determination can be challenging in case of unfavorable illumination, time-varying conditions due to rotational motion and relative orbit, and scale ambiguity resolution. To address these challenges, we propose a novel collaborative pose determination algorithm called Multi- Spacecraft Simultaneous Estimation of Pose and Shape algorithm or M-SEPS.Within M-SEPS, a team of chaser spacecraft, each equipped with a monocular camera, exchange information over a local network to jointly estimate the relative kinematic state of the target and its sparse shape landmarks. In this approach, each spacecraft processes its own images and observes particular target landmarks in parallel and in a distributed fashion. Then, the local network is exploited by the spacecraft to share their consensus proposals and aggregate them to achieve the joint estimate. We validate our algorithm using simulations of relative orbits and observations, captured by each chaser spacecraft. To the best of the authors’ knowledge, this is the first cooperative, vision-based algorithm for estimating the pose and shape of a space object for an arbitrary number of spacecraft.

Chung, Soon-Jo↗

The First Widespread Solar Energetic Particle Event Observed By Solar Orbiter on 2020 November 29

Context. On 2020 November 29, the first widespread solar energetic particle (SEP) event of solar cycle 25 was observed at four widely separated locations in the inner (. 1AU) heliosphere. Relativistic electrons as well as protons with energies > 50MeV were observed by Solar Orbiter (SolO), Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A and multiple near-Earth spacecraft. The SEP event was associated with an M4.4 class X-ray flare and accompanied by a coronal mass ejection (CME) and an extreme ultraviolet (EUV) wave as well as a type II radio burst and multiple type III radio bursts. Aims. We present multi-spacecraft particle observations and place them in context with source observations from remote sensing instruments and discuss how such observations may further our understanding of particle acceleration and transport in this widespread event. Methods. Velocity dispersion analysis (VDA) and time shift analysis (TSA) were used to infer the particle release times at the Sun. Solar wind plasma and magnetic field measurements were examined to identify structures that influence the properties of the energetic particles such as their intensity. Pitch angle distributions and first-order anisotropies were analyzed in order to characterize the particle propagation in the interplanetary medium. Results. We find that during the 2020 November 29 SEP event, particles spread over more than 230° in longitude close to 1AU. The particle onset delays observed at the different spacecraft are larger as the flare–footpoint angle increases and are consistent with those from previous STEREO observations. Comparing the timing when the EUV wave intersects the estimated magnetic footpoints of each spacecraft with particle release times from TSA and VDA, we conclude that a simple scenario where the particle release is only determined by the EUV wave propagation is unlikely for this event. Observations of anisotropic particle distributions at SolO, Wind, and STEREO-A do not rule out that particles are injected over a wide longitudinal range close to the Sun. However, the low values of the first-order anisotropy observed by near-Earth spacecraft suggest that diffusive propagation processes are likely involved.

A Kollhoff↗

Cluster in the Auroral Acceleration Region

Due to a fortuitous evolution of the Cluster orbit, the Cluster spacecraft penetrated for the first time in its mission the heart of Earth's auroral acceleration region (AAR) in December 2009 and January 2010. During this time a special AAR campaign was carried out by the various Cluster instrument teams with special support from ESA and NASA facilities. We present some of the first multi-spacecraft observations of the waves, particles and fields made during that campaign. The Cluster spacecraft configuration during these AAR passages was such that it allowed us to explore the differences in the signatures of waves, particles, and fields on the various spacecraft in ways not possible with single spacecraft. For example, one spacecraft was more poleward than the other three (C2), one was at higher altitude (C1), and one of them (0) followed another (C4) through the AAR on approximately the same track but delayed by three minutes. Their separations were generally on the order of a few thousand km or less and occasionally two of them were lying along the same magnetic field line. We will show some of the first analyses of the data obtained during the AAR campaign, where upward and downward current regions, and the waves specifically associated with those regions, as well as the auroral cavities, were observed similarly and differently on the various spacecraft, helping us to explore the spatial, as well as the temporal, aspects of processes occurring in the AAR.

Pickett, Jolene S.↗

Non-propagating structures and propagating waves in solar wind turbulence revealed by simulations and observations

Structures and waves are common features of solar wind turbulence at various scales. The interplay between structures and waves is important for processes such as the turbulent energy cascade, plasma heating, and particle scattering. Our understanding of turbulence has been advanced by not only new space missions and numerical simulations, but also techniques that have been developed to interpret the rapidly growing turbulence data. We review basic models of turbulence with a specific focus on the analysis methods for understanding magnetic structures and waves. MHD and kinetic waves in single-spacecraft time series measurements can be identified through mode decomposition or their characteristic polarization signatures. The structures in this paper are considered as zero-frequency, non-propagating or convected modes embedded in the solar wind. The synergy between observations and simulations is most evident in the application of spatial-temporal analysis to multi-spacecraft observation and turbulence simulations. The spatial-temporal analysis has greatly improved our understanding of structures and waves in turbulence. We conclude by discussing prospects for future research.

79 ASTRONOMY AND ASTROPHYSICS↗

Streamlining Collaborative Planning in Spacecraft Mission Architectures

During the past two decades, the planning and scheduling community has substantially increased the capability and efficiency of individual planning and scheduling systems. Relatively recently, research work to streamline collaboration between planning systems is gaining attention. Spacecraft missions stand to benefit substantially from this work as they require the coordination of multiple planning organizations and planning systems. Up to the present time this coordination has demanded a great deal of human intervention and/or extensive custom software development efforts. This problem will become acute with increased requirements for cross-mission plan coordination and multi -spacecraft mission planning. The Advanced Architectures and Automation Branch of NASA's Goddard Space Flight Center is taking innovative steps to define collaborative planning architectures, and to identify coordinated planning tools for Cross-Mission Campaigns. Prototypes are being developed to validate these architectures and assess the usefulness of the coordination tools by the planning community. This presentation will focus on one such planning coordination too], named Visual Observation Layout Tool (VOLT), which is currently being developed to streamline the coordination between astronomical missions

Misra, Dhariti↗

ULF waves in the foreshock

We review our current knowledge of ULF waves in planetary foreshocks. Most of this knowledge comes from observations taken within a few Earth radii of the terrestrial bow shock. Terrestrial foreshock ULF waves can be divided into three types, large amplitude low frequency waves (approximately 30-s period), upstream propagating whistlers (1-Hz waves), and 3-s waves. The 30-s waves are apparently generated by back-streaming ion beams, while the 1-Hz waves are generated at the bow shock. The source of the 3-s waves has yet to be determined. In addition to issues concerning the source of ULF waves in the foreshock, the waves present a number of challenges, both in terms of data acquisition, and comparison with theory. The various waves have different coherence scales, from approximately 100 km to approximately 1 Earth radius. Thus multi-spacecraft separation strategies must be tailored to the phenomenon of interest. From a theoretical point of view, the ULF waves are observed in a plasma in which the thermal pressure is comparable to the magnetic pressure, and the rest-frame wave frequency can be moderate fraction of the proton gyro-frequency. This requires the use of kinetic plasma wave dispersion relations, rather than multi-fluid MHD. Lastly, and perhaps most significantly, ULF waves are used to probe the ambient plasma, with inferences being drawn concerning the types of energetic ion distributions within the foreshock. However, since most of the data were acquired close to the bow shock, the properties of the more distant foreshock have to be deduced mainly through extrapolation of the near-shock results. A general understanding of the wave and plasma populations within the foreshock, their interrelation, and evolution, requires additional data from the more distant foreshock.

Greenstadt, E. W.↗