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All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

A review of metasurfaces: Physics and applications

Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam–Berry phase and Huygens' metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. In addition, we also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.

36 MATERIALS SCIENCE↗
DOE OSTI2025

MPEX AI Digital Twins

All magnetically confined plasma fusion power plant concepts (Tokamak, Spherical Tokamak, Stellarator, Mirror, ...) must exhaust the heat and plasma from the core confinement region to the material walls. The primary channel for this exhaust is through a plasma divertor which directs plasma along open magnetic field lines to a material target. The Material Plasma Exposure eXperiment (MPEX) illustrated in Figure 1, is a high-power, steady-state linear plasma device designed to produce the plasma material interaction (PMI) conditions of the divertor of future magnetic confinement fusion power plants: energy flux 20MW/m 2 , ion fluence 1031/m 2 , pulse duration 106 sec. These goals of plasma exposure in MPEX are well beyond those achieved in magnetic fusion experimental devices. Successfully achieving these high power steady state conditions for long pulses requires operational control of the heating and particle sources and the plasma flux to the walls and target. The MPEX AI Hot Spot Controller, proposed in this project, will help achieve the operational milestones of MPEX. The MPEX device will begin commissioning at the end of FY26. A smaller proto-MPEX was operated for 14,666 plasma discharges and will resume operation in September of 2025 as proto-MPEX-lite, with reduced capability, to test a new window for the Helicon plasma source. The proto-MPEX data has undergone surrogate modeling with machine learning methods (R. Archibald, 2022 IEEE International Conference on Big Data). This proto-MPEX data will be used to begin development of the AI digital twins described in this white paper. The scientific mission of MPEX is to qualify materials of different composition for use in the high energy and plasma flux conditions of a fusion power plant. The materials exposed in MPEX will in some cases be exposed to high neutron fluxes at other ORNL facilities to measure the changes to their PMI properties. The targets exposed in MPEX will be transported under vacuum to a Surface Analysis Station (SAS). The SAS will be equipped with the following diagnostics: Focused Ion Beam (FIB) for trench milling, 100-400 angstrom resolution scanning electron microscope (SEM), surface mapping x-ray spectrometer, high resolution camera, and a future upgrade to a laser induced breakdown spectroscopy quadruple mass spectrometer (LIBS-QMS). The MPEX experiments will generate diverse pre- and post-exposure measurement data of detailed material properties down to the crystal grain level in 3D for post-exposure assessment of PMI damage (e.g. cracking, melting, erosion and redeposition of the material). Physics models for the PMI, and how the material composition and manufacturing impact its performance under high energy plasma exposure, need to be validated with MPEX data to guide the selection of new candidate materials. Our vision for the MPEX AI Digital Twins project is to supply experimental and physics model simulation data to train Artificial Intelligence (AI) models for data processing, analysis, operational control, PMI and materials simulation to maximize the scientific output of the MPEX device. Ultimately, an AI digital twin of MPEX material assessment metrics for tested and synthetic material types with simulated PMI will be trained by the AI Modeling Teams on the experimental and physics simulation data submitted to the American Science Cloud by this project. A purely empirical search for the best material is inefficient given the finite number of samples that can be tested on MPEX. In order to expand the material properties database for training the MPEX Material Assessment AI Digital Twin, and to gain physics understanding of the PMI processes, physics models of the material properties and PMI processes are required. The physics simulations provide detailed simulation data, like impact angles for plasma ions, sputtering yields, transport of the ionized sputtered target material in the plasma, and redeposition locations. This simulation data expands the measurement data for deeper physics understanding. The experimental data is essential to validate the PMI and material structure simulation models. The validated models can then be used to generate new simulation data of MPEX material assessments for synthetic material compositions that have not been exposed in MPEX. These predictive simulations, plus the whole experimental dataset, will be used to train the MPEX Material Assessment AI Digital Twin allowing a rapid generative AI search for new materials with reduced PMI damage by interpolating the domain of the training set. These new optimum materials can be simulated with the physics codes and/or tested in MPEX. The ability of AI neural networks to interpolate multi-dimensional parameter spaces and generate virtual data is exploited for a more efficient search for optimum materials. The advent of the Transformational AI Models Consortium (TAIMC) is an opportunity to engage with state of the art private and public AI developers to achieve the goals of the AI digital twins and AI accelerated physics models proposed in this project. Our partners at ORNL from the Advance Scientific Computing Research (ASCR) organization will collaborate in accelerating the integrated plasma material interaction simulation framework. This simulation framework will provide a platform for generating simulation data across a range of physical fidelities, including hybrid methods that produce multi-fidelity results. This data will be leveraged for AI model development, both for generation of surrogates and the automation of simulation campaigns. A part of the research below will include collaborative efforts with the TAIMC to (i) adapt data storage approaches to ensure AI-readiness, (ii) provide a protypical exemplar to inform and exercise constructed workflows, and (iii) generate and share data, using the TAIMC unified AI data standard, for foundational models that will be trained from multiple sources across the DOE complex. We will also collaborate with the TAIMC, as well as the planned AI modeling teams, to develop approaches for reducing the cost of data generation. These include tailored multi-fidelity approaches as well as fine-tuning strategies to augment general, large-scale foundational models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Reduced fast-ion transport calculations of m = n = 1 fishbone-like instabilities in MAST-U

Fast-ion transport associated with an m = n = 1 fishbone-like burst in MAST-U discharge 47128 is investigated using a reduced guiding-center-based transport model (ORBIT-Kick) constrained by multi-diagnostic measurements. The two-dimensional beam-emission spectroscopy system provides measurements of the core poloidal mode structure and fluctuation amplitude, while EFIT++ reconstructions constrained by the motional Stark effect diagnostic indicate a flat q-profile with q 0 > 1⁠, indicating the absence of a resonant q = 1 surface and supporting a pressure-driven infernal-mode interpretation. Analytic m = n = 1 displacement profiles consistent with the measured core mode structure and equilibrium constraints are used as the mode structure inputs to ORBIT-Kick. The calculations show that the dominant resonances occur between the mode and co-passing fast ions, producing redistribution localized near the magnetic axis. Synthetic neutron camera signals from TRANSP-Kick recover up to 90% of the experimentally observed neutron deficit at the time of peak mode amplitude, indicating that the measured m = n = 1 mode is a dominant contributor to core fast-ion transport. However, the synthetic neutron signals recover rapidly, whereas the measured neutron emission continues to decrease after the peak amplitude. In conclusion, the remaining discrepancy may arise from contributions not included in the present single-harmonic model, including higher-m and higher-n harmonics, multi-harmonic interactions, and additional transport mechanisms, motivating future diagnostic development and modeling efforts to resolve and incorporate these additional contributions.

Wong, Henry H. [University of California, Los Ange↗
DOE OSTI2017

Roofline Analysis in the Intel® Advisor to Deliver Optimized Performance for applications on Intel® Xeon Phi™ Processor

In this session we show, in two case studies, how the roofline feature of Intel Advisor has been utilized to optimize the performance of kernels of the XGC1 and PICSAR codes in preparation for Intel Knights Landing architecture. The impact of the implemented optimizations and the benefits of using the automatic roofline feature of Intel Advisor to study performance of large applications will be presented. This demonstrates an effective optimization strategy that has enabled these science applications to achieve up to 4.6 times speed-up and prepare for future exascale architectures. # Goal/Relevance of Session The roofline model [1,2] is a powerful tool for analyzing the performance of applications with respect to the theoretical peak achievable on a given computer architecture. It allows one to graphically represent the performance of an application in terms of operational intensity, i.e. the ratio of flops performed and bytes moved from memory in order to guide optimization efforts. Given the scale and complexity of modern science applications, it can often be a tedious task for the user to perform the analysis on the level of functions or loops to identify where performance gains can be made. With new Intel tools, it is now possible to automate this task, as well as base the estimates of peak performance on measurements rather than vendor specifications. The goal of this session is to demonstrate how the roofline feature of Intel Advisor can be used to balance memory vs. computation related optimization efforts and effectively identify performance bottlenecks. A series of typical optimization techniques: cache blocking, structure refactoring, data alignment, and vectorization illustrated by the kernel cases will be addressed. # Description of the codes ## XGC1 The XGC1 code [3] is a magnetic fusion Particle-In-Cell code that uses an unstructured mesh for its Poisson solver that allows it to accurately resolve the edge plasma of a magnetic fusion device. After recent optimizations to its collision kernel [4], most of the computing time is spent in the electron push (pushe) kernel, where these optimization efforts have been focused. The kernel code scaled well with MPI+OpenMP but had almost no automatic compiler vectorization, in part due to indirect memory addresses and in part due to low trip counts of low-level loops that would be candidates for vectorization. Particle blocking and sorting have been implemented to increase trip counts of low-level loops and improve memory locality, and OpenMP directives have been added to vectorize compute-intensive loops that were identified by Advisor. The optimizations have improved the performance of the pushe kernel 2x on Haswell processors and 1.7x on KNL. The KNL node-for-node performance has been brought to within 30% of a NERSC Cori phase I Haswell node and we expect to bridge this gap by reducing the memory footprint of compute intensive routines to improve cache reuse. ## PICSAR is a Fortran/Python high-performance Particle-In-Cell library targeting at MIC architectures first designed to be coupled with the PIC code WARP for the simulation of laser-matter interaction and particle accelerators. PICSAR also contains a FORTRAN stand-alone kernel for performance studies and benchmarks. A MPI domain decomposition is used between NUMA domains and a tile decomposition (cache-blocking) handled by OpenMP has been added for shared-memory parallelism and better cache management. The so-called current deposition and field gathering steps that compose the PIC time loop constitute major hotspots that have been rewritten to enable more efficient vectorization. Particle communications between tiles and MPI domain has been merged and parallelized. All considered, these improvements provide speedups of 3.1 for order 1 and 4.6 for order 3 interpolation shape factors on KNL configured in SNC4 quadrant flat mode. Performance is similar between a node of cori phase 1 and KNL at order 1 and better on KNL by a factor 1.6 at order 3 with the considered test case (homogeneous thermal plasma).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

The MSP 2001 Mars Environmental Compatibility Assessment (MECA)

The Mars Environmental Compatibility Assessment (MECA) will evaluate the Martian environment for soil and dust-related hazards to human exploration as part of the Mars Surveyor Program 2001 Lander. Sponsored by the Human Exploration and Development of Space (HEDS) enterprise, MECA's goal is to evaluate potential geochemical and environmental hazards that may confront future Martian explorers, and to guide HEDS scientists in the development of high fidelity Mars soil simulants. The integrated MECA payload contains a wet-chemistry laboratory, a microscopy station, an electrometer to characterize the electrostatics of the soil and its environment, and arrays of material patches to study the abrasive and adhesive properties of soil grains. The instrument will acquire soil samples with a robotic arm equipped with a camera. MECA will examine surface and subsurface soil and dust in order to characterize particle size, shape, hardness, and also physical characteristics that may provide clues to mineralogy. MECA will characterize soil/water mixtures with respect to pH, redox potential, total dissolved ions, and trace toxins. MECA will determine the nature of electrostatic charging associated with excavation of soil, and the influence of ionizing radiation on material properties. It will also observe natural dust accumulation on engineering materials. To accomplish these objectives, MECA is allocated a mass of 10 kg within an enclosure of 35 x 25 x 15 cm. The Wet Chemistry Laboratory (WCL) consists of four identical cells that will accept samples from surface and subsurface regions accessible to the Lander's robotic arm, mix them with water, and perform extensive analysis of the solution. Ion-selective electrodes and related sensors will evaluate total dissolved solids, redox potential, pH, and the concentration of many soluble ions and gases in wet Martian soil. These electrodes can detect potentially dangerous heavy-metal ions, emitted pathogenic gases, and the soil's corrosive potential. Experiments will include cyclic voltammetry and anodic stripping voltammetry. Complementary to the Viking experiments, the chemical laboratory will characterize the water-soil solution rather than emitted gases. Nonetheless, through analysis of dissolved gases it will be able to replicate many of the Viking observations related to oxidants. MECA's microscopy station combines optical and atomic-force microscopy (AFM) in an actively focused, controlled illumination environment to image particles from millimeters to nanometers in size. Careful selection of substrates allows controlled experiments in adhesion, abrasion, hardness, aggregation, magnetic and other properties. Special tools allow primitive manipulation (brushing and scraping) of samples. Soil particle properties including size, shape, color, hardness, adhesive potential (electrostatic and magnetic), will be determined using an array of sample receptacles and collection substrates. The simple, rugged atomic-force microscope will image in the submicron size range and has the capability of performing a particle-by-particle analysis of the dust and soil. On Earth, the earliest forms of life are preserved as microfossils. The atomic-force microscope will have the required resolution to image down to the scale of terrestrial microfossils and beyond. Mounted on the end of the robot arm, MECA's electrometer actually consists of four types of sensors: an electric field meter, several triboelectricity monitors, an ion gauge, and a thermometer. Tempered only by ultraviolet-light-induced ions and a low-voltage breakdown threshold, the dry, cold, dusty martian environment presents an imposing electrostatic hazard to both robots and humans. The field meter will measure the ambient field on nearby objects while the triboelectric sensors, using identical circuitry, will measure the charge accumulated on test substances as they are dragged through the soil by the arm. The ion chamber, open to the environment, will sense both charged dust and free ions in the air. Over and above the potential threat to electronics, the electrostatic environment holds one of the keys to transport of dust and, consequently, Martian meteorology. Viewed with the robot arm camera, the abrasion and adhesion plates are strategically placed to allow direct observation of the interaction between materials and soils on a macroscopic scale. Materials of graded hardness are placed directly under the robot arm scoop to sense wear and soil hardness. A second array, placed on the lander deck, is deployed after the dust plume of landing has settled. It can be manipulated in a primitive fashion by the arm, first having dirt deposited on it from the scoop and subsequently shaken clean. A third array will passively collect dust from the atmosphere. In addition to objectives related to human exploration, the MECA data set will be rich in information relevant to basic geology, paleoclimate, and exobiology issues. To understand both contemporaneous and ancient processes on Mars, the mineralogy, petrology, and reactivity of Martian surface materials should be constrained. The MECA experiment will shed light on these quantities through its combination of chemistry and microscopy. MECA will be capable of measuring the composition of ancient surface water environments, observing microscopic evidence of geological (and biological?) processes, inferring soil and dust transport, comminution and weathering mechanisms, and characterizing soil horizons that might be encountered during excavation.

Hecht, M. H.↗
DOE OSTI2025

Molecular-Level Insights into the NMR Relaxivity of Gadobutrol Using Quantum and Classical Molecular Simulations

MRI is an indispensable diagnostic tool in modern medicine; however, understanding the molecular-level processes governing NMR relaxation of water in the presence of MRI contrast agents remains a challenge, hindering the molecular-guided development of more effective contrast agents. By using quantum-based polarizable force fields, the first-of-its-kind molecular dynamics (MD) simulations of Gadobutrol are reported where the 1 H NMR longitudinal relaxivity r 1 of the aqueous phase is determined without any adjustable parameters. The MD simulations of r 1 dispersion (i.e., frequency dependence) show good agreement with measurements at frequencies of interest in clinical MRI. Importantly, the simulations reveal key insights into the molecular level processes leading to r 1 dispersion by decomposing the NMR dipole–dipole autocorrelation function G(t) into a discrete set of molecular modes, analogous to the eigenmodes of a quantum harmonic oscillator. The molecular modes reveal important aspects of the underlying mechanisms governing r 1 , such as its multiexponential nature and the importance of the second eigenmodal decay. By simply analyzing the MD trajectories on a parameter-free approach, the Gadobutrol simulations show that the outer-shell water contributes ∼50% of the total relaxivity r 1 compared to the inner-shell water, in contrast to simulations of (nonchelated) gadolinium-aqua where the outer shell contributes only ∼15% of r 1 . The deviation between simulations and measurements of r 1 below clinical MRI frequencies is used to determine the low-frequency electron-spin relaxation time for Gadobutrol, in good agreement with independent studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Overview of ASDEX upgrade results in view of ITER and DEMO

Experiments on ASDEX Upgrade (AUG) in 2021 and 2022 have addressed a number of critical issues for ITER and EU DEMO. A major objective of the AUG programme is to shed light on the underlying physics of confinement, stability, and plasma exhaust in order to allow reliable extrapolation of results obtained on present day machines to these reactor-grade devices. Concerning pedestal physics, the mitigation of edge localised modes (ELMs) using resonant magnetic perturbations (RMPs) was found to be consistent with a reduction of the linear peeling-ballooning stability threshold due to the helical deformation of the plasma. Conversely, ELM suppression by RMPs is ascribed to an increased pedestal transport that keeps the plasma away from this boundary. Candidates for this increased transport are locally enhanced turbulence and a locked magnetic island in the pedestal. The enhanced D-alpha (EDA) and quasi-continuous exhaust (QCE) regimes have been established as promising ELM-free scenarios. Here, the pressure gradient at the foot of the H-mode pedestal is reduced by a quasi-coherent mode, consistent with violation of the high-n ballooning mode stability limit there. This is suggestive that the EDA and QCE regimes have a common underlying physics origin. In the area of transport physics, full radius models for both L- and H-modes have been developed. These models predict energy confinement in AUG better than the commonly used global scaling laws, representing a large step towards the goal of predictive capability. A new momentum transport analysis framework has been developed that provides access to the intrinsic torque in the plasma core. In the field of exhaust, the X-Point Radiator (XPR), a cold and dense plasma region on closed flux surfaces close to the X-point, was described by an analytical model that provides an understanding of its formation as well as its stability, i.e., the conditions under which it transitions into a deleterious MARFE with the potential to result in a disruptive termination. With the XPR close to the divertor target, a new detached divertor concept, the compact radiative divertor, was developed. Here, the exhaust power is radiated before reaching the target, allowing close proximity of the X-point to the target. No limitations by the shallow field line angle due to the large flux expansion were observed, and sufficient compression of neutral density was demonstrated. With respect to the pumping of non-recycling impurities, the divertor enrichment was found to mainly depend on the ionisation energy of the impurity under consideration. In the area of MHD physics, analysis of the hot plasma core motion in sawtooth crashes showed good agreement with nonlinear 2-fluid simulations. This indicates that the fast reconnection observed in these events is adequately described including the pressure gradient and the electron inertia in the parallel Ohm’s law. Concerning disruption physics, a shattered pellet injection system was installed in collaboration with the ITER International Organisation. Thanks to the ability to vary the shard size distribution independently of the injection velocity, as well as its impurity admixture, it was possible to tailor the current quench rate, which is an important requirement for future large devices such as ITER. Progress was also made modelling the force reduction of VDEs induced by massive gas injection on AUG. The H-mode density limit was characterised in terms of safe operational space with a newly developed active feedback control method that allowed the stability boundary to be probed several times within a single discharge without inducing a disruptive termination. Regarding integrated operation scenarios, the role of density peaking in the confinement of the ITER baseline scenario (high plasma current) was clarified. The usual energy confinement scaling ITER98(p,y) does not capture this effect, but the more recent H20 scaling does, highlighting again the importance of developing adequate physics based models. Advanced tokamak scenarios, aiming at large non-inductive current fraction due to non-standard profiles of the safety factor in combination with high normalised plasma pressure were studied with a focus on their access conditions. A method to guide the approach of the targeted safety factor profiles was developed, and the conditions for achieving good confinement were clarified. Based on this, two types of advanced scenarios (‘hybrid’ and ‘elevated’

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Sampling strategies for subsampled segmented EPI PRF thermometry in MR guided high intensity focused ultrasound

Purpose: To investigate k-space subsampling strategies to achieve fast, large field-of-view (FOV) temperature monitoring using segmented echo planar imaging (EPI) proton resonance frequency shift thermometry for MR guided high intensity focused ultrasound (MRgHIFU) applications. Methods: Five different k-space sampling approaches were investigated, varying sample spacing (equally vs nonequally spaced within the echo train), sampling density (variable sampling density in zero, one, and two dimensions), and utilizing sequential or centric sampling. Three of the schemes utilized sequential sampling with the sampling density varied in zero, one, and two dimensions, to investigate sampling the k-space center more frequently. Two of the schemes utilized centric sampling to acquire the k-space center with a longer echo time for improved phase measurements, and vary the sampling density in zero and two dimensions, respectively. Phantom experiments and a theoretical point spread function analysis were performed to investigate their performance. Variable density sampling in zero and two dimensions was also implemented in a non-EPI GRE pulse sequence for comparison. All subsampled data were reconstructed with a previously described temporally constrained reconstruction (TCR) algorithm. Results: The accuracy of each sampling strategy in measuring the temperature rise in the HIFU focal spot was measured in terms of the root-mean-square-error (RMSE) compared to fully sampled “truth.” For the schemes utilizing sequential sampling, the accuracy was found to improve with the dimensionality of the variable density sampling, giving values of 0.65 °C, 0.49 °C, and 0.35 °C for density variation in zero, one, and two dimensions, respectively. The schemes utilizing centric sampling were found to underestimate the temperature rise, with RMSE values of 1.05 °C and 1.31 °C, for variable density sampling in zero and two dimensions, respectively. Similar subsampling schemes with variable density sampling implemented in zero and two dimensions in a non-EPI GRE pulse sequence both resulted in accurate temperature measurements (RMSE of 0.70 °C and 0.63 °C, respectively). With sequential sampling in the described EPI implementation, temperature monitoring over a 192 × 144 × 135 mm{sup 3} FOV with a temporal resolution of 3.6 s was achieved, while keeping the RMSE compared to fully sampled “truth” below 0.35 °C. Conclusions: When segmented EPI readouts are used in conjunction with k-space subsampling for MR thermometry applications, sampling schemes with sequential sampling, with or without variable density sampling, obtain accurate phase and temperature measurements when using a TCR reconstruction algorithm. Improved temperature measurement accuracy can be achieved with variable density sampling. Centric sampling leads to phase bias, resulting in temperature underestimations.

42 ENGINEERING↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗