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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 217 records · Page 12

Development of a true single line of sight 3D hot-spot imaging for the National Ignition Facility

High resolution 3D self-emission x-ray imaging during inertial confinement fusion capsule implosion enables the measurement of the shape of the hotspot. While current 3D imaging capabilities use multiple lines of sight to perform image reconstruction, it would be highly desirable to use only one line of sight, as this would significantly reduce the number of windows in the target hohlraum and decrease their impacts on implosion symmetry. Such a goal is achievable using the zone plate coded imaging technique developed by N. M. Ceglio [Proc. SPIE 0106, 55-62 (1977)]. It consists of fielding a visible light Fresnel zone plate on shot to record a shadowgraph. Here, the image can then be reconstructed either by printing the shadowgraph on a transparent film and shining a suitable wavelength light through it or by numerical reconstruction. A new approach using numerical reconstruction is presented, and it relaxes the constraint by an order of magnitude on the optic design, thus enabling an easier fabrication process, as it allows a scaling-up of the optic dimensions. The design, fabrication process, and testing with an x-ray source of a prototype is presented. The reconstruction of an ~14.5 × 17 μm 2 broadband x-ray source was successful and shows that the performances are in line with expectation with an at least 5 mm axial resolution.

47 OTHER INSTRUMENTATION↗

Role of poloidal E × B drift in divertor heat transport in DIII‐D

Abstract Simulations for DIII‐D high confinement mode plasmas with the multifluid code UEDGE show a strong role of poloidal E × B drifts on divertor heat transport, challenging the paradigm of conduction‐limited scrape‐off layer (SOL) transport. While simulations with reduced drift magnitude are well aligned with the assumption that electron heat conduction dominates the SOL heat transport, simulations with drifts predict that the poloidal convective E × B heat transport dominates over electron heat conduction in both attached and detached conditions. As poloidal E × B flow propagates across magnetic field lines, poloidal transport with shallow magnetic pitch angles can reach values that are of the same order as would be provided by sonic flows parallel to the field lines. These flows can lead to strong convection‐dominated divertor heat transport, increasing the poloidal volume of radiative power front, consistent with previous measurements at DIII‐D. Due to these convective flows, the Lengyel integral approach, assuming zero convective fraction, is expected to provide a pessimistic estimate for the radiative capability of impurities in the divertor. For the DIII‐D simulations shown here, the Lengyel integral approach underestimates the radiated power by a factor of 6, indicating that, for reliable DIII‐D divertor power exhaust predictions, full two‐dimensional (2D) calculations, including drifts, would be necessary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The design of a line velocity interferometer for any reflector for inertial confinement experiments on the Z-machine

A line VISAR (Velocity Interferometer System for Any Reflector) has been designed and commissioned at the Sandia National Laboratory’s Z-machine. The instrument consists of an F/2 collection system, beam transport, and an interferometer table that contains two Mach–Zehnder type interferometers and an eight channel Gated Optical Imaging (GOI) system. The VISAR probe laser operates at the 532 nm wavelength, and the GOI bandpass is 540–600 nm. The output of each interferometer is passed to an optical streak camera with four selectable sweep speeds. The system is designed with three interchangeable optics modules to select a full field of view of 1 mm, 2 mm, or 4 mm. The optical beam transport system connects the target image plane to the interferometers and the gated optical imagers. The target is integrated into a sacrificial final optics assembly that is integral to the transport beamline.

Datte, P.↗

A wall interference assessment/correction system

A Wall Signature method originally developed by Hackett has been selected to be adapted for the Ames 12-ft Wind Tunnel WIAC system in the project. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in turn for estimating wall interference at the model location. The development and implementation of a working prototype will be completed, delivered and documented with a software manual. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free-air and confined wind-tunnel flow fields for each of the test articles over a range of test configurations. Specifically, the pressure signature at the test section wall will be computed for the tunnel case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method--Wall Signature method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free-air simulation. The following two additional tasks are included: (1) On-line wall interference calculation: The developed wall signature method (modified Hackett's method) for Ames 12-ft Tunnel will be the pre-computed coefficients which facilitate the on-line calculation of wall interference, and (2) Support system effects estimation: The effects on the wall pressure measurements due to the presence of the model support systems will be evaluated.

Lo, C. F.↗

Sensitivities of time-dependent temperature profile predictions for NSTX with the multi-mode model

The Multi-Mode Model (MMM) for turbulent transport was applied to a large set of well-analyzed discharges from the National Spherical Torus Experiment (NSTX) in order to evaluate its sensitivities to a wide range of plasma conditions. MMM calculations were performed for hundreds of milliseconds in each discharge by performing time-dependent predictive simulations with the 1.5D tokamak integrated modeling code TRANSP. A closely related study (Lestz et al 2025 Plasma Phys. Control. Fusion 67 105029) concluded that MMM predicted electron and ion temperature profiles that were in reasonable agreement with NSTX observations, generally outperforming a different reduced transport model, TGLF. This finding motivates the more thorough investigation of the characteristics of the MMM predictions conducted in this work. The simulations with MMM have electron energy transport dominated by electron temperature gradient modes in the examined discharges with relatively low plasma β (ratio of kinetic plasma pressure to magnetic field pressure) and high collisionality, transitioning to a mixture of different modes for higher β and lower collisionality. The thermal ion diffusivity predicted by MMM is much smaller than the neoclassical contribution, in line with previous experimental analysis of NSTX. Nonetheless, the electron and ion temperature profiles are coupled via collisional energy exchange and thus sensitive to which transport channels are predicted. The time-dependent simulations with MMM are robust to the simulation start time, converging to remarkably similar temperature profiles later during the discharge. MMM typically overpredicts confinement relative to NSTX observations, leading to the prediction of overly steep temperature profiles. Plasmas with spatially broader temperature profiles, higher plasma β, and longer energy confinement times tend to be predicted by MMM with better agreement with the experiment. As a result, these findings provide useful context for understanding the regime-dependent tendencies of MMM in anticipation of self-consistent, time-dependent predictive simulations of NSTX-U discharges with these same modeling tools.

MMM↗

Two dimensional imaging observations of meter-decameter bursts associated with the February 1986 flare activity

An analysis is presented of the two dimensional imaging observations of a flare observed on 3 Feb. l986 using the Clark Lake Multifrequency Radioheliograph. The flare produced almost all types of Meter-decimeter radio emission: enhanced storm radiation, type III/V bursts, II and IV and flare continuum. The flare continuum had early (FCE) and late (FC II) components and the type II occurred during the period between these two components. Comparing the source positions of type III/V and FCE it was found that these bursts must have occurred along adjacent open and closed field lines, respectively. The positional analysis of type II and FC II implies that the nonthermal electrons responsible for FC II need not be accelerated by type II shock and this conclusion is further supported by the close association of FC II with a microwave peak. Using the positional and temporal analysis of all these bursts and the associated hard X-ray and microwave emissions, a schematic model is developed for the magnetic field configuration in the flaring region in which the nonthermal particles responsible for these bursts are confined or along which they propagate.

Gopalswamy, N.↗

Detection of Extensive Equatorial Plasma Depletions after the 2022 Tongan Volcanic Eruption from Multiple Geodetic Satellite Ranging Systems

We present a number of unique observations of ionospheric anomalies following the Hunga-Tonga Hunga-Ha'apai (HTHH) volcanic eruption on 15 January 2022. All are based on non-dedicated geodetic satellite systems: Global Positioning System tracking of Low Earth Orbit (LEO) CubeSats, intersatellite tracking between two GRACE Follow-On satellites, satellite radar altimeters to the ocean surface, and Doppler radio beacons from ground stations to LEO geodetic satellites. Their observations revealed the development of anomalously large trough-like plasma depletions, along with plasma bubbles, in the equatorial regions of the Pacific and East Asian sectors. Trough-like plasma depletions appeared to be confined within approximately ±20° magnetic latitude, accompanied by density enhancements just outside this latitude range. These plasma depletions and enhancements were aligned with the magnetic equator and occurred across broad longitudes. They were detected in regions where atmospheric waves from the HTHH eruption passed through around the time of the sunset terminator. We interpret these phenomena in terms of the E dynamo electric fields driven by atmospheric waves from the eruption. The uplift of the ionosphere beyond satellite altitudes, followed by subsequent plasma diffusion to higher latitudes along magnetic field lines, results in the formation of trough-like plasma depletions around the magnetic equator and density enhancement at higher latitudes. The detection of plasma bubbles in the Asian sector during the non-bubble season (January) is likely associated with the uplift of the ionosphere at the sunset terminator.

Sentinel-3B↗

Periodic Korteweg–de Vries soliton potentials generate quasisymmetric magnetic field strength in a finite plasma- β equilibrium

Quasisymmetry (QS) is a hidden symmetry of the magnetic field strength, B , that enables effective confinement of charged particles in a fully three-dimensional (3D) toroidal plasma equilibrium. Such equilibria are typically modeled by the ideal magnetohydrostatic (MHS) equations. The nonlinear, overdetermined nature of the QS MHS equations severely complicates our understanding of the interplay between 3D shaping, equilibrium properties such as pressure and rotational transform, and B . Progress has been made through expansions near the magnetic axis; however, a more comprehensive theory is desirable. Using a combination of analysis and regression on a large dataset of numerically optimized quasisymmetric stellarators, we demonstrate that there is a hidden lower dimensionality of B on a magnetic flux surface with connections to the theory of periodic solitons. We show that B on a flux surface is determined by three or at most four flux functions, each of which determines a critical value of the derivative of B along the field line. While being consistent with the near-axis models, our results are global and hold even on the last closed flux surface.

Differential geometry↗

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↗

Role of current driven instabilities in the operation of plasma contactors used with electrodynamic tethers

The collection of current to an electrodynamic tether in low LEO is enhanced by a plasma cloud surrounding the anode (called a plasma contactor). The main mechanism by which this is achieved is the scattering, perpendicular to the lines of the magnetic field, of the electrons which enter the plasma cloud. The scattering may be a result of the interaction between the electrons and unstable EM waves, one example being lower-hybrid waves. The boundaries of instability are found for the lower-hybrid waves in a parametric study where, for the cases of Ar and NH3 clouds, the density, the ratio of electron to ion temperature, and the composition of the electron population, are varied. The main conclusion is that the lower-hybrid waves will be confined to the outer regions of the cloud and have the right properties to scatter electrons.

Gioulekas, A.↗

Stellar populations and merger rates of brightest cluster galaxies a billion years ago: SDSS MaNGA IFU spectroscopy

ABSTRACT We investigate the spectroscopic properties of 85 brightest cluster galaxies (BCGs) and their companions observed with the SDSS MaNGA integral field unit. Galaxy redshifts are between 0.08 < z < 0.15, allowing for a field-of-view up to 80 × 80 kpc. For the main galaxies: the average age of the BCG cores is 7.66$\, \pm \,$1.36 Gyr with no significant gradient out to $2\, R_ {e}$; the average metallicity of the BCG cores is $[Z/H]=0.23\, \pm \, 0.03$ with a negative gradient of Δ[Z/H]/Δ(R/Re) = –0.14$\, \pm \, 0.09$ which flattens beyond $1.2\, R_ {e}$. Velocity dispersion gradients are mostly flat, but a few positive slopes are seen in the most massive galaxies. Emission lines are present in 12 of the BCGs, most often confined to the central $\sim 2\,$ kpc with emission line ratios well-described by a LINER or AGN excitation source. There are 78 companion galaxies identified and 9 have nebular emission lines that indicate recent star formation. The companions with flux ratios of 4:1 and 20:1 within 30 kpc of their BCG’s core are studied. The companion galaxies have a median age of 7.65$\, \pm \,$1.55 Gyr and are high-metallicity systems, with a median [Z/H] = 0.17 ± 0.07. Close spectroscopic companions with higher merging probabilities have an average merging time of 0.5 ± 0.2 Gyr. The average merger rate is 0.08$\, \pm \, 0.12 \,$ Gyr−1 for 4:1 companions and 0.26$\, \pm \, 0.22 \,$ Gyr−1 for 20:1 companions, allowing for an increase in mass of 2.3$\, \pm \,$3.4 per cent Gyr−1 and 3.5$\, \pm \,$3.2 per cent Gyr−1, respectively.

Edwards, Louise O. V. (ORCID:000000029135997X)↗

Optical imagery and spectrophotometry of CTB 80

Narrow-band imagery and spectrophotometry of the central region of CTB 80 are presented. The images show weak forbidden O III and ubiquitous filamentary forbidden S II and H-alpha emission from the extended radio lobes in which the core is embedded. The data indicate that the extended component is shock heated. Balmer line-dominated emission is observed around the perimeter of the core. Assuming that the volume of the radio shell is similar to the volume of the thermal shell, it is found that a magnetic field of about 600 microG and a cosmic-ray proton-to-electron ratio of about 200 are required to explain the pressure and synchrotron volume emissivity in the radio shell. It is suggested that the optical emission form the core of CTB 80 arises behind shocks which are being driven into a magnetized thermal plasma by the confined relativistic wind from PSR 1951+32.

Hester, J. Jeff↗

A wall interference assessment/correction system

A Wall Signature method originally developed by Hackett was selected to be adapted for the Ames 12-ft Wind Tunnel Wall Interference Assessment/Correction (WIAC) System in the project. This method uses limited measurements of the static pressure at the wall, in conjunction with the solid wall boundary condition, to determine the strength and distribution of singularities representing the test article. The singularities are used in turn for estimating wall interference at the model location. The lifting interference will be treated separately by representing in a horseshoe vortex system for the model's lifting effects. The development and implementation of a working prototype will be completed, delivered, and documented with a software manual. The WIAC code will be validated by conducting numerically simulated experiments rather than actual wind tunnel experiments. The simulations will be used to generate both free-air and confined wind-tunnel flow fields for each of the test articles over a range of test configurations. Specifically, the pressure signature at the test section wall will be computed for the tunnel case to provide the simulated 'measured' data. These data will serve as the input for the WIAC method - Wall Signature method. The performance of the WIAC method then may be evaluated by comparing the corrected parameters with those for the free-air simulation. The following two additional tasks are included in the supplement No. 1 to the basic Grant. On-line wall interference calculation: The developed wall signature method (modified Hackett's method) for Ames 12-ft Tunnel will be the pre-computed coefficients which facilitate the on-line calculation of wall interference; and support system effects estimation: The effects on the wall pressure measurements due to the presence of the model support systems will be evaluated.

Lo, Ching F.↗

Temperature and Forward Flight Effects on an Underexpanded Jet Noise

An experimental investigation was carried out in the NASA Ames 40'x80' wind tunnel to investigate the far field noise characteristics of a supersonic jet exiting from an axisymmetric convergent nozzle. The nozzle geometry conforms to the ASME specifications for the long radius nozzle. The nozzle pressure ratio NPR, (stagnation pressure/ambient pressure) was varied from 2.5 to 4.5. The temperature ratio, TR (stagnation temperature/ambient temperature) was varied from 2.5 to 3.5. The resulting Reynolds number range, based on the nozzle exit diameter of 12.55cm, is from 0.98 -1.27 x 10(exp 6). The far field directivity was obtained using 1/4 inch diameter condenser microphone with the Flow-Induced Tone Eliminator (FITE) aerodynamic microphone fore body. Appropriate microphone corrections, developed by Allen et al., were made for accurate in-flow acoustic measurements at high frequencies. The narrow band (band width = 64 Hz) frequency spectra covering a range from 0 to 70 KHz were obtained with an accuracy of plus or minus 0.6dB. Typical narrow-band spectra representing far field noise in the forward quadrant, normal to the jet axis and the aft quadrant are shown. The three dominant components of the noise, the screech tone, broad-band shock associated noise and the mixing noise, are clearly identifiable in the spectra. The variation of the screech tone with the exit Mach number (calculated from the isentropic equation relating NPR to Mach number), is shown. The solid line in the figure is calculated using Tam's formula. The model developed by Tam seems to work well even at high temperatures. The appearance of the screech tone is confined to the forward quadrant (theta less than or equal to 60 degrees; the angle theta is measured from the inlet axis). The amplitude of the tone is about 10 dB higher than the broad band noise, which is less than the normally observed amplitude for cold jets operating at similar conditions.

Krothapalli, A.↗

Magnetohydrodynamics of atmospheric transients. I - Basic results of two-dimensional plane analyses

The dynamic behavior of transients in a stratified atmosphere in the presence of a magnetic field is investigated with the two-dimensional plane formulation, i.e., the formulation in which variations of the flow and magnetic field are confined within a plane. It is pointed out that, in the plane formulation, the noncompressible transverse waves (often called the Alfven waves) are excluded. The compressible responses of the atmosphere are then examined with a temperature perturbation (simulating a sudden local release of energy by a flare) as functions of the configuration of magnetic field and field strength. It is shown that (1) in the open (mostly radial) magnetic field, the propagation of 'bubble-like' density enhancements, the coronal transients, result; while (2) in the closed (mostly azimuthal) field, the density enhancement forms a pair of 'horns' near the foot points of field lines similar to that often observed by coronagraphs after flares. Discussions in interpreting the results in terms of the anisotropic propagation of the fast and slow waves (or shocks) are presented together with consideration of possible consequences with the inclusion of the transverse waves.

Nakagawa, Y.↗

Multi-delay coherence imaging spectroscopy optimized for ion temperature measurements in the divertor plasma of the Wendelstein 7-X stellarator

A new coherence imaging spectroscopy (CIS) diagnostic optimized to measure the C 2+ impurity ion temperature T i spatial distribution in the divertor plasma of the W7-X stellarator is designed, tested, and validated. Using CIS to obtain T i in the edge of magnetically confined plasmas has historically been challenging because Doppler broadening and Zeeman splitting have comparable effects on the shape of spectral emission lines. To distinguish between these two mechanisms, a novel approach to birefringent crystal design is employed to minimize the diagnostic’s sensitivity to Zeeman splitting. The recently developed pixelated multi-delay CIS approach is also used to obtain four times as much spectral information as traditional CIS approaches. The T i -optimized CIS diagnostic is validated in a long-pulse W7-X plasma by comparison with a high-resolution spectrometer whose sightlines overlap with the CIS field of view. The CIS and spectrometer T i profiles have the same shape and agree to within 10% on average and 25% in the worst case. Images of the T i distribution near the divertor show toroidally elongated bands aligned with the magnetic field, with T i ranging between 10 and 40 eV.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Structured DC Electric Fields With and Without Associated Plasma Density Gradients Observed with the C/NOFS Satellite

DC electric field observations and associated plasma drifts gathered with the Vector Electric Field Investigation on the Air Force Communication/Navigation Outage Forecasting System (C/NOFS) satellite typically reveal considerable variation at large scales (approximately 100's of km), in both daytime and nighttime cases, with enhanced structures usually confined to the nightside. Although such electric field structures are typically associated with plasma density depletions and structures, as observed by the Planar Langmuir Probe on C/NOFS, what is surprising is the number of cases in which large amplitude, structured DC electric fields are observed without a significant plasma density counterpart structure, including their appearance at times when the ambient plasma density appears relatively quiescent. We investigate the relationship of such structured DC electric fields and the ambient plasma density in the C/NOFS satellite measurements observed thus far, taking into account both plasma density depletions and enhancements. We investigate the mapping of the electric fields along magnetic field lines from distant altitudes and latitudes to locations where the density structures, which presumably formed the original seat of the electric fields, are no longer discernible in the observations. In some cases, the electric field structures and spectral characteristics appear to mimic those associated with equatorial spread-F processes, providing important clues to their origins. We examine altitude, seasonal, and longitudinal effects in an effort to establish the origin of such structured DC electric fields observed both with, and without, associated plasma density gradients

Pfaff, R.↗

Superconducting gravity gradiometer and a test of inverse square law

The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth.

Moody, M. V.↗