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NASA NTRS2005

Mars Orbiter Sample Return Power Design

Mars has greatly intrigued scientists and the general public for many years because, of all the planets, its environment is most like Earth's. Many scientists believe that Mars once had running water, although surface water is gone today. The planet is very cold with a very thin atmosphere consisting mainly of CO2. Mariner 4, 6, and 7 explored the planet in flybys in the 1960s and by the orbiting Mariner 9 in 1971. NASA then mounted the ambitious Viking mission, which launched two orbiters and two landers to the planet in 1975. The landers found ambiguous evidence of life. Mars Pathfinder landed on the planet on July 4, 1997, delivering a mobile robot rover that demonstrated exploration of the local surface environment. Mars Global Surveyor is creating a highest-resolution map of the planet's surface. These prior and current missions to Mars have paved the way for a complex Mars Sample Return mission planned for 2003 and 2005. Returning surface samples from Mars will necessitate retrieval of material from Mars orbit. Sample mass and orbit are restricted to the launch capability of the Mars Ascent Vehicle. A small sample canister having a mass less than 4 kg and diameter of less than 16 cm will spend from three to seven years in a 600 km orbit waiting for retrieval by a second spacecraft consisting of an orbiter equipped with a sample canister retrieval system, and a Earth Entry Vehicle. To allow rapid detection of the on-orbit canister, rendezvous, and collection of the samples, the canister will have a tracking beacon powered by a surface mounted solar array. The canister must communicate using RF transmission with the recovery vehicle that will be coming in 2006 or 2009 to retrieve the canister. This paper considers the aspect and conclusion that went into the design of the power system that achieves the maximum power with the minimum risk. The power output for the spherical orbiting canister was modeled and plotted in various views of the orbit by the Satellite Orbit Analysis Program (SOAP).

Mardesich, N.↗

NASA NTRS2006

TRMM On-Orbit Performance Reassessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an H-I1 rocket on November 27, 1997, and transitioned in August, 2001, from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost, the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with 1/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees.

Bilanow, Stephen↗

NASA NTRS2006

The Disposal of Spacecraft and Launch Vehicle Stages in Low Earth Orbit

As a result of the increasing number of debris in low Earth orbit (LEO), numerous national and international orbital debris mitigation guidelines recommend the removal of spacecraft and launch vehicle stages from LEO within 25 years after mission termination. The primary purpose of this action is to enhance space safety by significantly limiting the potential of future accidental collisions resulting in the creation of large numbers of new orbital debris. Likewise, the passivation of these objects, i.e., the removal of residual stored energies, while they remain in orbit is important to prevent the generation of debris via self-induced explosions. Characteristics and trends in the growth of the derelict spacecraft and launch vehicle stage populations in LEO are examined. Depending upon the final operational altitude of the vehicle, achieving the goal of orbital lifetime reduction can influence the design and deployment philosophy of a new space system. Some spacecraft and launch vehicle stages have combined their end-of-mission passivation operations with maneuvers to vacate long-lived orbital regimes. Perhaps the most dramatic demonstration of this type occurred in 2006 when a U.S. Delta IV second stage executed an unprecedented controlled-reentry maneuver from a circular orbit at an altitude near 850 km. For space systems in orbital regimes near the upper regions of LEO (i.e., between 1400 km and 2000 km altitude), maneuvers to place the vehicle above LEO might be more attractive than attempting to ensure an atmospheric reentry within 25 years, and at least one space system operator has selected this option. In some cases, careful consideration of natural orbital perturbations can also lead to reduced orbital lifetimes, although new launch constraints might need to be imposed.

Johnson, Nicholas L.↗

NASA NTRS2007

Mission Design for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) will be the first mission under NASA's Vision for Space Exploration. LRO will fly in a low 50 km mean altitude lunar polar orbit. LRO will utilize a direct minimum energy lunar transfer and have a launch window of three days every two weeks. The launch window is defined by lunar orbit beta angle at times of extreme lighting conditions. This paper will define the LRO launch window and the science and engineering constraints that drive it. After lunar orbit insertion, LRO will be placed into a commissioning orbit for up to 60 days. This commissioning orbit will be a low altitude quasi-frozen orbit that minimizes stationkeeping costs during commissioning phase. LRO will use a repeating stationkeeping cycle with a pair of maneuvers every lunar sidereal period. The stationkeeping algorithm will bound LRO altitude, maintain ground station contact during maneuvers, and equally distribute periselene between northern and southern hemispheres. Orbit determination for LRO will be at the 50 m level with updated lunar gravity models. This paper will address the quasi-frozen orbit design, stationkeeping algorithms and low lunar orbit determination.

Beckman, Mark↗

NASA NTRS2007

GPS-Based Reduced Dynamic Orbit Determination Using Accelerometer Data

Currently two gravity field satellite missions, CHAMP and GRACE, are equipped with high sensitivity electrostatic accelerometers, measuring the non-conservative forces acting on the spacecraft in three orthogonal directions. During the gravity field recovery these measurements help to separate gravitational and non-gravitational contributions in the observed orbit perturbations. For precise orbit determination purposes all these missions have a dual-frequency GPS receiver on board. The reduced dynamic technique combines the dense and accurate GPS observations with physical models of the forces acting on the spacecraft, complemented by empirical accelerations, which are stochastic parameters adjusted in the orbit determination process. When the spacecraft carries an accelerometer, these measured accelerations can be used to replace the models of the non-conservative forces, such as air drag and solar radiation pressure. This approach is implemented in a batch least-squares estimator of the GPS High Precision Orbit Determination Software Tools (GHOST), developed at DLR/GSOC and DEOS. It is extensively tested with data of the CHAMP and GRACE satellites. As accelerometer observations typically can be affected by an unknown scale factor and bias in each measurement direction, they require calibration during processing. Therefore the estimated state vector is augmented with six parameters: a scale and bias factor for the three axes. In order to converge efficiently to a good solution, reasonable a priori values for the bias factor are necessary. These are calculated by combining the mean value of the accelerometer observations with the mean value of the non-conservative force models and empirical accelerations, estimated when using these models. When replacing the non-conservative force models with accelerometer observations and still estimating empirical accelerations, a good orbit precision is achieved. 100 days of GRACE B data processing results in a mean orbit fit of a few centimeters with respect to high-quality JPL reference orbits. This shows a slightly better consistency compared to the case when using force models. A purely dynamic orbit, without estimating empirical accelerations thus only adjusting six state parameters and the bias and scale factors, gives an orbit fit for the GRACE B test case below the decimeter level. The in orbit calibrated accelerometer observations can be used to validate the modelled accelerations and estimated empirical accelerations computed with the GHOST tools. In along track direction they show the best resemblance, with a mean correlation coefficient of 93% for the same period. In radial and normal direction the correlation is smaller. During days of high solar activity the benefit of using accelerometer observations is clearly visible. The observations during these days show fluctuations which the modelled and empirical accelerations can not follow.

VanHelleputte, Tom↗

NASA NTRS2002

Using GEO Optical Observations to Infer Orbit Populations

NASA's Orbital Debris measurements program has a goal to characterize the small debris environment in the geosynchronous Earth-orbit (GEO) region using optical telescopes ("small" refers to objects too small to catalog and track with current systems). Traditionally, observations of GEO and near-GEO objects involve following the object with the telescope long enough to obtain an orbit. When observing very dim objects with small field-of-view telescopes, though, the observations are generally too short to obtain accurate orbital elements. However, it is possible to use such observations to statistically characterize the small object environment. A telescope pointed at a particular spot could potentially see objects in a number of different orbits. Inevitably, when looking at one region for certain types of orbits, there are objects in other types of orbits that cannot be seen. Observation campaigns are designed with these limitations in mind and are set up to span a number of regions of the sky, making it possible to sample all potential orbits under consideration. Each orbit is not seen with the same probability, however, so there are observation biases intrinsic to any observation campaign. Fortunately, it is possible to remove such biases and reconstruct a meaningful estimate of the statistical orbit populations of small objects in GEO. This information, in turn, can be used to investigate the nature of debris sources and to characterize the risk to GEO spacecraft. This paper describes these statistical tools and presents estimates of small object GEO populations.

Matney, Mark↗

NASA NTRS2011

Solar Radiation Pressure Binning for the Geosynchronous Orbit

Orbital maintenance parameters for individual satellites or groups of satellites have traditionally been set by examining orbital parameters alone, such as through apogee and perigee height binning; this approach ignored the other factors that governed an individual satellite's susceptibility to non-conservative forces. In the atmospheric drag regime, this problem has been addressed by the introduction of the "energy dissipation rate," a quantity that represents the amount of energy being removed from the orbit; such an approach is able to consider both atmospheric density and satellite frontal area characteristics and thus serve as a mechanism for binning satellites of similar behavior. The geo-synchronous orbit (of broader definition than the geostationary orbit -- here taken to be from 1300 to 1800 minutes in orbital period) is not affected by drag; rather, its principal non-conservative force is that of solar radiation pressure -- the momentum imparted to the satellite by solar radiometric energy. While this perturbation is solved for as part of the orbit determination update, no binning or division scheme, analogous to the drag regime, has been developed for the geo-synchronous orbit. The present analysis has begun such an effort by examining the behavior of geosynchronous rocket bodies and non-stabilized payloads as a function of solar radiation pressure susceptibility. A preliminary examination of binning techniques used in the drag regime gives initial guidance regarding the criteria for useful bin divisions. Applying these criteria to the object type, solar radiation pressure, and resultant state vector accuracy for the analyzed dataset, a single division of "large" satellites into two bins for the purposes of setting related sensor tasking and orbit determination (OD) controls is suggested. When an accompanying analysis of high area-to-mass objects is complete, a full set of binning recommendations for the geosynchronous orbit will be available.

Hejduk, M. D.↗

NASA NTRS2011

Constraining the Absolute Orientation of eta Carinae's Binary Orbit: A 3-D Dynamical Model for the Broad [Fe III] Emission

We present a three-dimensional (3-D) dynamical model for the broad [Fe III] emission observed in Eta Carinae using the Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS). This model is based on full 3-D Smoothed Particle Hydrodynamics (SPH) simulations of Eta Car's binary colliding winds. Radiative transfer codes are used to generate synthetic spectro-images of [Fe III] emission line structures at various observed orbital phases and STIS slit position angles (PAs). Through a parameter study that varies the orbital inclination i, the PA(theta) that the orbital plane projection of the line-of-sight makes with the apastron side of the semi-major axis, and the PA on the sky of the orbital axis, we are able, for the first time, to tightly constrain the absolute 3-D orientation of the binary orbit. To simultaneously reproduce the blue-shifted emission arcs observed at orbital phase 0.976, STIS slit PA = +38deg, and the temporal variations in emission seen at negative slit PAs, the binary needs to have an i approx. = 130deg to 145deg, Theta approx. = -15deg to +30deg, and an orbital axis projected on the sky at a P A approx. = 302deg to 327deg east of north. This represents a system with an orbital axis that is closely aligned with the inferred polar axis of the Homunculus nebula, in 3-D. The companion star, Eta(sub B), thus orbits clockwise on the sky and is on the observer's side of the system at apastron. This orientation has important implications for theories for the formation of the Homunculus and helps lay the groundwork for orbital modeling to determine the stellar masses.

Madura, T. I.↗

NASA NTRS2012

The Effect of Geocenter Motion on Jason-2 and Jason-1 Orbits and the Mean Sea Level

We have investigated the impact of geocenter motion on Jason-2 orbits. This was accomplished by computing a series of Jason-1, Jason-2 GPS-based and SLR/DORIS-based orbits using ITRF2008 and the IGS repro1 framework based on the most recent GSFC standards. From these orbits, we extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. The fitted annual and seasonal terms of these time-series are compared to two different geocenter motion models. Subsequently, we included the geocenter motion corrections in the POD process as a degree-1 loading displacement correction to the tracking network. The analysis suggested that the GSFC's Jason-2 std0905 GPS-based orbits are closely tied to the center of mass (CM) of the Earth whereas the SLR/DORIS std0905 orbits are tied to the center of figure (CF) of the ITRF2005 (Melachroinos et al., 2012). In this study we extend the investigation to the centering of the GPS constellation and the way those are tied in the Jason-1 and Jason-2 POD process. With a new set of standards, we quantify the GPS and SLR/DORIS-based orbit centering during the Jason-1 and Jason-2 inter-calibration period and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the full term of the geocenter motion correction.

Melachroinos, Stavros A.↗

NASA NTRS2013

The Eccentric Behavior of Nearly Frozen Orbits

Frozen orbits are orbits which have only short-period changes in their mean eccentricity and argument of periapse, so that they basically keep a fixed orientation within their plane of motion. Nearly frozen orbits are those whose eccentricity and argument of periapse have values close to those of a frozen orbit. We call them "nearly" frozen because their eccentricity vector (a vector whose polar coordinates are eccentricity and argument of periapse) will stay within a bounded distance from the frozen orbit eccentricity vector, circulating around it over time. For highly inclined orbits around the Earth, this distance is effectively constant over time. Furthermore, frozen orbit eccentricity values are low enough that these orbits are essentially eccentric (i.e., off center) circles, so that nearly frozen orbits around Earth are bounded above and below by frozen orbits.

spacecraft↗

NASA NTRS2016

The Impact of New Trends in Satellite Launches on Orbital Debris Environment

The main goal of this study is to examine the impact of new trends in satellite launch activities on the orbital debris environment and collision risk. Starting from the launch of the first artificial satellite in 1957, space borne technology has become an indispensable part of our lives. More than 6,000 satellites have been launched into Earth orbit. Though the annual number of satellites launched stayed flat for many decades, the trend has recently changed. The satellite market has been undergoing a major evolution with new space companies replacing the traditional approach of deploying a few large, complex and costly satellites with an approach to use a multitude of smaller, less complex and cheaper satellites. This new approach creates a sharp increase in the number of satellites and so the historic trends are no longer representative. As a foundation for this study, a scenario for satellite deployments based on the publicly announced future satellite missions has been developed. These constellation-deploying companies include, but are not limited to, Blacksky, CICERO, EROS, Landmapper, Leosat, Northstar, O3b, OmniEarth, OneWeb, Orbcomm, OuterNet, PlanetIQ, Planet Labs, Radarsat, RapidEye Next Generation, Sentinel, Skybox, SpaceX, and Spire. Information such as the annual number of launches, the number of orbital planes to be used by the constellation, as well as apogee, perigee, inclination, spacecraft mass and area were included or approximated. Besides the production of satellites, a widespread ongoing effort to enhance orbital injection capabilities will allow delivery of more spacecraft more accurately into Earth orbits. A long list of companies such as Microcosm, Rocket Lab, Firefly Space Systems, Sierra Nevada Corporation and Arca Space Corporation are developing new launch vehicles dedicated for small satellites. There are other projects which intend to develop interstages with propulsive capabilities which will allow the deployment of satellites into their desired orbits beyond the restrictions of the launch vehicle used. These near future orbital injection technologies are also covered in the developed scenario. Using the above-mentioned background information, this study aims to examine how the orbital debris environment will be affected from the new dynamics of the emerging space markets. We developed a simulation tool that is capable of propagating the objects in a given deployment scenario with variable-sized time-steps as small as one second. Over the course of the run, the software also detects collisions; additional debris objects are then created according to the NASA breakup model and are fed back into the simulation framework. Examining the simulation results, the total number of particles to accumulate in different orbits can be monitored and the number of conjunctions can be tracked to assess the collision risks. The simulation makes it possible to follow the short- and long-term effects of a particular satellite or constellation on the space environment. Likewise, the effects of changes in the debris environment on a particular satellite or constellation can be evaluated. It is authors hope that the results of this paper and further utilization of the developed simulation tool will assist in the investigation of more accurate deorbiting metrics to replace the generic 25-year disposal guidelines, as well as to guide future launches toward more sustainable and safe orbits.

New Space↗

NASA NTRS2017

Small Orbital Stereo Tracking Camera Technology Development

Any exploration vehicle assembled or Spacecraft placed in LEO or GTO must pass through this debris cloud and survive. Large cross section, low thrust vehicles will spend more time spiraling out through the cloud and will suffer more impacts.Better knowledge of small debris will improve survival odds. Current estimated Density of debris at various orbital attitudes with notation of recent collisions and resulting spikes. Orbital Debris Tracking and Characterization has now been added to NASA Office of Chief Technologists Technology Development Roadmap in Technology Area 5 (TA5.7)[Orbital Debris Tracking and Characterization] and is a technical gap in the current National Space Situational Awareness necessary to safeguard orbital assets and crews due to the risk of Orbital Debris damage to ISS Exploration vehicles. The Problem: Traditional orbital trackers looking for small, dim orbital derelicts and debris typically will stare at the stars and let any reflected light off the debris integrate in the imager for seconds, thus creating a streak across the image. The Solution: The Small Tracker will see Stars and other celestial objects rise through its Field of View (FOV) at the rotational rate of its orbit, but the glint off of orbital objects will move through the FOV at different rates and directions. Debris on a head-on collision course (or close) will stay in the FOV at 14 Km per sec. The Small Tracker can track at 60 frames per sec allowing up to 30 fixes before a near-miss pass. A Stereo pair of Small Trackers can provide range data within 5-7 Km for better orbit measurements.

Bryan, Tom↗

NASA NTRSDate not supplied

TechEdSat 7, 10, 13, 15: Exo-brake Experiments on the ISS, First Virgin Orbit, and First Firefly-Alpha Test Flights.

The TechEdSat flight series (TES-n), developed by the Nano Orbital Workshop (NOW) group at NASA Ames, has been studying cube satellite re-entry technologies with a focus on Exo-Brake drag device research. An exo-atmospheric braking device, the Exo-Brake uses the tenuous upper atmosphere acting in a free molecular flow regime to enable controllable adjustment of the drag profile of the host spacecraft, currently enabling rapid disposal of small spacecraft after mission conclusion, and eventual targeted de-orbit to a desired entry point at the Von Karman line, or approximately 100km in altitude. The TES-7 mission, flown on the first successful Virgin Orbit flight January 17, 2021, was injected into a 500km, 61-degree inclination orbit, with an expected orbital lifetime of approximately ten years. After successful deployment of a unique hydrogen gas-cell inflation design ‘disposal’-type Mylar Exo-Brake intended to rapidly de-orbit the spacecraft, the maximum expected orbital lifetime of the TES-7 spacecraft was successfully reduced from ten years to 1.3 years, an 87% reduction in orbit lifetime via a passive, fuel-less system. The subsequent TES-13 mission utilized a new, less complex ‘disposal’-type Exo-Brake design made from collapsible rigid struts rather than inflated struts to reduce the engineering, construction, and safety complexities introduced by the prior hydrogen gas inflation design. The rigid strut Exo-Brake design is stowed via rotational compression and deploys using only stored spring energy once released via electronic actuator. This new rotation compression storage design has become the new Exo-Brake design standard used on TES missions thanks to its simplicity. Following on the success of this new Exo-Brake design demonstrated by TES-13, the design was further refined to enabled active manipulation of the Exo-Brake effective drag area though a winch-like system. Both the TES-10 and TES-15 spacecraft were equipped with geometrically similar Exo-Brake devices capable of such active drag modulation, with the intent of studying the operational impact of having such devices on cube satellite missions. To increase the survival time of the Exo-Brake at low altitudes and thus gain more experiment time and better guidance capability, TES-15 was equipped with a modulated Exo-Brake constructed from 3M™ Nextel™ 440 ceramic oxide fiber, the same fabric material used in the Space Shuttle TPS system, rather than Mylar. After launching on Alpha Flight 2 October 1st, 2022, Firefly’s first successful launch, TES-15 met the same modulation restrictions as TES-10, with modulation prohibited above 200km to avoid possible collision with other spacecraft. In this case, a low deployment orbit caused an extremely short mission life, which, coupled with delayed spacecraft identification, exacerbated collision concerns and caused performance data of the high-temperature Exo-Brake design to be inconclusive. As such, the Nano Orbital Workshop has taken a new approach of only conducting modulated Exo-Brake research on missions deploying below ISS altitude to avoid collision avoidance restrictions, and is working to improve spacecraft identification and location reporting techniques to increase experiment durations. Upcoming TES mission will therefore use one of two classes of Exo-Brake depending on their target altitude, as to be described in the submission.

M Murbach↗

NASA NTRSDate not supplied

TechEdSat 7, 10, 13, 15: Exo-brake Experiments on the ISS, First Virgin Orbit, and First Firefly-Alpha Test Flights

Marcus Murbach↗

DOE OSTI2021

Effect of the inversion symmetry breaking on the orbital Hall effect: A model study

The orbital Hall effect (OHE) is the transverse flow of orbital moment in a solid in response to an applied electric field, analogous to the flow of spin moment in the spin Hall effect (SHE). Although the effect has not been directly observed, there is ample indirect evidence for its existence in a number of experiments. Here, we show that the OHE is enhanced in solids with broken inversion symmetry, which may be more suitable to observe the effect. The mechanism of the OHE is fundamentally different in solids with inversion symmetry, where the orbital moment is quenched in the Brillouin zone (BZ), from that in a solid with broken inversion symmetry, where an intrinsic orbital moment is already present, the motion of which under the applied electric field could lead to a robust OHE. Using a tight-binding model Hamiltonian of a simple cubic lattice with two atoms in the unit cell, we study the effect of the inversion symmetry breaking on the OHE. We show that with the increase in the strength of the broken symmetry, the magnitude of the intrinsic orbital moment in the Brillouin zone increases. This, in turn, enhances the orbital Hall conductivity, in particular, the part that is directly proportional to the orbital moment in the BZ, which we call the “noncentrosymmetric contribution.” If the spin-orbit coupling is present, which couples the orbital and spin moments, the OHE leads to the SHE, which also becomes enhanced by the broken inversion symmetry. Furthermore, our work has important implications for experimenters, suggesting that noncentrosymmetric solids may be more suitable for direct observation of the OHE.

36 MATERIALS SCIENCE↗

DOE OSTI2020

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

A unified approach for computing (i) spin-transfer torque in magnetic trilayers like spin valve and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces, and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupled material, where injected charge current flows parallel to the interface, was reviewed. The experimentally explored and technologically relevant spin-orbit-coupled materials include 5d heavy metals, topological insulators, Weyl semimetals, and transition metal dichalcogenides. This approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green’s functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. Illustrative examples are provided by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations, as well as by computing spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, it is shown here how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green’s function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. Furthermore, errors made in the calculation of spin-transfer torque are quantified when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Drift orbit islands of energetic particles due to 3D fields in ITER

In this study, we report a comparative study of the orbit islands formed by the guiding center drift motion of test energetic particles (EPs), including both high-energy deuterium ions and fusion-born α-particles, with respect to the magnetic islands formed by tracing the field lines, for an ITER plasma representing the 15 MA baseline scenario. The particle drift orbit is modified by the presence of static resonant magnetic perturbations (RMPs) of different toroidal mode numbers n (n = 1 and 3 in this study), forming orbit islands in the Poincaré plane by passing EPs. The key findings are as follows. (i) With an n = 1 RMP field, the size of the orbit islands combined with the total RMP field, including the plasma response, is about three times smaller than that obtained by assuming the corresponding vacuum field. (ii) The orbit island size is not sensitive to the EP energy, and is comparable to those of the magnetic islands. (iii) Passing EPs with outward radial orbital drift form orbit islands that shift inward with respect to the corresponding magnetic islands, and vice versa. This radial shift, ΔΨ, measured in the normalized equilibrium poloidal flux, is quantified as ΔΨ ≃ 0.03X for the ITER baseline plasma and assuming n = 1 RMPs, with $X\equiv {(M/{M}_{\mathrm{p}})}^{1/2}{(E[\mathrm{M}\mathrm{e}\mathrm{V}])}^{1/2}{Z}^{-1}$, where M is the particle mass, Mp is the proton mass, E is the particle energy, and Z is the particle charge number. (iv) Trapped EPs do not form drift orbit islands, even in the presence of the 3D fields produced by the 90 kAt ELM control coil current in ITER, and thus possess good confinement properties. Nevertheless, the deformation of the trapped particle drift orbits in the Poincaré plane shows that the canonical toroidal angular momentum of EPs is no longer conserved in the presence of the RMP fields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Novel Phases and Dynamics of Multi-orbital Mott Insulators

The goal of this project is to gain theoretical insight into magnetism in the presence of spin-orbit coupling (SOC) for multi-orbital Mott insulators. Inspired by the exact solution of the Kitaev model that harbors a quantum spin liquid with novel excitations and struck by its relevance for materials with anisotropic orbital interactions, the PI will explore various new classes of 4d and 5d transition metal oxides. Starting with all electron Hamiltonians, the PI will derive minimal magnetic models. The aim will be to understand the role played by orbital frustration, even in the absence of any geometric frustration, in creating orbitally ordered as well as spin-orbital liquid phases. Orbital frustration arises primarily from the directional or anisotropic nature of d-orbitals in contrast to the isotropic nature of the spin degree of freedom. These models will be investigated by a variety of theoretical and numerical methods, including exact diagonalization, mean field theories, density matrix renormalization group and quantum Monte Carlo methods. Testable predictions for three experiments: nuclear magnetic resonance (NMR) and resonant x-ray scattering (RXS) to probe orbital ordering and pump-probe experiments to probe quantum dynamics will test the validity of these models for materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗