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NASA NTRSDate not supplied

The Space Superhighway: Enabling Active Debris Remediation Through an In-Space Logistics Infrastructure

The Space Superhighway is a future space infrastructure concept intended to support civil, commercial, and national security space interests by providing In-Space Servicing, Assembly, and Manufacturing (ISAM) services across low Earth orbit (LEO), geosynchronous orbit (GEO), and cislunar space. This concept was originally developed by an interagency working group and commissioned by the Executive Office of the President. The Space Superhighway is comprised of three primary components: regional hubs, a sustainable transportation network, and Earth-to-orbit logistics. This study establishes methods which may be used to quantify the cost-savings from use of the Space Superhighway infrastructure and interrogates the effects of the use of this logistics network on a specific use case – removal of 26 pieces of large space debris within LEO. Through application of the established methods and assuming an emplaced Space Superhighway infrastructure with no cost implications related to deployment of infrastructure-related spacecraft, this study found that the cost to use an established Space Superhighway infrastructure to remove the targeted debris may be cheaper than removal of the targeted debris through traditional methods when the ΔV between a regional hub hosting propellant and the debris field is less than 1500 m/s. Through determining optimized locations of regional hubs within LEO, this study estimates that such a ΔV is within expectations for a LEO environment supported by a fully evolved Space Superhighway logistics infrastructure. This study provides a blueprint for future Space Superhighway value proposition studies for other use cases which, when combined, may provide the ultimate benefit and justification for the proliferation of an interconnected Space Superhighway.

Space Superhighway↗

NASA NTRSDate not supplied

The Space Superhighway: Enabling Active Debris Remediation Through an In-Space Logistics Infrastructure

Space Superhighway↗

NASA NTRS2024

Flight Path Control Error Analysis for the Helioswarm Observatory

The HelioSwarm Observatory requires specific geometries be formed by the nine satellites in the swarm to resolve different scales of solar wind turbulence. Maneuver execution and state estimation drive flight path control errors that could disrupt the swarm geometry. Using a Monte-Carlo analysis, flight path control errors for dispersed trajectories were generated and the impact to science performance and other mission constraints evaluated. The results highlight the unique aspects of swarm-type multi-satellite missions in terms of maneuver planning and error tolerance.

Swarm↗

NASA NTRS2005

Bulk Velocities, Chemical Composition and Ionization Structure of the X-ray Shocks in WR140 near Periastron as Revealed by the Chandra Gratings

The Wolf-Rayet WC7+O4.5 binary WR140 went through the periastron passage of its 8-year eccentric binary orbit in early 2001 as the two stars made their closest approach. Both stars have powerful supersonic stellar winds which crash into each other between the stars to produce X-rays. Chandra grating observations were made when the X-rays were at their brightest making WR140 the brightest hot-star X-ray source in the sky and giving the opportunity to study the velocity profiles of lines, all of which were resolved and blue-shifted. In the general context of shock physics, the measurements constrain the flow of hot gas and where different ions were made. The lower velocity widths of cool ions imply a plasma that was not in equilibrium. The brightness of lines relative to the strong continuum in conjunction with plasma models gives interim abundance estimates for eight different elements in WC-type material including an Ne/S ratio in good agreement with earlier long-wavelength measurements.

Pollock, A. M. T.↗

NASA NTRS2006

Consistency of Post-Newtonian Waveforms with Numerical Relativity

General relativity predicts the gravitational radiation signatures of mergers of compact binaries, such as coalescing binary black hole systems. Derivations of waveform predictions for such systems are required for optimal scientific analysis of observational gravitational wave data, and have so far been achieved primarily with the aid of the post-Newtonian (PN) approximation. The quality of this treatment is unclear, however, for the important late inspiral portion. We derive late-inspiral waveforms via a complementary approach, direct numerical simulation of Einstein's equations, which has recently matured sufficiently for such applications. We compare waveform phasing from simulations covering the last approximately 14 cycles of gravitational radiation from an equal-mass binary system of nonspinning black holes with the corresponding 3PN and 3.5PN orbital phasing. We find agreement consistent with internal error estimates based on either approach at the level of one radian over approximately 10 cycles. The result suggests that PN waveforms for this system are effective roughly until the system reaches its last stable orbit just prior to the final merger/

Baker, John G.↗

DOE OSTI2021

Spatial distributions of X CO 2 seasonal cycle amplitude and phase over northern high-latitude regions

Satellite-based observations of atmospheric carbon dioxide (CO 2 ) provide measurements in remote regions, such as the biologically sensitive but undersampled northern high latitudes, and are progressing toward true global data coverage. Recent improvements in satellite retrievals of total column-averaged dry air mole fractions of CO 2 (X CO 2 ) from the NASA Orbiting Carbon Observatory 2 (OCO-2) have allowed for unprecedented data coverage of northern high-latitude regions, while maintaining acceptable accuracy and consistency relative to ground-based observations, and finally providing sufficient data in spring and autumn for analysis of satellite-observed X CO 2 seasonal cycles across a majority of terrestrial northern high-latitude regions. Here, we present an analysis of X CO 2 seasonal cycles calculated from OCO-2 data for temperate, boreal, and tundra regions, subdivided into 5° latitude by 20° longitude zones. We quantify the seasonal cycle amplitudes (SCAs) and the annual half drawdown day (HDD). OCO-2 SCAs are in good agreement with ground-based observations at five high-latitude sites, and OCO-2 SCAs show very close agreement with SCAs calculated for model estimates of X CO 2 from the Copernicus Atmosphere Monitoring Services (CAMS) global inversion-optimized greenhouse gas flux model v19r1 and the CarbonTracker2019 model (CT2019B). Model estimates of X CO 2 from the GEOS-Chem CO 2 simulation version 12.7.2 with underlying biospheric fluxes from CarbonTracker2019 (GC-CT2019) yield SCAs of larger magnitude and spread over a larger range than those from CAMS, CT2019B, or OCO-2; however, GC-CT2019 SCAs still exhibit a very similar spatial distribution across northern high-latitude regions to that from CAMS, CT2019B, and OCO-2. Zones in the Asian boreal forest were found to have exceptionally large SCA and early HDD, and both OCO-2 data and model estimates yield a distinct longitudinal gradient of increasing SCA from west to east across the Eurasian continent. In northern high-latitude regions, spanning latitudes from 47 to 72° N, longitudinal gradients in both SCA and HDD are at least as pronounced as latitudinal gradients, suggesting a role for global atmospheric transport patterns in defining spatial distributions of X CO2 seasonality across these regions. GEOS-Chem surface contact tracers show that the largest X CO 2 SCAs occur in areas with the greatest contact with land surfaces, integrated over 15–30d. The correlation of X CO 2 SCA with these land surface contact tracers is stronger than the correlation of X CO 2 SCA with the SCA of CO 2 fluxes or the total annual CO 2 flux within each 5° latitude by 20° longitude zone. This indicates that accumulation of terrestrial CO 2 flux during atmospheric transport is a major driver of regional variations in X CO 2 SCA.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Moon, Mars and Minds: Evaluating Parkinson’s disease mortality among U.S. radiation workers and veterans in the million person study of low-dose effects

Background: Radiation is one of the most important stressors related to missions in space beyond Earth’s orbit. Epidemiologic studies of exposed workers have reported elevated rates of Parkinson’s disease. The importance of cognitive dysfunction related to low-dose rate radiation in humans is not defined. A meta-analysis was conducted of six cohorts in the Million Person Study (MPS) of low-dose health effects to learn whether there is consistent evidence that Parkinson’s disease is associated with radiation dose to brain. Materials and methods: The MPS evaluates all causes of death among U.S. radiation workers and veterans, including Parkinson’s disease. Systematic and consistent methods are applied to study all categories of workers including medical radiation workers, industrial radiographers, nuclear power plant workers, atomic veterans, and Manhattan Projects workers at the Los Alamos National Laboratory and at Rocky Flats. Consistent methods for all cohorts are used to estimate organ-specific doses and to obtain vital status and cause of death. Results: The meta-analysis include 6 cohorts within the MPS, consisting of 517,608 workers and 17,219,001 person-years of observation. The mean dose to brain ranged from 6.9 to 47.6 mGy and the maximum dose from 0.76 to 2.7 Gy. Five of the 6 cohorts revealed positive associations with Parkinson’s disease. The overall summary estimate from the meta-analysis was statistically significant based on 1573 deaths due to Parkinson’s disease. The summary excess relative risk at 100 mGy was 0.17 (95% CI: 0.05; 0.29). Conclusions: Parkinson’s disease was positively associated with radiation in the MPS cohorts indicating the need for careful evaluation as to causality in other studies, delineation of possible mechanisms, and assessing possible implications for space travel as well as radiation protection guidance for terrestrial workers.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗

NASA NTRS2012

The NASA Soil Moisture Active Passive (SMAP) Mission - Science and Data Product Development Status

The Soil Moisture Active Passive (SMAP) mission, planned for launch in late 2014, has the objective of frequent, global mapping of near-surface soil moisture and its freeze-thaw state. The SMAP measurement system utilizes an L-band radar and radiometer sharing a rotating 6-meter mesh reflector antenna. The instruments will operate on a spacecraft in a 685 km polar orbit with 6am/6pm nodal crossings, viewing the surface at a constant 40-degree incidence angle with a 1000-km swath width, providing 3-day global coverage. Data from the instruments will yield global maps of soil moisture and freeze/thaw state at 10 km and 3 km resolutions, respectively, every two to three days. The 10-km soil moisture product will be generated using a combined radar and radiometer retrieval algorithm. SMAP will also provide a radiometer-only soil moisture product at 40-km spatial resolution and a radar-only soil moisture product at 3-km resolution. The relative accuracies of these products will vary regionally and will depend on surface characteristics such as vegetation water content, vegetation type, surface roughness, and landscape heterogeneity. The SMAP soil moisture and freeze/thaw measurements will enable significantly improved estimates of the fluxes of water, energy and carbon between the land and atmosphere. Soil moisture and freeze/thaw controls of these fluxes are key factors in the performance of models used for weather and climate predictions and for quantifYing the global carbon balance. Soil moisture measurements are also of importance in modeling and predicting extreme events such as floods and droughts. The algorithms and data products for SMAP are being developed in the SMAP Science Data System (SDS) Testbed. In the Testbed algorithms are developed and evaluated using simulated SMAP observations as well as observational data from current airborne and spaceborne L-band sensors including data from the SMOS and Aquarius missions. We report here on the development status of the SMAP data products. The Testbed simulations are designed to capture various sources of errors in the products including environment effects, instrument effects (nonideal aspects of the measurement system), and retrieval algorithm errors. The SMAP project has developed a Calibration and Validation (Cal/Val) Plan that is designed to support algorithm development (pre-launch) and data product validation (post-launch). A key component of the Cal/Val Plan is the identification, characterization, and instrumentation of sites that can be used to calibrate and validate the sensor data (Level l) and derived geophysical products (Level 2 and higher).

Nloku, E.↗

NASA NTRS2017

NIAC Swarm Flyby Gravimetry Phase II Report

This NASA Innovative Advanced Concept (NIAC) grant has enabled the research and development of a method for conducting small body gravimetry from a spacecraft, using relative measurements to a set of deployed test-masses. The test-masses are tracked from a host spacecraft, which dispenses them near to the small body's surface. Thanks to this close proximity, the probes' orbits can be highly perturbed, which yields useful gravimetric measurements. The most readily achievable approach for tracking the probes is to use an optical instrument on- board the spacecraft. The probes then need only be reflective to sunlight. This implementation, called optical gravimetry (OpGrav), has the fewest requirements for the host spacecraft and probes.The results of this study indicate that OpGrav is feasible and offers meaningful improvement over existing methods. Parametric studies suggest roughly an order of magnitude improvement in accuracy or asteroid accessibility (how small an asteroid one can measure) over Earth-based Doppler-only mass estimation. This exponentially expands the number of potential near-Earth objects that one could study, which has implications for planetary defense.As a sample mission, we evaluated OpGrav as an added instrument on a main- belt asteroid tour mission. In this case, simulations show that OpGrav would increase the number of asteroid mass estimates from 3 of 9 to 7 of 9. That is, OpGrav has sufficient sensitivity to offer utility in missions for which it is not explicitly designed for.We designed and fabricated a prototype hardware implementation for this concept called the Small-body In-situ Multi-probe Mass Estimation Experiment (SIMMEE). This hardware provides a basis for many inputs into the simulations and grounds the models with physical values. The primary design driver for the hardware is a long life, on the order of five years prior to operation, and a need for high pointing accuracy to enable flybys of the smallest objects.The next steps include further hardware testing and extension of the concept to rendezvous cases. We believe that this concept offers planetary scientists a new and relevant means of better understanding small-bodies.

Atchison, Justin A.↗

NASA NTRS2017

MOA-2012-BLG-505Lb: A Super-Earth-Mass Planet that Probably Resides in the Galactic Bulge

We report the discovery of a super-Earth-mass planet in the microlensing event MOA-2012-BLG-505. This event has the second shortest event timescale of t(sub E) = 10 ± 1 days where the observed data show evidence of a planetary companion. Our 15 minute high cadence survey observation schedule revealed the short subtle planetary signature. The system shows the well known close/wide degeneracy. The planet/host-star mass ratio is q = 2.1 × 10(exp −4) and the projected separation normalized by the Einstein radius is s = 1.1 or 0.9 for the wide and close solutions, respectively. We estimate the physical parameters of the system by using a Bayesian analysis and ﬁnd that the lens consists of a super-Earth with a mass of 6.7(sup +10.7)(sub -3.6) Mꚛ orbiting around a brown dwarf or late-M-dwarf host with a mass of 0.10(sup +0.16)(sub -0.05) Mꙩ with a projected star–planet separation of 0.9(sup +0.3)(sub -0.2) au. The system is at a distance of 7.2 ± 1.1 kpc, i.e., it is likely to be in the Galactic bulge. The small angular Einstein radius (θ(sub E) = 0.12 ± 0.02 mas) and short event timescale are typical for a low-mass lens in the Galactic bulge. Such low-mass planetary systems in the Bulge are rare because the detection efﬁciency of planets in short microlensing events is relatively low. This discovery may suggest that such low-mass planetary systems are abundant in the Bulge and currently ongoing high cadence survey programs will detect more such events and may reveal an abundance of such planetary systems.

super-Earth-mass planet↗

NASA NTRS1993

The Interstellar Gas Experiment: Analysis in progress

The Interstellar Gas Experiment (IGE) exposed thin metallic foils aboard the LDEF spacecraft in low Earth orbit in order to collect neutral interstellar particles which penetrate the solar system due to their motion relative to the sun. By mechanical penetration these atoms were imbedded in the collecting foils along with precipitating magnetospheric ions and, possibly, with ambient atmospheric atoms. During the entire LDEF mission, seven of these foils collected particles arriving from seven different directions as seen from the spacecraft. After the foils were returned to Earth, a mass spectrometric analysis of the noble gas component of the trapped particles was begun. The isotopes of He-3, He-4, Ne-20, and Ne-22 were detected. We have given a first account of the experiment. In order to infer the isotopic ratios in the interstellar medium from the concentrations found in the foils, several lines of investigation had to be initiated. The flux of ambient atmospheric noble gas atoms moving toward the foils due to the orbital motion of LDEF was estimated by detailed calculations. Any of these particles which evaded the baffles in the IGE collector could be entrapped in the foils as a background flux. However, the calculations have shown that this flux is negligible, which was the intent of the experiment hardware design. This conclusion is supported by the measurements. However, both the concentration of trapped helium and its impact energy indicate that the flux of magnetospheric ions which was captured was larger than had been expected. In fact, it appears that the magnetospheric particles constitute the largest fraction of the particles in the foils. Since little is known about this particle flux, their presence in the IGE foils appears fortunate. The analysis of these particles provides information about their isotropic composition and average flux.

Buehler, F.↗

NASA NTRS2012

Representation of Probability Density Functions from Orbit Determination using the Particle Filter

Statistical orbit determination enables us to obtain estimates of the state and the statistical information of its region of uncertainty. In order to obtain an accurate representation of the probability density function (PDF) that incorporates higher order statistical information, we propose the use of nonlinear estimation methods such as the Particle Filter. The Particle Filter (PF) is capable of providing a PDF representation of the state estimates whose accuracy is dependent on the number of particles or samples used. For this method to be applicable to real case scenarios, we need a way of accurately representing the PDF in a compressed manner with little information loss. Hence we propose using the Independent Component Analysis (ICA) as a non-Gaussian dimensional reduction method that is capable of maintaining higher order statistical information obtained using the PF. Methods such as the Principal Component Analysis (PCA) are based on utilizing up to second order statistics, hence will not suffice in maintaining maximum information content. Both the PCA and the ICA are applied to two scenarios that involve a highly eccentric orbit with a lower apriori uncertainty covariance and a less eccentric orbit with a higher a priori uncertainty covariance, to illustrate the capability of the ICA in relation to the PCA.

Mashiku, Alinda K.↗

NASA NTRS2016

Analysis of One-Way Laser Ranging Data to LRO, Time Transfer and Clock Characterization

We processed and analyzed one-way laser ranging data from International Laser Ranging Service ground stations to NASA's Lunar Reconnaissance Orbiter (LRO), obtained from June 13, 2009 until September 30, 2014. We pair and analyze the one-way range observables from station laser fire and spacecraft laser arrival times by using nominal LRO orbit models based on the GRAIL gravity field. We apply corrections for instrument range walk, as well as for atmospheric and relativistic effects. In total we derived a tracking data volume of approximately 3000 hours featuring 64 million Full Rate and 1.5 million Normal Point observations. From a statistical analysis of the dataset we evaluate the experiment and the ground station performance. We observe a laser ranging measurement precision of 12.3 centimeters in case of the Full Rate data which surpasses the LOLA (Lunar Orbiting Laser Altimeter) timestamp precision of 15 centimeters. The averaging to Normal Point data further reduces the measurement precision to 5.6 centimeters. We characterized the LRO clock with fits throughout the mission time and estimated the rate to 6.9 times10 (sup -8), the aging to 1.6 times 10 (sup -12) per day and the change of aging to 2.3 times 10 (sup -14) per day squared over all mission phases. The fits also provide referencing of onboard time to the TDB (Barycentric Dynamical Time) time scale at a precision of 166 nanoseconds over two and 256 nanoseconds over all mission phases, representing ground to space time transfer. Furthermore we measure ground station clock differences from the fits as well as from simultaneous passes which we use for ground to ground time transfer from common view observations. We observed relative offsets ranging from 33 to 560 nanoseconds and relative rates ranging from 2 times 10 (sup -13) to 6 times 10 (sup -12) between the ground station clocks during selected mission phases. We study the results from the different methods and discuss their applicability for time transfer.

Bauer, S.↗

NASA NTRS2022

The Transmission of ULF Waves From the Solar Wind to the Magnetosphere: An Analysis of Some Critical Aspects

Several critical aspects may influence the analysis of the relationship between the solar wind (SW) and magnetospheric fluctuations, for example, the characteristics and frequency of SW fluctuations that are expected to impinge the magnetosphere may not be the same when they are observed by spacecraft located at different places in front of the magnetosphere; similarly, the choice of analytical methods adopted for the spectral analysis might influence the frequency estimate (as well as the wave identification itself) both in the SW and magnetosphere. Focusing our attention on these aspects, we present an analysis of SW compressional fluctuations (f ≈ 1–5 mHz), following two interplanetary shocks observed by two interplanetary spacecraft, regarded as two different situations in terms of spacecraft separation and distance from the magnetosphere. Our results show that some differences in the characteristics of SW fluctuations emerge when the same stream is observed at different places and confirm the critical role of analytical methods in determining fluctuation characteristics. We compared aspects of SW fluctuations with those of magnetospheric fluctuations following the sudden impulses due to the impact of interplanetary shocks. For this scope, we examined observations by two satellites at geostationary orbit and at several ground-based stations. We found that the magnetospheric fluctuations were related to compressional SW fluctuations approximately at the same frequencies, with no evidence for wave activity of internal origin or directly driven by the shock impact.

ULF waves↗

DOE OSTI2025

Prediction of Redox Potentials for the Late Actinides Cm to Lr Using Electronic Structure Methods

Our previously developed computational method for calculating the aqueous redox potentials of the early actinides has been extended to the later elements in the actinide series: Cm, Bk, Cf, Es, Fm, Md, No, and Lr in multiple oxidation states. These calculations were performed using density functional theory with small-core pseudopotentials and their associated basis sets. Solvation effects were considered via a supermolecule-continuum approach, with 30 water molecules representing two solvation shells. Both the COSMO and SMD implicit solvation models were utilized. The structural parameters and hydration numbers for Cm(III), Bk(III), Bk(IV), and Cf(III) are in reasonable agreement with the available experimental data. For redox processes involving atomic cations in solution, the B3LYP/COSMO approach predicted redox potentials to within ±0.2 V of experiment for most redox couples, consistent with our prior work. Inclusion of spin-orbit corrections in specific redox pairs, especially those with the later actinides in high oxidation states, yields improved results relative to calculations including only scalar-relativistic corrections. The An +m /An(0) redox potentials were calculated using a Born-Haber cycle incorporating sublimation, ionization, and hydration energies. Due to a lack of experimental data, three sets of ionization energies were used for the Born-Haber cycle. The calculated An(III/0) potentials showed better agreement with experimental data when using the COSMO solvation model and the test set comprising the NIST recommended ionization energies. Furthermore, the Md(II/0) potential was better described with the SMD model, whereas No(II/0) was not well described by all methods. Finally, the computational approach was able to predict redox potentials that for most cases agreed with the current available experimental or estimated data.

Actinides↗

NASA NTRS1989

Stress distribution and topography of Tellus Regio, Venus

The Tellus Regio area of Venus represents a subset of a narrow latitude band where Pioneer Venus Orbiter (PVO) altimetry data, line-of-sight (LOS) gravity data, and Venera 15/16 radar images have all been obtained with good resolution. Tellus Regio also has a wide variety of surface morphologic features, elevations ranging up to 2.5 km, and a relatively low LOS gravity anomaly. This area was therefore chosen in order to examine the theoretical stress distributions resulting from various models of compensation of the observed topography. These surface stress distributions are then compared with the surface morphology revealed in the Venera 15/16 radar images. Conclusions drawn from these comparisons will enable constraints to be put on various tectonic parameters relevant to Tellus Regio. The stress distribution is calculated as a function of the topography, the equipotential anomaly, and the assumed model parameters. The topography data is obtained from the PVO altimetry. The equipotential anomaly is estimated from the PVO LOS gravity data. The PVO LOS gravity represents the spacecraft accelerations due to mass anomalies within the planet. These accelerations are measured at various altitudes and angles to the local vertical and therefore do not lend themselves to a straightforward conversion. A minimum variance estimator of the LOS gravity data is calculated, taking into account the various spacecraft altitudes and LOS angles and using the measured PVO topography as an a priori constraint. This results in an estimated equivalent surface mass distribution, from which the equipotential anomaly is determined.

Williams, David R.↗

NASA NTRS1993

Particle drift in the Earth's plasma sheet

We generalize the derivation of the average gradient/curvature-drift for a flux tube filled with an isotropic distribution of particles at specified kinetic energy. The present treatment is restricted to a two-dimensional magnetic field with zero electric field, but it includes all chaotic and Speiser orbits, which do not correspond to the simple picture of gradient/curvature drift. We assume that particles are evenly distributed throughout the regions of phase space allowed by their energy and canonical momentum. This assumption is closely related but not exactly equivalent to the assumption of isotropic pitch-angle distribution. Our derivation assumes that the maximum Larmor radius is small compared to the scale length for equatorial variations in the flux tube volume, but it does not involve any restrictions on the curvature of the field line. The resulting expression for the drift rate is valid for situations where the particle drift velocity is comparable to the thermal speed in some regions. The apparent implication of this generalized treatment is that the existence of very complex non-adiabatic particle trajectories in the plasma sheet may not invalidate previous estimates of the average rate of particle drift out the sides of the tail, estimates that were made under the assumption of simple guiding-center drifts.

Wolf, R. A.↗